PREDICTING TENDERNESS OF BEEF USING
MACHINE VISION
By
ANAND LAKSHMIKANTH
Bachelor of Engineering
College of Agricultural Engineering
Tamil Nadu Agricultural University
Kumulur, Tamilnadu, India
1998
Submitted to the Faculty of the
Graduate College of the
Oklahoma State University
in partial fulfillment of
the requirements for
the Degree of
MASTER OF SCIENCE
December, 2002
PREDICTING TENDERNESS OF BEEF USING
MACHINE VISION
Thesis Approved:
ii
ACKNOWLEDGMENTS
I would like to express my sincere thanks to Dr. Glenn Kranzler, my advisor, for his
support, guidance and encouragement throughout my graduate program. I would also like
to extend my thanks to Dr. Marvin Stone and Dr. Paul Weckler, members of my graduate
committee.
I would also like to express my gratitude towards Dr. Brad Morgan, Dr. Chance Brooks
Jacob Nelson and other laboratory personnel, and graduate students in the Animal
Science Department for their efforts in gathering steak samples and testing them.
I would also like to extend a special thanks to my colleague, Jeyamkondan Subbiah for
extending his support, and encouragement, and also to my family for giving me the
encouragement at times I needed most.
iii
TABLE OF CONTENTS
Chapter
ABSTRACT .
Page
I. INTRODUCTION. 3
Background. .. .. . ... . . . . .. .. . . . . ... .. . .. . . . . .. . .. . .. . .. . . .. ... . .. . .. .. . .. . ... .. . 3
Beef Tenderness 4
II. REVIEW OF LITERATURE 6
Introduction.................................................................................................... 6
Historical Background................................................................................... 7
Tenderness Probes 9
Near-Infrared Spectroscopy 12
Video Image Analysis 13
Wavelet-based Textural Feature Analysis 17
Objectives 19
III. MATERIALS AND METHODS 20
Overview 20
Hardware Components 20
Software Components 23
Calibration 23
Samples 23
Shear-Force Measurement 24
Textural Features 26
Wavelet Transform 28
Wavelet Decomposition of Images 33
Wavelet-based Textural Features 34
Gray-Level Cooccurence Matrix Textural Features 37
Feature Reduction 38
Statistical Analysis 39
iv
Neural Network Analysis 42
IV. RESULTS AND DISCUSSION 48
Statistical Analysis Results 48
Neural Network Analysis Results 51
Conclusions 53
Further Research 54
REFERENCES 56
APPENDICES 61
APPENDIX A- STATISTICAL TABLES 62
APPENDIX B- FIGURES 68
APPENDIX C- IMAGE ANALYSIS AND NEURAL
NETWORK PROGRAMS 72
v
LIST OF TABLES
Table Page
I. Mean WBS scores for samples taken on 7th and 14th
day of aging 63
II. Descriptive statistics of shear-force values for training
and tests data sets for WT-based textural features 42
III. Descriptive statistics of shear-force values for training
and tests data sets for GLDH-based textural features 42
IV. Samples sorted based on predicted scores with certification
levels for WT-based textural features (test set) 66
V. Samples sorted based on predicted scores with certification .
levels for GLDH-based textural features (test set) 67
VI. Statistical differences of mean shear-force values between
"certified tender" and "not certified tender" groups for
WT-based textural features 50
VII. Statistical differences of mean shear-force values between
"certified tender" and "not certified tender" groups for
GLDH-based textural features 50
vi
LIST OF FIGURES
Figure Page
1. Video image analysis system 21
2. Image of sample beef steak 22
3. Lighting chamber detail 69
4. Close-up image of sample steak ribeye 22
5. Steaks loaded into impingement oven 25
6. Cooked steaks removed from oven and monitored for temperature 25
7. Warner-Bratzler shear force measurements on core samples 26
8. Filter implementation of the discrete wavelet transform 70
9. Five level wavelet-decomposition using Daubechies wavelets 71
vii
AMSA
ANN
AT
BPNN
CIE
CWT
DWT
FAPC
FT
GLDH
GLCM
HSI
MIRINZ
MRA
MLR
MSE
NBIAP
NCBA
NIR
NOMENCLATURE
American Meat Science Association
Artificial Neural Network
Armour Tenderometer
Backpropagation Neural Network
Commission Intemationale de l'Eclairage
Continuous Wavelet Transform
Discrete Wavelet Transform
Food and Agricultural Products Center
Fourier Transform
Gray-Level Difference Histogram
Gray-Level Cooccurence Matrix
Hue-Saturation-Intensity
Meat Industry Research Institute ofNew Zealand
Multiresolution Analysis
Multi-Linear Regression
Mean Square Error
National Beef Instrument Assessment Plan
National Cattlemen's Beef Association
Near-Infrared
viii
PCA Principal Component Analysis
PLS Partial Least Squares
RGB Red-Green-Blue
STFT Short-Time Fourier Transform
USDA United States Department of Agriculture
UV Ultraviolet
VIA Video Image Analysis
WT Wavelet Transform
WBS Wamer-Bratzler Shear-force
IX
ABSTRACT
Tenderness is a critical factor in consumer perception of beef quality. A computer
vision system was developed to predict 14-day aged cooked-beef tenderness. Steak
samples (n== 186) were acquired from regional packing plants and imaged at I-day
postmortem. Steak images were decomposed using Haar and Daubechies wavelets.
Textural features were derived from wavelet transforms (WT). Gray-level difference
histograms (GLDH) were extracted from the decomposed images.
WT- and GLDH-based features from the red-green-blue (RGB) and the CIE L* a* b*
color spaces were combined, separately. Features were reduced in number by linear
regression to eliminate redundancy. The two separate reduced sets of features were
pre-processed using principal component analysis. Each set of features was split into
training and test sets with a count ratio of 3: 1. Statistical and neural network analysis
was performed to predict 14-day postmortem Warner-Bratzler shear-force (WBS)
tenderness scores. Stepwise regression yielded a correlation coefficient of 0.57 for
WT-based features and 0.48 for GLDH-based features. A backpropagation (BPNN)
neural network model with Bayesian regularization was developed. The BPNN
network predicted WBS scores with a correlation coefficient range of 0.57-0.59 for
WT·-based features (training and test sets) and 0.55 and 0.31 for training and test sets,
respectively, for GLDH-based features.
A t-test analysis was performed to determine the ability of the model to sort' certified
tender" samples from "not certified tender" samples, at certification levels of 10% to
100%, for both training and test data sets. This approach was more applicable because
of an insufficient number of "tough" samples in the data. Except for the 10% and
70% certification levels in the test set of GLDH-based features, there was a
significant difference (a=O.05) between the "certified tender" and "not certified
tender" categories. For both WT- and GLDH-based features, 71.4% and 66.7% of
"tough" samples in the test and training set, respectively, were successfully sorted
from the "tender" samples.
WT-based features were found to be more effective than GLDH-based features in
predicting 14-day postmortem WBS tenderness scores, and in terms of accurately
sorting "tender" and "tough" samples. The system was capable of sorting and
categorizing fresh beef samples on the basis of aged-beef tenderness with moderate
accuracy.
2
CHAPTER I
INTRODUCTION
Background
Oklahoma ranks fifth in the nation in receipts from cattle production. The output
represents 65% of the total state agricultural receipts, provides jobs for 105,000
laborers, and accounts for approximately $2.4 billion of the Gross State Product
(OBIC, 2002). The motto of the National Cattlemen's Beef Association (NCBA) is
" . .. to maximize consumer confidence in and acceptance of beef by focusing the
industry's attention on beef quality assurance through the use of science, research,
and educational initiatives" (NCBA, 2002). Beef quality is what accounts for profits
for beef producers, and visual grading by USDA-approved graders assigns the
quality. The manual grading procedure involves a visual examination of the
characteristics of the Longissimus dorsi muscle, commonly known as the ribeye. The
carcass is sectioned between the 12th and the 13th rib to expose the ribeye. This
method of visual grading has often been criticized for being too subjective and errorprone.
In a beef packing plant, a carcass passes by every 9-18 s, giving the grader a
limited amount of time to determine grade. In addition, emotional strain caused by
monotonous work, inadequate lighting, and dangerous working conditions make it
difficult for manual graders to maintain accuracy.
3
Instrumented carcass evaluation provides an objective system of grading that ensures
consistency and enables value-based marketing. The National Beef Instrument
Assessment Plan of the National Livestock and Meat Board (Schutte et al. 1998)
suggested the application of instrumented grading for objective carcass evaluation.
The Plan stated that the system of grading should be accurate, tamper proof, capable
of "on-line" operation, and provide repeatable results. Video image analysis (VIA)
was identified as the most promising technique for objective grading, and was thus
been given top research priority. This technology has been an active topic of research,
because it simulates the human eye for grade assessment. Kranzler et al. (1998)
developed a VIA system to measure ribeye area, marbling or intramuscular fat, lean
color, and to assign a quality grade based on USDA standards. Results from the VIA
system were compared with those of expert graders and found to be statistically
equivalent. Jeyamkondan et al. (2000) utilized the VIA system developed at
Oklahoma State University to segment the ribeye from beef steak images and predict
quality grade. The quality grades predicted by the VIA system were statistically
equivalent to the grades assigned by expert graders for the same samples. The R2
value for prediction was 0.72. These tests indicated that the VIA system was highly
suitable for objective, on-line grading.
Beef Tenderness
Tenderness is a critical factor in consumer perception of beef quality (Koohmaraie et
aI., 2002). The 1994 National Beef Quality Audit (Smith et aI., 1995) and various
consumer surveys indicate 25% of beef eating experiences are unsatisfactory.
4
Consumers have ranked beef tenderness as the most important characteristic for
palatability, along with juiciness and flavor.
Current USDA beef grading standards do not account for tenderness. These standards
assign two grades; yield and quality (Biju, 1998). Graders assess the ribeye area, rib
fat thickness, and carcass weight to determine yield grade. Ribeye marbling, color
features, and maturity are judged to assign quality grade. Unfortunately, tenderness is
a quality that is not easily discernable to the human eye. An accepted measure of
tenderness is the Warner-Bratzler shear-force test. This technique, however, destroys
the sample. Thus, there is need for a non-destructive and objective system to predict
tenderness.
5
CHAPTER II
REVIEW OF LITERATURE
Introduction
Tenderness is a quality attribute of beef that is widely accepted as important. Smith et
al. (1995) estimated an annual loss of $250 million to the beef industry, due to lack of
tenderness in beef cuts. Many tender and palatable carcasses have been discounted in
value because of insufficient marbling. Yet sensory panel tests at the USDA Meat
Animal Research Center indicate that marbling accounts for only 100/0 of the variation
in beef ribeye tenderness (USDA, 1999).
Commercial packers have utilized several methods to improve tenderness in beef.
Considerable research has been conducted on beef tenderness improvement. Packers
generally employ methods like aging, special packaging, avoiding animal stress prior
to slaughter, and electrical stunning. Nutritional methods, like incorporating vitamin
D3 in cattle feed (Berry et aI., 2000) and genetic manipulation by biological
engineering and selective breeding, are methods that have been researched to improve
tenderness in beef. Plant derivatives, such as 'papain' from papaya, have been found
to contain enzymes that increase tenderness. These enzymes are proteolytic in nature.
Enzymes of the calpain system in the muscle, calpain I and calpain II, increase
tenderness in beef by inducing proteolysis (Auburn University, 1996). They have a
natural inhibitor known as calpastatin. Injection of calcium chloride in the carcass
6
(Whipple et aI., 1992) and electrical stimulation (Ferguson et aI., 2000) are two
methods that have been found to increase the activity of the calpain system enzymes.
Historical Background
The importance of connective tissue in meat toughness has been a topic of debate
among scientists (Swatland, 1995). They argue that characteristics like sarcomere
length and integrity, and the state of the myofibrils and cytoskeleton are better
indicators of beef toughness. Epley (2002) reported that aging the beef for a period of
11 days, while maintaining the temperature at - 1.1 to 1.6°C, gives the beef a "gamy"
flavor and also increases tenderness. Reasons given for the increase in tendetness are
changes that take place in the muscle fibers and the collagen, the latter being a major
component of the connective tissue. Although the flavor increases as the aging period
is prolonged, there is no increase in tenderness beyond 11 days of aging.
Minick et al. (2001) reported that steak samples with greater marbling were found to
be more tender than those with less marbling. However, the test was performed on a
small data set, and the correlation coefficient between shear force and marbling was a
low - 0.26. Thus, there was no conclusive proof that there is strong correlation
between tenderness and marbling.
The current industry accepted test for measuring tenderness is the Wamer-Bratzler
shear-force (WBS) test. The shear-force test is a standardized procedure
recommended by the American Meat Science Association (AMSA, 1995). The WBS
7
test is assumed to simulate the chewing action of the teeth during the consumption of
beef.
The shear-force test is a better alternative than testing for tenderness by a taste panel,
because the latter introduces the element of subjective grading. An issue of concen1 is
the fact that procedures for the WBS test have varied with application. Wheeler et al.
(1997) suggested a set of procedures developed by Savell et al. (1994). One of the
main reasons for the variation in procedures is the fact that consumers use different
cooking methods, based on preference. Tenderness of the cooked beef varies with the
method and the extent of cooking. Currently, a majority of the research institutions
cook the meat to 71°C as required by the AMSA standard.
The WBS test procedure outlined in the AMSA (1995) standard is as follows:
1. Determine sample size based on appropriate statistical analysis or consult
statisticians.
2. Remove primals from the carcasses no sooner than 24 h post mortem.
3. Time post-mortem for processing into cuts and freezing should be 14 days,
including time for aging.
4. Thickness of the beef steaks should be 2.54 em.
~. Steaks should be vacuum packaged or packaged in material with low oxygen
permeability, and frozen to a temperature no higher than -18°C.
6. Steaks should be evaluated within 6 months of frozen storage time.
7. Thaw steaks until the internal temperature is 2-5°C.
8
8. Insert iron/constantan or copper/constantan thermocouple WIres with a
diameter less than 0.05 cm and error limits less than 2°C.
9. Roast or broil the steaks, as per recommended procedure, until the internal
temperature is 71°C.
10. Chill the cooked samples overnight at 2-5°C or cool the samples (if they are
not chilled) until they attain a uniform temperature between 24-28°C, prior to
coring.
11. Obtain at least 6 cores from the samples, either manually or by machine drill
coring, parallel to the longitudinal orientation of the muscle fibers. Cores
should be 1.27 cm in diameter.
12. Shear each core once in the center USing an Instron Universal Testing
Machine, with a Warner-Bratzler shear head attachment. The crosshead speed
of the machine should be 250 mm/min.
The disadvantages of the WBS test are that the procedure is destructive, much time
and labor are involved, and the procedure is not suited for on-line evaluation.
Scientists have sought out methods of detecting tenderness that would be nondestructive,
time and labor efficient, and compatible with online evaluation.
Tenderness Probes
The Armour Tenderometer (AT) was one of the first developed probe systems (Belk
et aI., 2000). The system utilized a group of probes that predicted tenderness as a
measure of the force required to penetrate the ribeye muscle. Huffman (1974)
9
reported an R2 of 0.22 when the AT readings were correlated with WBS scores. No
relationship was established between the AT readings and taste panel scores. Smith et
al. (1984) reported a low correlation coefficient value of 0.10 (P<O.05) between the
AT readings and taste panel scores. These studies concluded that the method was
ineffective due to its inability to accurately predict tenderness.
The Meat Industry Research Institute ofNew Zealand (MIRINZ) developed a torsionbased
tenderness probe. The instrument consists of two concentric sets of radially
placed pins. The outer set of pins is static, while the inner set rotates. The meat is
impaled on the pins, and the torque to the inner set of pins is generated by a
synchronous motor. The torque and degree of rotation required to tear the meat are
determined (Swatland, 1995). Jeremiah et al. (2000) evaluated the performance of the
MIRINZ probe and reported that the probe was a faster alternative to WBS testing.
However, the correlation coefficients for the relationships between the probe values
and WBS scores, a trained sensory panel, and consumer ratings ranged from a low
- 0.19 to - 0.26.
The Tendertec Mark III Beef Grading Instrument is a probe system developed by the
Australian Meat Research Corporation to measure the amount of connective tissue
and.other factors contrib ting to meat toughness (Belk et aI., 2000). The probe was a
hand-held, battery-powered tenderometer (Swatland, 1995). The meat surface
resistance to penetration of the needle in the probe was plotted as a function of depth.
Belk et al. (2001) evaluated the effectiveness of the Australian Tendertec probe and
10
found significant correlation between the probe readings and other variables i.e.
WBS score, muscle fiber tenderness, overall tenderness, and amount of connective
tissue. The variables; muscle fiber tenderness, overall tenderness, and amount of
connective tissue were based on sensory panel scores. The probe, however, failed at
sorting carcasses of young animals consistently, and the correlation coefficient
declined for steaks as the degree of doneness increased. Higher correlation coefficient
values were observed for steaks that were cooked to a rare or medium-rare degree of
doneness. This study showed that the Tendertec probe had limited capacity to be used
commercially.
The CT-probe or Connective Tissue probe is a prototype probe developed by the
University of Guelph, Canada, supported by Ontario Cattlemen's Association and the
Danish Meat Research Institute (Swatland et aI., 1999). Functioning of the probe is
based on ultra-violet fluorescence of the connective tissue. Most collagen types in
meat have a peak excitation at 375 nm (Swatland, 1995). The CT-probe is hand-held
and has an optical window that penetrates the meat. This probe measures the whole
band of the fluorescence emission spectrum against the depth of penetration of the
probe. Peaks in the spectrum are recorded whenever the probe penetrates a layer of
connective tissue. Damage to the carcass due to penetration is imperceptible.
Swatland et al. (1998) evaluated the CT-probe for use in predicting taste and
tenderness of broiled beef steaks. Samples were tested after aging periods of 3 days
and 21 days. Probe readings were correlated with taste panel scores, with correlation
coefficients ranging from 0.42 to 0.58.
11
Near-Infrared Spectroscopy
Near-infrared (NIR) spectroscopy has been demonstrated to be a promising method
for assessing meat quality, because it offers a non-invasive, and usefully accurate
approach to predicting tenderness. Hildrum et al. (1995) studied the use of NIR
reflectance spectroscopy in the prediction of sensory hardness, tenderness and
juiciness of bovine Longissimus dorsi muscles. For these three sensory features,
principal component regression analysis of NIR reflectance data and sensory panel
scores yielded correlation coefficients of 0.74, 0.70, and 0.61, respectively.
Park et al. (1998) used NIR reflectance spectra from a sample set of 119 steaks to
predict WBS tenderness scores. Absorption was higher for extremely tough steaks,
than for tender steaks. A partial least-square (PLS) model was developed to predict
meat tenderness and a multi-linear regression (MLR) model was developed for meat
tenderness classification. The PLS model yielded an R2 value of 0.67 for the training
set, and 0.63 for the validation set. The MLR model correctly classified 89% of the
samples as "tender" or "tough."
Rodbotten et al. (2001) used NIR absorbance spectra to predict WBS scores. Two
models were developed. The first model utilized the NIR spectra alone, and the
second utilized NIR spectra in combination with information about post-slaughter
treatments. Prediction models from NIR spectra alone gave correlation coefficients in
the range of 0.52-0.83. When variables for post-slaughter treatments were included in
the models, the correlation coefficients for predicting WBS scores were in the range
12
of 0.71-0.85. Based on these prediction models, the beef samples were classified into
two tenderness groups. When classified into two groups, 73-98% of the samples were
correctly classified.
Although the NIR approach shows promise, the technique has yet to be refined for
on-line use at the processing plant. The fragile nature of a fiberglass NIR probe and
its susceptibility to interfering light sources make the system precarious to use and
prone to error.
Video Image Analysis
Video image analysis also offers a non-invasive approach to meat grading. One of the
earliest efforts to develop an objective method of grading beef carcasses was carried
out by the National Aeronautics and Space Administration (NASA). In 1978, NASA
conducted research to determine the application of its technology to beef grading.
They concluded that ultrasound and image analysis were the best available methods
for automated and objective beef grading (Biju, 1998). The 1994 National Beef
Instrument Assessment Plan (NBIAP) Symposium identified VIA systems, among the
systems evaluated, as most promising for improving consistency and quality of beef
(Wyle et aI., 1999).
Belk (1999) reported that fat and lean color of beef muscle could indicate the ultrastructural
status of the connective tissue. Tatum et al. (1997) reported a relation
between calpastatin activity in the carcass and the lean color. Fiems et al. (2000) used
13
fat characteristics and lean color to predict tenderness in Belgian Blue bulls, using the
Hunterlab Lab Scan-II. Lean color and fat characteristics both showed high
correlation coefficient values, with respect to shear-force scores, ranging from 0.700.85.
Basset et al. (1999) proposed the use of texture analysis to classify images of meat
slices. The selection of texture analysis was based on the ability of the human eye to
discern various textures. First-order statistical features like the mean, and features
based on second-order gray-level cooccurence matrices (GLCM) (Haralick et al.
1973) like correlation, entropy, and angular second moment were calculated. These
features were extracted from the images in visible and ultraviolet (UV) portions of the
spectrum. The features were correlated with dry-matter content, lipid content,
collagen content, and four mechanical features. Correlation coefficients ranging from
0.1 to 0.67 were obtained for the classification. Basset et al. (1999) stated that texture
analysis could be extended to prediction of tenderness in meat, because the meat
tissue characteristics that influence meat quality, and the connective tissue quantity
and spatial distribution that define the grain of meat are directly related to tenderness.
Li et al. (1999) utilized color features, marbling features, and image textural features
for predicting beef tenderness. Mean, standard deviation, and skewness of the values
of red-green-blue (RGB) components of the image, marbling features such as number
of flecks and total area of the flecks, and image textural features such as pixel-value
run length and pixel-value spatial dependence were extracted from the images. The
14
features were correlated with sensory panel scores. Color and marbling features were
able to predict tenderness with an R2 value of only 0.17. Color and marbling features
were able to explain only 30% of the variation in tenderness. The inclusion of image
textural features improved the R2 to 0.62.
Basset et al. (2000) utilized the concept of ultraviolet fluorescence of collagen and
image analysis to predict meat tenderness. In order to enhance the contrast between
collagen and fat, images of the steaks were captured using both visible and UV light.
Textural features based on the GLCM were used for predicting tenderness in meat.
Gray-level cooccurence features, i.e., neighboring gray-level dependence matrix
gray-level run-length matrix, Fourier power spectrum, fractal method, and relative
extrema measures, were correlated with the collagen content of the meat. A
correlation coefficient of 0.49 was obtained.
Wyle et al. (1999) evaluated the performance of the HunterLab Video Imaging
System, known popularly as BeefCam™, to predict WBS scores. The BeefCam™ is
a self-contained, portable, handheld video-imaging unit that utilizes an internal mirror
to reflect the image onto a horizontally positioned camera lens, while maintaining
proper focal length. BeefCam™ operates, based on measurements of lean and fat
color reflectance that are captured using VIA images containing up to 250,000 data
points (pixels) per measurement. It can separate out different colors from irregularly
shaped surfaces and be used to calculate relative areas that each color represents
within the video image. Images are acquired in RGB color space and converted to
15
CIE L*, a*, and b* color space. The CIE L* a* b* color space is a perceptually
uniform color space that simulates the functioning of the human eye. Wulf et al.
(1997) correlated the values of CIE L* a* b* color space with both WBS scores and
taste panel scores. The b* color band values showed the highest correlation.
Correlation of b* values with WBS scores and taste panel scores was 0.38 and 0.37,
respectively. Wyle et al. (1999) conducted two separate trials to predict tenderness
and found that the BeefCam™ was able to correctly classify as ' tender' or ' tough'
150 out of 156 carcasses in the first trial and 139 of 150 carcasses in the second trial.
Using the Oklahoma State University VIA system, Jeyamkondan et al. (2001)
explored textural features based on the GLCM to predict tenderness in meat. Instead
of GLCM-based features, they chose to extract features derived from the gray-level
difference histogram (GLDH). GLDH yields textural features similar to those based
on GLCM, and offers the advantage of rapid computation. Seven textural features;
energy, correlation, entropy, contrast, homogeneity, cluster shade, and cluster
prominence were calculated in the RGB, CIE L* a* b*, and hue, saturation, and
intensity (HSI) color spaces. Features were extracted from full and close-up images of
the ribeyes. Textural features extracted from the full images predicted WBS scores
with an R2 value of 0.5 and correctly classified the steaks into categories of "tender"
and. "tough" with a 79% success rate. Features extracted from the close-up images
predicted WBS scores with an R2 value of 0.72 and classified the steaks with a 92%
success rate. The close-up images produced better results, because they contained
more detailed textural features than the full images.
16
Wavelet-based Textural Feature Analysis
Wavelets are mathematical functions that section data into separate frequency
components and then address each component with resolution matched to its scale.
They are superior to Fourier analysis methods in analyzing signals that are
discontinuous and noisy. Wavelets have been utilized in the field of image and sound
compression, de-noising signals, simulating human vision, earthquake predictions,
etc.
Targeting beef quality grading, Kim et al. (1998) utilized the wavelet transform (WT)
for multiresolutional texture analysis on ultrasound images of live cows. WT-based
features included energy ratios, central moments of the decomposed sub-images, and
wavelet edge density. Performance of the WT-based features was compared with
GLCM-based features in predicting marbling distribution. The GLCM-based features
predicted marbling distribution with a correlation coefficient of 0.58, whereas the
WT-based features predicted with a value of 0.78. The WT-based features performed
better, because they provided significant information about textural differences such
as coarseness, orientation, and variations using spatial-scale localized texture
information. These prediction models showed potential for objective quality grading
using WT-based features.
Huang et al. (1997) utilized wavelet-based textural features for beef tenderness
prediction. Ultrasonic elastogram images of beef samples were acquired for the study.
GLCM-based features were extracted and compared with the WT-based features. The
17
WT-based textural features predicted WBS scores obtained after aging for 2 14, 28
and 42 days with R2 values ranging from 0.72-0.95. The R2 value of prediction for the
OLCM-based features ranged from 0.19 to 0.77. This study showed that WT-based
features could make a unique contribution to beef tenderness prediction.
Li et al., (2001) utilized wavelet-based decomposition algorithms to extract textural
features from images of beef samples. The images were transformed to the HSI color
space from the standard ROB format. Textural features such as pixel-value run-length
and primitive fraction were calculated from the decomposed images. Neural network
and statistical models were used to compare the textural features with sensory panel
scores. They achieved an 83.3% success rate classifying the beef samples into
categories of "tender" and "tough."
The studies cited above indicate that there is potential for utilizing WT-based texture
analysis for beef tenderness evaluation. The work conducted by Huang et al. (1997)
reported high correlation between textural features and WBS scores. However, the
study was conducted on ultrasound elastogram images taken from live cattle, and the
sample size (n == 29) was too small to enable proper validation. Li et al. (200 1) also
reported a high success rate using wavelet-based texture analysis. However, they
correlated the textural features with taste panel scores, rather than objective WBS
scores.
18
Employing a sufficient sample size, this study will capture digital color images of
beef steaks and extract textural features using computer analysis to predict beef
tenderness.
Objectives
The overall objective of this study is to extend the Oklahoma State University VIA
beef grading system to include prediction of tenderness. Specific objectives are to:
1. Develop image-processing algorithms to extract WT-based and GLDH-based
textural features from steak ribeye images.
2. Develop statistical and neural network models to predict 14-day WBS
tenderness scores using the image textural features.
3. Evaluate the performance of the algorithms in terms of the correlation of WBS
scores with the textural features and the accuracy of classifying the steaks as
"tender" and "tough."
4. Compare the ability of WT-based and GLDH-based features to predict beef
tenderness.
19
CHAPTER III
MATERIALS AND METHODS
Overview
This chapter discusses the development and application of the VIA beef tenderness
prediction system. The system consists of hardware components and supporting
software. An algorithm was developed to extract WT-based textural features from
images of beef steak ribeyes. Statistical and neural network models were developed.
These models used the image textural features to predict WBS tenderness.
Hardware Components
The VIA system was comprised of a color video camera, a digitizer board and a
computer and monitor (Fig.l). Images of the steaks were captured by the camera. The
digitizer converted the analog signal from the camera to digital format. Digital images
were processed and analyzed by the computer.
Images of the beef steaks were captured in a diffuse lighting chamber (Fig. 2). The
chamber consisted of a vaulted cover with a white interior to direct base lighting to a
20xJO-cm imaging area (Fig. 3, Appen. B). Six 50-watt halogen lamps, powered by a
stabilizing feedback controller, provided diffuse interior lighting. The camera was
positioned on a graduated light stand equipped with a rack-and-pinion mount to raise
or lower the camera. Steak samples were viewed through a circular viewing port in
20
the cover. Samples of beef steaks were placed on a removable pan and positioned in
the viewing area beneath the camera. The pan had a black, non-reflective surface.
Figurel. Video image analysis system showing video camera,
lighting chamber, positioning pan, and monitor.
A Microimage A209 ROB color video camera equipped with a 50-mm lens was used
to acquire close-up images (Fig. 4). Fixing the F-stop between 5.6 and 8.0 prevented
color saturation. The camera was set at a height of 46 em above the surface of the
beef steak ribeye.
An Integral Technologies Flashpoint 128 digitizer board was installed in a 1 GHz
Dell Precision 420 computer equipped with 512 MB of RAM and a 40 GB hard disk.
21
Figure 2. Image of sample beef steak.
Fat
Bone
Ribeye
Figure 4. Close-up image of sample steak ribeye.
22
Software Components
Images were captured and stored using Optimas Ver. 6.5 (Media Cybelnetics Silver
Spring, tvlD). Images were acquired in RGB format. Resolution of the images was
640 x 480 pixels. Images were stored in uncompressed TIF format.
Algorithms were written in Matlab Ver. 6.0 (The Math Works, Inc., Natick MA).
The software is coded in C and has toolboxes for applications in signal and image
processing, including WT-based analysis.
Calibration
A calibration grid (Newport Corp.,1988) was used to relate the pixel SIze to
measurable units. The grid, consisting of a 0.060-inch square mesh pattern, was
placed beneath the camera. By calculating the number of squares on the captured
image, the pixel size was determined to be 0.064 by 0.064 mm.
Samples
Steak samples (n==186) were acquired from regional packing plants during three
visits. One-hundred and twenty-six samples from Future Beef, Arkansas City, KS,
and 60 samples were acquired from Sam Kane's, Corpus Christi, TX. The samples
were prepared for imaging at the OSU Food and Agricultural Products Center
(FAPe). Steaks of 2.5-cm thickness were cut, labeled, and placed on trays. To allow
for color to develop, steaks were 'bloomed' for a period of 30 minutes prior to
ImagIng.
23
Shear-Force Measurement
Procedures recommended by AMSA (1995) were followed for measuring shear-force
tenderness. After acquiring images, the steaks were vacuum packaged and aged for 14
days at 1ce. The steaks were then cooked in an impingement oven to an internal
temperature of 700e (Figs. 5 and 6). An impingement oven improves heat transfer by
reducing the boundary-layer resistance through increased air velocity (Burrington,
1997). The result is a uniformly cooked sample. The cooked steaks were cooled and
six 12-mm diameter core samples were removed from each ribeye. Each core was
then sheared, perpendicular to the muscle fibers, in an Instron Universal Testing
Machine fitted with a Warner-Bratzler shear-head attachment (Fig. 7). The mean of
the peak shear-force values from six core samples was taken as the tenderness
reference value. Higher values indicated "tougher" samples. Shear-force values
exceeding 4.53 kg-force (kg-f) were defined as "tough" samples. Values below 4.53
kg-f were defined as "tender." Table I shows mean WBS scores (kg-f) for the
samples, taken on 7th and 14th day of aging.
24
Shear-Force Measurement
Procedures recommended by AMSA (1995) were followed for measuring shear-force
tenderness. After acquiring images, the steaks were vacuum packaged and aged for 14
days at l°e. The steaks were then cooked in an impingement oven to an internal
temperature of 70°C (Figs. 5 and 6). An impingement oven improves heat transfer by
reducing the boundary-layer resistance through increased air velocity (Burrington,
1997). The result is a uniformly cooked sample. The cooked steaks were cooled and
six 12-mm diameter core samples were removed from each ribeye. Each core was
then sheared, perpendicular to the muscle fibers, in an Instron Universal Testing
Machine fitted with a Wamer-Bratzler shear-head attachment (Fig. 7). The mean of
the peak shear-force values from six core samples was taken as the tenderness
reference value. Higher values indicated "tougher" samples. Shear-force values
exceeding 4.53 kg-force (kg-±) were defined as "tough" samples. Values below 4.53
kg-f were defined as "tender." Table I shows mean WBS scores (kg-±) for the
samples, taken on 7th and 14th day of aging.
24
Figure 5. Steaks loaded into impingement oven.
Figure 6. Cooked steaks removed from the oven and
monitored for temperature.
25
all textural features share is that they express spatial interactions between the pi els
of an image neighborhood (Van de Wouwer et. aI., 1999).
Textural features are often random in nature. Numerous attempts at modeling texture
have included random field modeling, cooccurence matrices, and spatial-frequency
techniques. Thus, no single best texture model has been defined.
1'extural features contain both spatial and frequency information. The raw signal is a
time-domain or temporal representation. This representation is not the most useful,
because it gives no information regarding the frequency content.
According to Heisenberg's uncertainty principle, the position and momentum of a
moving particle cannot be known simultaneously at a given instant (Polikar, 2002).
This principle also applies to signal and image processing. Frequency and spatial
information of a signal cannot be determined simultaneously.
The Fourier transform (FT) is a mathematical function that determines the frequency
content of the signal (Polikar, 2002). The FT analyzes the signal, globally. The
frequency spectrum shows what frequencies exist in a signal, and the amplitude
represents the frequency content. Digital images are spatial representations. The FT
of an image yields a spatial frequency spectrum in which the high-frequency
components are depicted in the center, and the low-frequency components are
represented toward the outside. The FT is a global representation of the signal.
27
The short-time Fourier transform (STFT) analyzes the signal locally. The signal is
divided into small and equal segments, within which the signal is assumed to be
stationary. A window function is used to separate the signal into equal segments.
However, the length of the window is fixed for a given representation. Choice of a
window function is based on the nature of application. A wider window gives good
frequency resolution, but poor spatial resolution. Narrower windows give poor
frequency resolution, but good spatial resolution. Thus, choosing a window presents a
challenge when the need arises to select an optimum window length for the whole
signal.
Wavelet Transform
The wavelet transform (WT) overcomes the shortcomings of the STFT by using a
variable-length window. A variable-length window is able to represent low-frequency
components by using a wider window, and high-frequency components with a smaller
window.
Evaluation according to scale is the principle behind wavelet analysis. Scale is
defined as l/frequency. The scale parameter in the wavelet analysis is similar to the
scale used in maps. High-scale maps provide a global view, and thus provide lowfrequency
information. Low-scale maps give a more detailed view, and thus provide
information of high intricacy or high frequency.
28
The analytical approach utilized in WT is termed multiresolution analysis (MRA).
This procedure implies that the signal is analyzed at different frequencies with
different resolutions (Polikar, 2002). MRA is designed to give good spatial resolution
and poor frequency resolution at high frequencies, while yielding good frequency
resolution and poor spatial resolution at low frequencies. Thus, the MRA approach is
best suited when a given signal has high-frequency components for short durations
and low-frequency components for longer durations. Fortunately, most signals
encountered in practical applications follow this pattern.
The continuous wavelet transform (CWT) is similar to the STFT in the sense that a
window function is multiplied by the signal, and the transform is computed separately
for different segments of the spatial-domain signal. However, the transforn1 computed
using the CWT is not an FT. Wavelets are compactly supported functions of finite
width. In contrast, an FT has cosine- and sine-based functions that are of infinite
width. In wavelet transformation, negative frequencies of a sinusoidal signal are not
computed, and thus a single peak corresponds to a sinusoid.
In the WT, a prototype function called an analyzing wavelet or 'mother' wavelet, is
adopted. The mother wavelet is a prototype for generating other window functions.
All the windows used are dilated or compressed and shifted versions of the mother
wavelet. Spatial analysis is performed on a contracted, high-frequency version of the
prototype, while frequency analysis is done on a dilated, low-frequency version. The
29
wavelet functions of the prototype can be truncated or modified according to
requirements.
The continuous one-dimension wavelet transform of a signalf(x) is defined by Livens
et al. (1997), as:
(Waf) (b) = If(x) '.;/a,b (x) dx, (1)
where: lfa,b is computed from the mother wavelet, lj/, by translation and dilation
given by:
lfa,b (x) == Ilf (x-b)
~a a
where: a == translation parameter, measure of time
b == scale parameter, l/frequency.
(2)
The Haar wavelet is the simplest of all mother wavelets. It is a square step-function.
Other types of wavelets are termed biorthogonal, Daubechies, Mexican hat, Morlets,
symlets, and coiflets.
Discretizing the CWT or making the CWT mathematically discrete, offers a feasible
computational approach. Solving the FT, STFT, or CWT by hand, using integrals
and equations, is not practical. These computations require the use of computers, and
hence, the need to discretize the transforms.
30
The Nyquist theorem states that the highest frequency that can be accurately
represented is less than one-half of the sampling rate. In other words, the sampling
frequency should be twice that of the original frequency. This rule is followed in
order to prevent aliasing.
A variable-resolution tool such as WT can be utilized to discretize the signal by
varying the sampling rate. At higher scales or lower frequencies, the sampling rate
can be reduced. This operation can be represented by the equation:
(3)
where: 81 and 82 == scales for the sampling rates ofNl and N2.
The discretized CWT is merely a sampled version of the CWT. The sampled version
still contains redundant information, which increases computation time (Polikar,
2002). This redundancy is of concern where reconstruction or synthesis of the signal
is required.
The discrete wavelet transform (DWT) provides sufficient information both for
analysis and synthesis of the raw signal. In the discrete case, filters of different cut-off
frequencies are used to analyze the signal at different scales. The signal is passed
through a series of high-pass filters to analyze the high frequencies and passed
through a series of low-pass filters to analyze the low frequencies. The filtering
31
process changes the resolution of the signal whereas subsampling or upsampling
operations change the scale. Filter implementation of the DWT is shown in Figure 8,
Appendix B.
An important property of the DWT is the relationship between the impulse responses
of the low-pass and high-pass filters. The relationship is given by:
g[L-l-n] == (_l)n h[n]
where: g[n] == high-pass filter
h[n] == low-pass filter
L == filter length.
(4)
These filters are known as quadrature mirror filters (QMF), because each filter is an
odd-index alternated, reversed version of the other. Conversion into the other type of
filter is brought about by the (_l)n term.
The raw signal is passed through the filter banks that are comprised of low- and highpass
filters. Approximation coefficients of the signal are obtained through the lowpass
filter, whereas the high-pass filter gives detailed coefficients. After the filtering,
half of the samples can be eliminated according to Nyquist's rule, since the signal
now has a highest frequency of nl2 radians, instead of n. This process of upsampling
and subsampling, along with the filtering operations is known as decomposition.
32
The amount of subsampling increases as the number of levels of decomposition
increases. The higher-frequency components are extracted with higher resolution at
the first level of decomposition. As the levels of decomposition increase 10 frequency
components are extracted at lower resolution. Due to successive
subsampling by 2, the signal length must be a power of 2, or at least a multiple of a
power of 2, in order for this scheme to be efficient. Length of the signal determines
the number of levels to which the signal can be decomposed. For example, if the
signal length is 1024, ten levels of decomposition are possible (Polikar, 2002).
Wavelet Decomposition of Images
The two-dimensional (2-D) WT is the result of filtering by the product of two onedimensional
(I-D) wavelet transforms. Wavelet decomposition of a 2-D image can be
obtained by performing the filtering operations consecutively in the horizontal and
vertical directions (Livens et aI., 1997). Rows of the input image are passed through
the low- and high- pass filter bank, followed by subsampling by a factor of 2.
Columns of the resulting images from the filter bank are filtered further by low- and
high-pass filters. This sequence of filtering is followed by subsampling by a factor of
2. The entire process represents a single level of decomposition.
Each level of decomposition yields four subimages, namely; approximation,
horizontal, vertical, and diagonal. The approximation subimage consists of highfrequency
components of the original image. Horizontal, vertical, and diagonal
subimages consist of low-frequency components. Decomposed images can be viewed
33
by reconstructing the coefficients of the subimages at each level. Since eery
subimage is subsampled by a factor of 2, there is complete reconstruction. This
procedure leads to a representation with the same number of pixels as the original
image.
Wavelet image decomposition provides a representation that is easy to interpret.
Every subimage has conveniently separated information of specific scale and
orientation. Spatial information is retained within the images (Livens et aI., 1997).
Wavelet-based Textural Features
Coefficients of a detailed subimage resulting from wavelet decomposition sum to
zero. It is therefore necessary to compute a non-linear function of the coefficients in
order to obtain textural features. The most commonly used function is the square,
which gives the energy of the subimage when summed. Wavelet energy signatures
indicate the distribution of energy of a subimage along the frequency axis, with
respect to scale and orientation. Wavelet energy signatures have proven to be very
useful for gray-level texture characterization (Van de Wouwer et aI., 1999).
Van de Wouwer et al. (1999) define energy ofa subimage as:
(5)
where: Dni =: directional detail information at a given scale, n.
34
The most straightforward extension of energy signatures to color images is to
transform each color space separately and extract the energies of each transformed
plane. The number of features will be tripled, because they are extracted in a
tristimulus plane such as RGB, HSI, or CIE L* a* b* color spaces. RGB and CIE L*
a* b* color spaces were utilized for extracting features in this study.
The images were decomposed using Haar and Daubechies wavelets up to five levels
of decomposition. Since the decomposition is performed by a factor of 2 the
maximum allowable decomposition was five, using images with a resolution of 640
by 480 pixels.
Wavelet transform operations were performed separately in the RGB and CIE L* a*
b* color spaces. Both Haar and Daubechies wavelets were used for decomposing the
images. Subimages at the 5th level of decomposition showed highly detailed features
(Fig. 9, Appen. B). This characteristic enabled the extraction of highly detailed
textural features at the higher leveis of decomposition.
The first trial involved WT operations on regular images. The second trial involved
contrast stretching of the images prior to WT operations. Contrast stretching (often
called normalization) is a simple image enhancement technique that attempts to
improve the contrast in an image by 'stretching' the range of intensity values it
contains to span a desired range of values, e.g., the full range of pixel values allowed
by the type of image involved (University of Edinburgh, 2002). One method to
35
enhance contrast of an image by contrast stretching is histogram equalization.
Histogram equalization is a non-linear, monotonic mapping method that re-assigns
the intensity values of pixels in the input image to achieve a uniform distribution of
intensities in the output image. In this study, contrast stretching was conducted by
finding limits or pairs of intensities to increase contrast of an image. These limits
were then used to adjust the image intensity values, or colormap.
Wavelet textural features were obtained for both the regular and contrast-stretched
images in each color band of the RGB and CIE L* a* b* color spaces. The features
were extracted after reconstructing the subimages from the coefficients. These
features were:
1. Energy signatures
2. Energy ratios
3. Variance
4. Skewness
5. Kurtosis
6. Wavelet edge density.
Energy of the subimages was calculated using Eq. (5). Energy ratios between the
levels of decomposition were calculated separately for the approximation, horizontal,
vertical, and diagonal subimages. These ratios were computed to compare the amount
of energy in each directional subimage (Kim et aI., 1998).
36
Central moments of the pixel values, including variance (second moment) skewness
(third moment), and kurtosis (fourth moment) were also calculated from the
reconstructed subimages. Skewness values for the detailed subimages (horizontal,
vertical, and diagonal) were very low and, thus, were not calculated in further
simulations.
Wavelet edge density measures the coarseness or smoothness of texture (Kim et al.
1998). Edges of the decomposed subimages were enhanced by replacing the lowfrequency
components of the subimages with zero, thus emphasizing the highfrequency
components. After reconstruction the subimages energy was calculated
using Eq. (5) to estimate the edge density.
Gray-Level Cooccurence Matrix Textural Features
The concept of gray-level cooccurence matrices was proposed by Haralick et al.
(1973) to extract second-order textural features from images. The concept was based
on the spatial distribution of the gray levels. The proposed 14 textural features
depended on the ability to capture textural information in a matrix containing relative
frequencies by which a gray-level 'i' occurs with a neighboring gray-level 'j',
separated by a distance 'd' and gray-level orientation. Features such as contrast,
correlation, energy, entropy, etc., were proposed for gray-level orientations of 0°, 45°
90°, and 135°. Unser (1986) proposed the gray-level difference histogram (GLDH) as
an alternative to the computationally intensive GLCM. Sum images were constructed
by adding the value of a given pixel to the neighboring pixel values. Difference
37
images were constructed by subtracting the value of a given pixel from the
neighboring pixels.
For this study, six GLDH features were calculated from the reconstructed subimages
with distance of 1 pixel and an angle of 0°. Distance of 1 pixel was selected to reveal
fine textural details. Initially, four angles (0, 45, 90, and 135°) were used to extract
the textural features. Because the textures were uniform on the images of the steaks
all angles yielded similar features. Therefore, only the angle of 0° was used in this
study. The GLDH-based features were as follows:
1. Contrast
2. Entropy
3. Homogeneity
4. Correlation
5. Cluster Shade
6. Cluster Prominence.
Performance of the WT-based textural features and GLCM-based features were
compared.
Feature Reduction
A problem in WI-based textural analysis is redundancy, which occurs when the
textural features are extracted in tristimulus color spaces such as RGB, eIE L* a* b*,
or HSI. A large number of textural features are derived from each subimage, which
38
makes classification very difficult. One method of reducing the number of redundant
features is normalizing. This method is a post-generation operation, i.e. performed
after the features have been extracted.
In this project, post-generation feature reduction was achieved by using linear
regression to obtain the best features from each color space and from regular and
contrast-stretched images. These features were then combined, and principal
component analysis (PCA) was performed on these combined features to further
reduce redundancy. This analysis transforms the input data so that the elements of the
input vectors will be uncorrelated. In addition, the size of the input vectors may be
reduced by retaining only those components that contribute more than a specified
fraction of the total variation in the data set. Before conducting PCA, the textural
features were standardized to have zero mean and unit variance. The number of
principal components selected explained 99% of the variation of the original features.
Both, GLDH- and WT- based features, were reduced and normalized separately for
analysis.
Statistical Analysis
Stepwise regression analysis techniques were used to predict 14th day postmortem
average WBS scores. Samples were separated into two sets; training and test.
Training and test sets were formed using random number generation. The ratio of
sample sizes between the training and test sets was 3: 1. The training and test sets
consisted of 137 samples and 49 samples, respectively. Use of the random approach
39
for forming test and training sets removed human bias. Both training and test data sets
included a truncated data set, which gave the best fits when predicting WBS scores.
This truncated data set was obtained by linear regression, described earlier in relation
to feature reduction.
The truncated set of features was evaluated by stepwise regression to obtain the
regression equation and correlation coefficient for predicting WBS tenderness scores.
The training set alone was used to find the regression equation and report the
correlation coefficient values.
Procedures described by Wheeler et al. (2002) were then implemented for evaluation
of the VIA system. This procedure was considered better able to analyze the project
sample set, which was deficient in number and range of "tough" samples in our data.
This judgement is corroborated in following paragraphs.
Wheeler et al. (2002) assessed performance of three instrumented tenderness
prediction systems on the basis of progressive certification of steak sample
"tenderness" in 10% certification increments. In their procedure, WBS scores
predicted by linear regression, were sorted in ascending order. Values of WBS scores
less than 4.53 kg-f (10 lb-f) were certified "tender", and values equal to or greater
than 4.53 kg-f were certified "tough." Based on the sorted, ascending order of the
predicted WBS scores, actual WBS scores were sorted. Assuming that the model
performed as desired, the actual WBS scores would also be sorted in ascending order.
40
A 10% certification level implied that 10% of the steak samples having the lowest
predicted WBS scores were classified into a "certified tender' category and the rest
into a "not certified tender" category. Mean observed WBS scores from these two
categories were compared using a t-test for independent samples at a significance
level of 0.05 (u==0.05). Satterthwaite approximation was used to estimate variance
when the variances of the two categories were not equal. If the variances were equal
a pooled variance estimate was used in the t-test.
This procedure was repeated in 10% increments up to a 100% certification level. A
significant difference in mean observed shear force values between the two groups
indicated that the VIA system had successfully sorted the "tender" from the "tough'
samples at that certification level.
The data set (n==186) used for this project contained only 10 tough samples,
constituting only 5.4% percent of the total. As mentioned earlier, if the samples were
sorted properly based on the ascending order of WBS scores, the training and test sets
should consist of only "tender" samples up to the 90% certification level.
Descriptive statistics for WT- and GLDH-based textural features, for both training
and test sets, are shown below in Tables II and III.
41
Table II: Descriptive statistics of shear-force values for training and test data sets
for WT-based textural features
Data Set N Range Mean (kg-±) SD (kg-±) > 4.53 kg-f
Training 137 2.25-5.81 3.39 0.65 7
Test 49 2.39-4.81 3.46 0.60
,.,
j
Table III: Descriptive statistics of shear-force values for training and test data sets
for GLDH-based textural features
Data Set N Range Mean (kg-±) SD (kg-±) > 4.53 kg-f
Training 137 2.25-5.21 3.35 0.62 7
Test 49 2.30-5.81 3.56 0.69 3
It can be inferred from the mean values of the WBS scores that the samples in the
data set were predominantly "tender." Due to the lack of sufficient "tough" samples, a
confusion m~trix could not be plotted to estimate the accuracy of prediction. The t-test
suggested by Wheeler et al. (2002) was a better option because it could separate
the "tough" samples and contain them in the 100% certification level.
Statistical analysis was performed using SAS Ver. 8.1 ( SAS World Headquarters
Cary, NC).
Neural Network Analysis
Artificial neural networks (ANN) are one of the widely used techniques in data
mining and machine learning. Modeled on the functioning of the human brain, an
ANN is comprised of interconnected nodes arranged in layers. The ANN has an
42
activation function and a learning rule to map the input to the output b adjusting the
input weights and bias. The adjustment is based on the input pattern.
The backpropagation neural network (BPNN) is a multi-layer perceptron.
Backpropagation was created by generalizing the Widrow-Hoff learning rule, or delta
learning rule, to multi-layer networks and nonlinear differentiable transfer functions
(Demuth et aI., 1998). Widrow-Hoff learning is an approximate steepest-descent
algorithm, in which the performance index is the mean square error (MSE) between
the predicted and targeted values (Hagan et aI., 1996). The learning rule is a
supervised operation occurring in each cycle or 'epoch' through a forward flow of
outputs and a backward propagation of the error resulting from the adjustment of
weights. The first layer has weights coming from the input. Each subsequent layer
has a weight coming from the previous layer. All layers have bias. The last layer is
the network output. The transfer functions can be any differentiable transfer function
such as hyperbolic tangent sigmoid, log-sigmoid, or linear. Details regarding transfer
functions can be found in Hagan et aI. (1996).
The performance function for a backpropagation neural network is the MSE, which is
the same as that for Widrow-Hoff learning. This performance function does not
prevent the use of large weights and bias that can lead to overfitting and poor
performance of the network. The performance function given by Demuth et al. (1998)
prevents the use of larger weights and bias. As a result, the network response is
43
smoother and less likely to overfit. The performance function is represented in the
given equation as:
F == MSE + (l-y) MSW
where: F == performance function
MSE == mean square error between output and target values
y == regularization parameter
MSW == mean square of network weights and biases.
BPNN was employed using the following training functions:
1. Quasi-Newton algorithm
2. Levenberg-Marquardt algorithm
3. Variable learning rate
4. Resilient backpropagation
5. Bayesian regularization.
(6)
Newton's method is based on the second-order Taylor series expansion (Hagan et aI.,
1996). The basic step ofNewton's method is given by the equation below:
(7)
where: Ak == Hessian matrix or second derivative of the performance index
gk == gradient or first derivative of the function.
44
(8)
Quasi-Newton methods belong to a class of algorithms that are based on Newton s
methods, but don't require the tedious calculation of the Hessian matrix. Instead an
approximation of the Hessian matrix is updated during each iteration of the algorithm
(Demuth et aI., 1998).
The Levenberg-Marquardt algorithm is similar to quasi-Newton methods in that it
involves second-order training, without calculating the Hessian matrix. The
approximation used for the Hessian matrix by this algorithm is given by:
Xk+l == Xk- [JT J+ J1 I] -1 JT e
where: J == Jacobian matrix that contains derivatives of network errors
e == vector of network errors
J.l == scalar function, with adjustable values to speed up or improve the
performance function.
Variable learning rate is an improvement on the steepest-descent algorithm, that uses
a constant learning rate. Large values of the learning rate will speed up the
convergence, but cause oscillations and instability during training. Small values of the
learning rate stabilize the algorithm, but lengthen the time to converge. Instead,
performance of the algorithm is improved by varying the learning rate during
training. An adaptive learning rate attempts to keep the learning step size as large as
possible, without subjecting the algorithm to instability or oscillation.
45
Resilient backpropagation is another improvement of the steepest-descent algorithm
that resembles the variable learning rate algorithm. Networks that employ sigmoid
transfer functions require that the slope of the transfer function approach zero as the
input size increases. When steepest-descent algorithms are used to train, convergence
is very slow. This effect occurs because the magnitude of gradient is very small
causing small changes in weights and bias (Demuth et aI., 1998). Resilient
backpropagation training utilizes only the sign of the gradient to determine the
direction of weight update. The size of the weight change is determined by a separate
function. Weight size is increased when the sign does not change after two successive
iterations and decreases when the sign changes from the previous iteration.
The Bayesian regularization algorithm is a network training function that updates the
weights and bias values according to Levenberg-Marquardt optimization. Weights
and biases of the network are assumed to be random variables with specified
distributions. The algorithm minimizes a combination of squared errors and weights,
and then determines the correct combination so as to produce a network that
generalizes well (Demuth et aI., 1998). More details regarding Bayesian
regularization techniques can be found in Mackay (1992).
In this project, the BPNN was trained using all five training functions, separately.
Results of each of the training functions were evaluated separately, based on network
46
stability and value of the correlation coefficient. Neural network analysis was
performed using Matlab Ver. 6.0.
47
CHAPTER IV
RESULTS AND DISCUSSION
A sample set of beef steaks (n==186), were imaged for tenderness evaluation b the
VIA system. Statistical and neural network models were developed from textural
features to predict shear-force tenderness values. Success of the model was based on
the prediction correlation coefficient and on the accuracy of classifying steaks as
"tender" or "tough."
Statistical Analysis Results
Truncated WT- and GLDH-based textural features were analyzed separately in two
sets by stepwise linear regression. Both sets contained features derived from Haar and
Daubechies decomposition. This truncated set of features did not contain information
from contrast-stretched images, thus confirming that contrast stretching did not
improve performance of the model. The significance level for the features to be
entered and remain in the stepwise regression model was 0.15 (a == 0.15).
Results from the preliminary stepwise regression analysis showed that WT-based
textural features predicted the 14th day postmortem WBS tenderness with a
correlation coefficient value of 0.57. GLDH-based textures predicted WBS
tenderness with a correlation coefficient of 0.48. Both Haar and Daubechies wavelets
contributed equally in predicting tenderness. Among the features extracted from the
48
detailed subimages, those from the approximation subimages contributed least to
prediction of WBS tenderness. Regression equations derived from the training set
were used to predict WBS scores in the training and test sets.
For both WT- and GLDH-based features, the training and the test set contained seven
and three "tough" samples, respectively. The training set of the WT-based features
had two misclassified samples at the 80% and 90% "certified tender" levels. No
errors were found up to the 70% level. In the test set, one "tough" sample was
misclassified at the 80% level (signified by the asterisk in Table IV, Appendix A). At
all certification levels for both training and test sets, there were significant differences
between the means of the shear-force values for "certified tender" and' not certified
tender" samples.
In the training set for GLDH-based features, two "tough" samples were incorrectly
classified at the 800/0 "certified tender" level. There were no errors up to the 70%
level. The test set had one misclassified "tough" sample at the 90% level (signified by
the asterisk in Table V, Appendix A), and had no errors up to the 80% level. At all
certification levels for the training set, there were significant differences between
means of the shear force values for "certified tender" and "not certified tender"
samples. ,However, in the test set, at the 10% and the 70% certification levels
(signified by asterisk in Tables VI and VII), there were no significant differences
between means of the shear-force values of the two groups. Tables V and VI are
given on the following page.
49
Table VI: Statistical differences of mean shear-force values between "certified
tender" and "not certified tender" groups for WT-Based textural
features
Percentage Training Set (n==137) Test Set (n=49)
Certified
Certified Not Difference Certified Not Difference
Tender Certified Tender Certified
Tender Tender
90 3.2876 4.2872 0.9996 3.4076 3.9636 0.5560
80 3.2439 3.9839 0.7400 3.3279 3.9968 0.6689
70 3.1911 3.8716 0.6805 3.2382 3.9771 0.7389
60 3.1296 3.7896 0.6600 3.2528 3.7712 0.5184
50 3.1271 3.6563 0.5292 3.2250 3.6942 0.4692
40 3.0732 3.6021 0.5289 3.1609 3.6566 0.4957
30 2.9773 3.5721 0.5948 3.0514 3.6296 0.5782
20 2.9391 3.5055 0.5660 2.9891 3.5862 0.5969
10 2.7684 3.4605 0.6920 2.8674 3.5322 0.6650
Table VII: Statistical differences of mean shear-force values between "certified
tender" and "not certified tender" groups for GLDH-based textural
features
Percentage Training Set (n==137) Test Set (n==49)
Certified
Certified Not Difference Certified Not Difference
Tender Certified Tender Certified
Tender l'ender
90 3.2914 4.1715 0.8801 3.4729 3.6261 0.1532
80 3.2297 3.9737 0.7440 3.4523 3.6430 0.1910
70 3.2054 3.7679 0.5630 3.4207 3.7091 0.3064*
60 3.1644 3.6974 0.5330 3.3122 3.7665 0.4543
50 3.1676 3.5938 0.4262 3.2253 3.7588 0.5335
40 3.0760 3.5825 0.5065 3.1548 3.7130 0.5582
30 2.9953 3.5493 0.5540 3.1192 3.6615 0.5423
20 3.0347 3.4687 0.4340 3.1169 3.5908 0.4739
10 3.0115 3.4224 0.4109 3.0144 3.5476 0.5332*
* Mean observed shear force values for "certified tender" and "not certified
tender" were not significantly different at a == 0.05.
50
Neural Network Analysis Results
The BPNN model consisted of two hidden layers. The first hidden layer had ten
neurons with a log-sigmoid transfer function, and the second hidden layer had twenty
neurons with a tangent sigmoid transfer function. The output layer had one neuron
with a linear transfer function.
The truncated GLDH- and WT-based features were analyzed separately. Both data
sets contained features derived from Haar and Daubechies wavelet decomposition. As
mentioned earlier, features obtained from contrast-stretched images were not present
in the two sets.
Prior to feeding the textural features into the network, the input vectors were
normalized. Normalization was followed by PCA to remove redundant features. The
number of principal components selected explained 99% of the variation of the
original features. After preliminary analysis, the input vectors were split into training
and test sets. Based on sample size, the ratio between the training and test data sets
was 3:1.
Of the five training functions used, Bayesian regularization provided equal or near
equal correlation coefficient values for the training and test sets. The Bayesian-based
network was trained for 25 to 30 epochs. The MSE remained constant after training
the network for 20 epochs, so no further training was performed in order to avoid'
overfitting. Networks utilizing the other four training functions were trained for
51
higher numbers of epochs. However, they performed poorly in predicting WBS
tenderness, despite the substantial reduction in MSE. The correlation coefficient in
the training and test sets varied considerably. Correlation coefficient values for the
training set ranged from 0.75 to 1.0. For the test set, values ranged from 0.35 to 0.56.
The large difference in the correlation coefficient values between the test and training
sets indicated that none of the four training functions was able to stabilize the
network.
For WT-based textural features, correlation between the observed WBS and predicted
values for both training and test data sets ranged from 0.57 to 0.59. GLDH-based
textural features predicted WBS tenderness with correlation coefficients of 0.55 and
0.31 for training and test data sets, respectively. It can be inferred from the correlation
coefficients that WT-based textural features were able to predict WBS scores more
accurately than GLDH-based features. Training and test sets of the WT-based
features gave nearly similar values of correlation coefficients, indicating that the
network was more stable working with WI-based features, than with GLDH-based
features.
Results of the statistical and neural network analysis indicated that WT-based features
predicted WBS scores better than GLDH-based features. The analyses also showed
that features derived from contrast-stretched images did not contribute to predicting
WBS scores.
52
Conclusions
The OSU VIA system was extended to extract textural features from the ribeye
images and create models to predict meat tenderness, with moderate success. The
results indicated that WT-based features were better predictors of WBS tenderness
than GLDH-based features, on the basis of correlation coefficients and results of the
statistical (-test. The (-test indicated that 71.4% and 66.70/0 of "tough" samples in the
training and test set, respectively, were successfully sorted from the "tender" samples.
However, the correlation coefficients for predicting WBS tenderness scores were very
low. There were also errors in classification of "certified tender" and "not certified
tender" at two certification levels in the (-test. These discrepancies are probably
magnified by the following data conditions:
1. The data were highly skewed towards the "tender" side. Only ten "tough"
samples, approximately 5.4%, were included in the entire set of 186 samples.
This distribution lacked the balance needed to formulate an effective statistical or
neural network model.
2. The WBS data obtained from the Department of Animal Science Meat
Laboratory was not entirely reliable. Many samples showed an increase in WBS
scores on the 14th day of aging when compared with scores taken on the 7th day
(Indicated by asterisk, Table I, Appen. A). Since aging is found to increase
tenderness up to the 11 th day, these data contradicted the established pattern.
53
Despite the anomalies in the data, both WT- and GLDH-based textural feature models
were able to establish a moderate correlation between the textural features and WBS
tenderness, and the t-test was able to sort the "tender" and "tough" samples with
acceptable accuracy_
Further Research
The goal of including tenderness prediction in the USDA quality grading procedures
is a major task. The OSU system demonstrated the use of textural features extracted
from images of fresh steaks to predict cooked-beef tenderness and the ability to sort
steaks on the basis of cooked tenderness. Hence, this project has shown that VIA
systems offer an objective, efficient, and non-destructive method for predicting
tenderness in meat. Several modifications to the VIA system might improve results.
Suggestions for further research are listed below:
1. Having a greater number of "tough" samples in the data set should give the
model better balance in predicting tenderness. Therefore, samples from
mature animals, or those not subjected to artificial tenderizing procedures,
should be included in the data set.
2. Frequency-domain features derived from Fourier transforms should be
explored for extracting textural features. Directionality and coarseness
features of a Fourier power spectrum could yield information regarding
tenderness.
54
3. Despite the fact that extent of marbling features has been found to explain
only 10% of variation beef tenderness, there is a possibility that marbling
features, combined with other textural features and color scores, could enrich
data related to tenderness. Scores for lean maturity could also be incorporated.
4. NIR analysis has shown promise for tenderness prediction and classification.
Application is hampered by difficulty in implementing for on-line use. This
drawback might be corrected by employing cameras that cover a sufficient
portion of the NIR spectrum.
5. Extracting textural features in the UV spectrum is another worthy approach to
tenderness prediction. UV light causes collagen to fluoresce. Since one of the
factors associated with meat toughness is the collagen in the connective tissue,
this approach could quantify the relationship between collagen and tenderness.
Among the suggested approaches, I see the most promise in NIR and UV
technology. These two methods could objectively identify contributors to meat
tenderness, due to their ability to scan in a spectral range invisible to the human
eye. In time, a well established and approved tenderness rating for beef carcasses
will be developed to add value to the product and optimize consumer satisfaction.
55
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60
APPENDICES
61
APPENDIX A- STATISTICAL TABLES
62
Table I: Mean WBS scores for samples taken on 7th and 14th
day of aging
Sample ill Harvest Date Day 7 Mean (kg-t) Day 14 Mean (kg-t) Shear Force Difference
OBIC 1 1/11/02 3.539 2.818 0.721
OBIC2 1/11/02 3.088 2.250 0.838
OBIC3 1/11/02 2.824 2.650 0.173
OBIC4 1111/02 3.529 3.182 0.347
OBIC 5 1111/02 3.073 2.729 0.344
OBIC6 1/11/02 3.973 2.824 1.150
OBIC7 1/11/02 5.256 3.139 2.117
OBIC 8 1/11102 3.235 2.440 0.795
OBIC9 1/11102 5.918 3.558 2.361
OBIC 10 1/11/02 4.278 4.196 0.083
OBIC 11 1111/02 3.062 2.730 0.332
OBIC 12 1111102 3.645 3.306 0.339
OBIC 13 1/11/02 3.591 3.071 0.520
OBIC 14 1/11/02 2.678 2.608 0.070
OBIC 15 1/11/02 3.747 3.310 0.437
OBIC 16 1/11/02 3.392 2.677 0.715
OBIC 17 1111102 2.738 3.743 -1.006*
OBIC 18 1111/02 2.550 3.101 -0.551 *
OBIC 19 1/11/02 2.741 3.315 -0.574*
OBIC 20 1/11102 3.108 3.648 -0.540*
OBIC 21 1111102 3.436 3.239 0.197
OBIC 22 1/11/02 3.103 3.047 0.056
OBIC 23 1/1 1102 3.374 2.459 0.915
OBIC 24 1/11/02 3.198 2.552 0.647
OBIC 25 1/11/02 2.934 2.682 0.252
OBlC 26 1/11/02 2.707 2.696 0.011
OBIC 27 1/11/02 3.468 2.447 1.021
OBIC 28 1/11/02 2.880 2.988 -0.108*
OBIC 29 1/11/02 2.962 2.392 0.570
OBIC 30 1/11/02 3.154 3.837 -0.682*
OBIC31 1111/02 2.860 2.601 0.260
OBIC 32 1111/02 4.580 3.873 0.707
OBIC 33 1111/02 2.736 2.689 0.048
OBIC 34 1/11/02 3.854 3.440 0.414
OBIC 35 1/11/02 3.700 3.623 0.077
OBIC 36 1111102 2.824 2.596 0.228
OBlC 37 1/11/02 5.547 3.309 2.238
OBIC 38 1/11/02 3.401 3.004 0.397
OBIC 39 1111/02 3.850 3.067 0.783
OBIC 40 1111/02 5.705 4.816 0.890
OBIC 41 1111102 3.960 3.507 0.453
OBIC 42 1111102 4.574 4.163 0.411
OBIC 43 1/11/02 4.676 3.797 0.879
OBIC 44 1/11/02 3.804 2.893 0.912
OBIC 45 1/11/02 3.270 2.908 0.362
OBIC 46 1/11/02 7.157 4.163 2.994
OBlC 47 1111102 3.549 2.646 0.904
OBIC48 1111102 3.840 2.830 1.01 I
OBIC49 1/11/02 4.231 3.744 0.486
OBIC 50 1/11/02 2.977 3.013 -0.036*
OBIC 51 1/11/02 3.703 3.613 0.090
OBIC 52 1/11102 3.517 3.620 -0.103
OBIC 53 1/11102 3.472 3.307 0.165
OBIC 54 1111102 3.660 2.870 0.790
OBIC 55 1111102 4.225 3.057 1.167
OBIC 56 1/11/02 3.876 2.380 1.496
OBIC 57 1/lli02 4.866 3.527 1.339
OBIC 58 1/11102 3.447 3.359 0.088
OBIC 59 1111/02 5.166 4.392 0.774
OBIC60 1/11/02 4.205 4.482 -0.278*
OBIC 61 1/11/02 3.778 3.910 -0.132*
63
OBIC62 1/11/02 2.935 2.894 0.041
OBIC 63 1/11/02 4.692 4.044 0.648
OBIC 64 1/11/02 4.125 3.401 0.724
OBIC 65 1/11/02 3.261 2.821 0.439
OBIC 66 1/11/02 3.635 3.253 0.382
OBIC 67 1/11/02 4.949 3.686 1.263
OBIC 68 1/11/02 4.201 4.129 0.072
OBIC 69 1/11/02 3.340 3.306 0.034
OBIC 70 1/11/02 5.758 5.809 -0.051 *
OBIC 71 1/11/02 3.467 3.112 0.354
OBIC 72 1/11/02 2.827 2.767 0.061
OBIC 73 1/11/02 4.162 2.984 1.177
OBIC 74 1/11/02 3.054 3.682 -0.628*
OBIC 75 1/11/02 3.482 2.915 0.567
OBIC 76 1/11/02 3.568 3.678 -0.111 *
OBIC 77 1/11/02 5.037 3.939 1.098
OBIC 78 1/11/02 5.561 3.769 1.792
OBIC 79 2/13/02 4.488 3.315 1.173
aBIC 80 2/13/02 2.935 2.856 0.079
aBIC81 2/13/02 3.562 2.805 0.757
OBIC 82 2/13/02 3.729 2.943 0.786
OBIC 83 2/13/02 3.789 2.845 0.944
OBIC 84 2/13/02 3.399 3.864 -0.465*
aBIC 85 2/13/02 4.291 3.926 0.365
OBIC 86 2/13/02 3.293 3.447 -0.154*
OBIC 87 2/13/02 3.470 2.989 0.480
OBIC 88 2/13/02 3.404 3.353 0.051
OBIC 89 2/13/02 2.934 2.674 0.260
OBIC90 2/13/02 3.210 3.384 -0.175*
aBIC91 2/13/02 2.902 3.056 -0.154*
OBIC92 2/13/02 3.514 4.068 -0.554*
OBIC 93 2/13/02 2.899 2.690 0.210
OBIC 94 2/13/02 3.887 2.686 1.201
OBIC 95 2/13/02 2.787 3.948 -1.161 *
OBIC 96 2/13/02 3.471 3.257 0.214
OBIC 97 2/13/02 4.001 3.018 0.983
OBIC 98 2/13/02 2.497 2.303 0.194
OBIC 99 2/13/02 2.871 3.106 -0.235*
OBIC 100 2/13/02 3.176 3.189 -0.013*
aBIC 101 2/13/02 3.751 3.211 0.540
OBIC 102 2/13/02 3.584 3.619 -0.034*
OBIC 103 2/13/02 3.953 2.957 0.996
OBIC 104 2/13/02 3.499 3.365 0.135
OBIC 105 2/13/02 3.197 3.126 0.070
aBIC 106 2/13/02 3.826 3.635 0.191
aBIC 107 2/13/02 3.212 3.802 -0.590*
OBIC 108 2/13/02 3.494 3.221 0.273
aBIC 109 2/13/02 3.783 3.268 0.516
OBIC 110 2/13/02 4.978 3.058 1.920
OBIC 111 2/13/02 5.204 4.483 0.721
OBIC 112 2/13/02 4.038 2.737 1.301
OBIC 113 2/13/02 3.126 4.140 -1.014*
OBIC 114 2/13/02 3.302 3.143 0.159
OBle 115 2/13/02 2.783 3.714 -0.931 *
OBIC 116 2/13/02 4.288 5.213 -0.924*
OBIC 117 2/13/02 3.263 2.951 0.312
OBIC 118 2/13/02 2.874 2.959 -0.086*
OBIC 119 2/13/02 3.382 3.558 -0.176*
OBIC 120 2/13/02 4.993 3.306 1.687
OBIC 121 2/13/02 2.918 3.648 -0.729*
OBIC 122 2/13/02 2.851 2.489 0.362
OBIC 123 2/13/02 3.648 4.122 -0.474*
OBIC 124 2/13/02 2.796 3.168 -0.372*
OBIC 125 2/13/02 3.278 2.509 0.769
OBIC 126 2/13/02 4.896 3.452 1.444
OBIC 127 1/15/02 3.736 4.299 -0.563*
64
OBIC 128 1/15/02 4.278 2.639 1.639
OBIC 129 1/15/02 4.753 4.302 0.451
OBIC 130 1/15/02 3.308 2.591 0.717
OBlC 131 1/15/02 4.455 3.112 1.343
OBIC 132 1/15/02 3.987 4.173 -0.186*
OBIC 133 1/15/02 2.962 3.509 -0.547*
OBIC 134 1/15/02 4.964 3.157 1.807
OBIC 135 1/15/02 4.992 4.792 0.199
OBIC 136 1/15/02 4.464 2.987 1.477
OBIC 137 1/15/02 3.770 3.204 0.566
OBIC 138 1/15/02 4.709 4.332 0.377
OBIC 139 1/15/02 4.710 3.086 1.623
OBIC 140 1/15/02 5.796 5.167 0.629
OBIC 141 1/15/02 4.037 2.783 1.254
OBIC 142 1/15/02 4.263 3.478 0.784
OBIC 143 1/15/02 3.342 3.243 0.099
OBIC 144 1/15/02 4.771 3.369 1.402
OBIC 145 1/15/02 4.077 3.777 0.300
OBIC 146 1/15/02 5.032 5.159 -0.127*
OBIC 147 1/15/02 3.722 3.483 0.239
OBIC 148 1/15/02 3.803 4.047 -0.244*
OBIC 149 1/15/02 5.104 2.480 2.624
OBIC 150 1/15/02 4.146 3.609 0.537
OBIC 151 1/15/02 3.048 3.951 -0.903*
OBIC 152 1/15/02 3.247 4.208 -0.961 *
OBIC 153 1/15/02 2.958 2.953 0.005
OBIC 154 1/15/02 3.990 3.698 0.292
OBIC 155 1/15/02 3.535 3.493 0.041
OBIC 156 1/15/02 3.717 3.527 0.189
OBIC 157 1/15/02 3.764 3.370 0.394
OBIC 158 1/15/02 3.366 3.058 0.308
OBIC 159 1/15/02 3.692 3.829 -0.137*
OBIC 160 1/15/02 3.251 4.156 -0.906*
OBIC 161 1/15/02 4.435 3.892 0.543
OBIC 162 1/15/02 3.593 2.951 0.642
OBIC 163 1/15/02 3.089 3.293 -0.204*
OBIC 164 1/15/02 3.438 3.173 0.265
OBIC 165 1/15/02 5.197 4.613 0.584
OBIC 166 1/15/02 3.927 3.699 0.229
OBIC 167 1/15/02 3.304 3.425 -0.121 *
OBIC 168 1/15/02 4.536 3.772 0.765
OBIC 169 1/15/02 3.335 2.958 0.377
OBIC 170 1/15/02 4.160 3.890 0.270
OBIC 171 1/15/02 4.280 4.332 -0.052*
OBIC 172 1/15/02 3.333 3.337 -0.004*
OBIC 173 1/15/02 3.907 3.916 -0.010*
OBIC 174 1/15/02 3.853 3.250 0.603
OBIC 175 1/15/02 4.273 3.174 1.099
OBIC 176 1/15/02 3.884 3.221 0.663
OBIC 177 1/15/02 5.197 4.341 0.855
OBIC 178 1/15/02 4.629 3.924 0.706
OBIC 179 1/15/02 3.490 3.317 0.174
OBIC 180 1/15/02 4.381 4.667 -0.286*
OBIC 181 1/15/02 4.951 5.079 -0.128*
OBIC 182 1/15/02 4.096 3.666 0.430
OBIC 183 1/15/02 4.252 3.079 1.173
OBIC 184 1/15/02 3.211 3.658 -0.446*
OBIC 185 1/15/02 4.964 4.226 0.739
OBIC 186 1/15/02 4.242 4.689 -0.447*
* Suspect WBS reading, indicating decrease in tenderness with
increase in aging period.
65
IL_~ I -~--- --l_~ ------~-------'--'____..llII~_lLi_iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii.!!!
Table V: Samples sorted based on predicted scores with certification levels for
GLDH-based textural features (test set)
Sample 10 Predicted Scores (kg-f) Actual Scores (kg-f) Tenderffough Categories Certification Le els
OBIC 17 3.073 3.743 Tender
OBIC 10 3.104 4.196 Tender
OBIC 98 3.139 2.303 Tender 10%
OBIC 50 3.141 3.013 Tender
OBIC 15 3.154 3.310 Tender
OBIC 125 3.197 2.509 Tender
OBIC 43 3.201 3.797 Tender
OBIC 63 3.207 4.044 Tender 20%
OBIC 14 3.212 2.608 Tender
OBIC7 3.214 3.139 Tender
OBIC 94 3.218 2.686 Tender
OBIC 16 3.219 2.677 Tender
OBIC 176 3.232 3.221 Tender 300/0
OBIC 167 3.233 3.425 Tender
OBIC 74 3.234 3.682 Tender
aBIC 88 3.279 3.353 Tender
OBIC 53 3.282 3.307 Tender
OBlC 11 3.308 2.730 Tender 400/0
OBlC 147 3.331 3.482 Tender
OBIC 106 3.360 3.635 Tender
aBIC 75 3.362 2.914 Tender
aBIC 13 3.364 3.071 Tender 500/0
aBIC 156 3.399 3.527 Tender
OBlC 49 3.399 3.744 Tender
OBIC 42 3.401 4.163 Tender
OBlC 54 3.415 2.870 Tender
aBlC 60 3.418 4.482 Tender 600/0
aBIC 104 3.425 3.364 Tender
OBIC 78 3.434 3.769 Tender
aBIC 97 3.447 3.018 Tender
aBIC 59 3.456 4.392 Tender
OBIC 134 3.465 3.157 Tender 700/0
OBIC 41 3.473 3.507 Tender
OBIC 68 3.484 4.129 Tender
OBIC 127 3.511 4.299 Tender
OBIC 32 3.530 3.873 Tender
OBIC 175 3.541 3.174 Tender 80%
OBIC 30 3.571 3.837 Tender
OBIC 159 3.583 3.829 Tender
OBIC 144 3.637 3.369 Tender
OBIC 111 3.645 4.483 Tender
aBIC 40 3.649 4.816 Tough* 90%
OBIC 77 3.680 3.939 Tender
OBIC 51 3.688 3.613 Tender
aBIC 132 3.696 4.173 Tender
OBIC 110 3.728 3.058 Tender
OBIC 89 3.829 2.674 Tender 1000/0
OBIC 70 3.841 5.809 Tough
aBIC·I80 3.879 4.667 Tough
*Misclassified "tough" sample at the indicated certification level
67
'fa.
I
Table V: Samples sorted based on predicted scores with certification levels for
GLDH-based textural features (test set)
Sample 10 Predicted Scores (kg-f) Actual Scores (kg-f) Tenderffough Categories Certification Le els
aBIC 17 3.073 3.743 Tender
OBIC 10 3.104 4.196 Tender
aBIC 98 3.139 2.303 Tender 10%
aBIC 50 3.141 3.013 Tender
aBIC 15 3.154 3.310 Tender
aBIC 125 3.197 2.509 Tender
aBIC 43 3.201 3.797 Tender
OBIC 63 3.207 4.044 Tender 20%
aBIC 14 3.212 2.608 Tender
aBIC7 3.214 3.139 Tender
aBIC 94 3.218 2.686 Tender
aBIC 16 3.219 2.677 Tender
OBIC 176 3.232 3.221 Tender 300/0
OBIC 167 3.233 3.425 Tender
aBIC 74 3.234 3.682 Tender
aBIC 88 3.279 3.353 Tender
aBIC 53 3.282 3.307 Tender
OBlC 11 3.308 2.730 Tender 400/0
OBlC 147 3.331 3.482 Tender
OBIC 106 3.360 3.635 Tender
OBIC 75 3.362 2.914 Tender
OBIC 13 3.364 3.071 Tender 500/0
OBIC 156 3.399 3.527 Tender
aBlC 49 3.399 3.744 Tender
OBIC 42 3.401 4.163 Tender
aBlC 54 3.415 2.870 Tender
OBlC 60 3.418 4.482 Tender 600/0
OBIC 104 3.425 3.364 Tender
aBIC 78 3.434 3.769 Tender
aBIC 97 3.447 3.018 Tender
aBIC 59 3.456 4.392 Tender
aBIC 134 3.465 3.157 Tender 700/0
aBIC 41 3.473 3.507 Tender
OBIC 68 3.484 4.129 Tender
aBIC 127 3.511 4.299 Tender
aBIC 32 3.530 3.873 Tender
OBIC 175 3.541 3.174 Tender 80%
OBIC 30 3.571 3.837 Tender
OBIC 159 3.583 3.829 Tender
OBIC 144 3.637 3.369 Tender
OBIC 111 3.645 4.483 Tender
OBIC 40 3.649 4.816 Tough* 90%
OBIC 77 3.680 3.939 Tender
OBIC 51 3.688 3.613 Tender
OBIC 132 3.696 4.173 Tender
OBIC 110 3.728 3.058 Tender
OBIC 89 3.829 2.674 Tender 1000/0
OBIC 70 3.841 5.809 Tough
OBIC·I80 3.879 4.667 Tough
*Misclassified "tough" sample at the indicated certification level
67
APPENDIX B- FIGURES
68
~23cm~
I I
Viewing Port
for Camera
Light Ports
f-- 25 em e/e~
TOP VIEW
Light Baffle
1< 51 em --~
Video
Camera
-~
/ Level-Adjusting Knob
Heat Vent
36cm
Steak Sample
Halogen
Lamp
'1-~~1
-..Jl I~""
tt?fr,
I , '_ ..
1<
FRONT VIEW SIDE VIEW
Figure 3. Lighting chamber detail.
69
x[n] f=O-1t
Levell
DWI coefficients
Level 2
DWT coefficients
f=1t/8 - 1tI4
Levell
DWT coefficients • • •
Figure 8. Filter implementation of the discrete wavelet transform
(Pollikar, 2002). g[n]: high-pass filter, h[n]: low-pass filter.
70
Original Image
Figure 9. Five-level wavelet decomposition using Daubechies wavelets. Aapproximation
details; H- horizontal details; V-vertical details;
D- diagonal details, from levels 1 to 5.
71
APPENDIX C- IMAGE ANALYSIS AND NEURAL NETWORK PROGRAMS
72
1. Function program to convert RGB color space to CIE L*a*b* (Jeyamkondan et
aI., 2001)
function [L, a, b]==rgb2Lab(rgb)
[h,w,b] == size(rgb);
rgbv == reshape (rgb, [h*w, b]);
[X, Y, Z] == rgb2xyz (rgbv);
Xr == X/95.04;
Yr == Y/I00.0;
Zr == Z/I08.89;
gy == Yr>0.008856;
fgY==gy.*(Yr.1\(113));
Lg==(116*fgY-16).*gy;
ly == Yr<==0.008856;
Ll==903.3*Yr. *ly;
flY==(7.787*Yr+16/116).*ly;
L == Lg +Ll;
fY == fgY +flY;
gx == Xr>0.008856;
fgX==gx. *(Xr.I\(1/3));
Ix ==Xr<==0.008856;
flX==(7.787*Xr+ 16/116).*lx;
fX == fgX+flX;
gz == Zr>0.008856;
fgZ==gz. *(Zr.I\(1/3));
lz == Zr<==0.008856;
flZ==(7 .787*Zr+16/116).*lz;
fZ == flZ+fgZ;
a==500*(fX-fY);
b==200*(fY-fZ);
L == reshape (L, [h w]);
a == reshape (a, [h w]);
b == reshape (b, [h w]);
%Function to convert RGB color space to XYZ
function [x, y, z]==rgb2xyz(rgb)
73
r==double(rgb(:, 1));
g==double(rgb(:,2));
b==double(rgb(:,3));
x== O.4124*r+O.3576*g+O.1805*b;
y == O.2126*r+O.7152*g+O.0722*b;
z == O.0193*r+O.1192*g+O.9505*b;
2. Program for extracting WT-based textural features from wavelet decomposition
Images
%Creating a file for writing data
feat=fopen ('WT-Rspace.txt','w');
pref=='OBIC';
path==[pwd '\'];
tic;
for filenum==1:186
file==strcat(pref,num2str(filenum),' .tif);
I == (imread([path file],'tif));
% R color band ofthe RGB color space
xl==I(:,:,l);
% G color band ofthe RGB color space
x2==I(:, :,2);
% B color band ofthe RGB color space
x3==I(:,:,3);
% CIE L *a *b * color space calculation by calling the function program
[L, a, b] == rgb2Lab (I);
% Wavelet decomposition using Haar wavelet in R,G and B color bands, each band
calculated separately
[C,S]==wayedec2(xl,5,'haar');
[C,S]==wavedec2(x2,5,'haar');
[C,S]==wavedec2(x3,5,'haar');
%Wavelet decomposition using Haar wavelet in L*,a* and b* color bands, each band
calculated separately
[C,S]==wavedec2(L,5,'haar');
[C,S]==wavedec2(a,5,'haar');
[C,S]==wavedec2(b,5,'haar');
74
%Wavelet decomposition using Daubechies wavelet in R,G and B color bands, each
band calculated separately
[C,S}==wavedec2(xl,5, 'db2');
[C,S]==wavedec2(x2,5,'db2');
[C,S]==wavedec2(x3,5,'db2');
%Wavelet decomposition using Daubechies wavelet in L *, a* and b* color bands,
each band calculated separately
[C,S]==wavedec2(L,5,'db2');
[C,S]==wavedec2(a,5,'db2');
[C,S]==wavedec2(b,5,'db2');
%Wavelet decompositionfor contrast stretched images in R,G,and B color bands
//Contrast stretching operation
j==imadjust(xI, stretchlim(xI ),[]);
j==imadj ust(x2, stretchlim(x2),[]);
j=imadj ust(x3, stretchlim(x3), []);
j==doubleQ);
[C,S]==wavedec2Q,5,'haar');
[C,S]==wavedec2Q,5, 'db2');
% Extracting wavelet coefficients from all levels
cA2 == appcoef2(C,S,'haar',5);
[cII5,cV5,cD5] == detcoef2('all',C,S,5);
[cH4,cV4,cD4] == detcoef2('all',C,S,4);
[cH3,cV3,cD3] == detcoef2('all',C,S,3);
[cH2,cV2,cD2] == detcoef2('all',C,S,2);
[cHI,cVI,cDI] == detcoef2('all',C,S,I);
%Reconstructing approximation coefficients from 1 to 5
A5 == wrcoef2('a',C"S 'haar'"5)-
A4 == wrcoef2('a',C"S 'haar'"4)-
A3 == wrcoef2('a',C"S 'haar'"3)-
A2 == wrcoef2('a',C"S 'haar'"2)-
Al == wrcoef2('a',C"S 'haar'"1)-
% Reconstructing horizontal coefficients from 1 to 5
H5 == wrcoef2('h',C,S,'haar',5);
H4 == wrcoef2('h',C,S,'haar',4);
H3 == wrcoef2('h',C,S,'haar',3);
H2 == wrcoef2('h',C,S,'haar',2);
HI == wrcoef2('h',C,S,'haar',I);
75
EA4== (1/X)*(sum(A4/'2));
EA3== (1/X)*(sum(A3/'2));
EA2== (1/X)*(sum(A2.A2));
EAl== (l/X)*(sum(Al.A2));
EH5== (1/X)*(sum(H5.A2));
EH4== (1/X)*(sum(H4.A2));
EH3== (1/X)*(sum(H3.A2));
EH2== (1/X)*(sum(H2.A2));
EHI== (1/X)*(sum(Hl.A2));
EV5== (1/X)*(sum(V5.A2));
EV4== (1/X)*(sum(V4/'2));
EV3== (1/X)*(sum(V3.A2));
EV2== (1/X)*(sum(V2.A2));
EVl== (1/X)*(sum(Vl.A2));
ED5== (1/X)*(sum(D5/'2));
ED4== (1/X)*(sum(D4.A2));
ED3== (1/X)*(sum(D3.A2));
ED2== (1/X)*(sum(D2.A2));
EDl== (1/X)*(sum(Dl.A2));
EL5== (1/X)*(sum(L5.A2));
EL4== (1/X)*(sum(L4.A2));
EL3== (1/X)*(sum(L3.A2));
EL2== (1/X)*(sum(L2.A2));
ELl== (1/X)*(sum(LI.A2));
%Wedge calculation at each level using Sobel operator
rL5 == reshape(L5, [480 640]);
rL4 == reshape(L4, [480 640]);
rL3 == reshape(L3, [480 640]);
rL2 == reshape(L2, [480 640]);
rLl == reshape(Ll, [480 640]);
[BWLR5,thLR5] == EDGE(rL5,'sobel');
WED5 == sum(sum(BWLR5));
[BWLR4,thLR4] = EDGE(rL4,'sobel');
WED4 == sum(sum(BWLR4));
[BWLR3,thLR3] = EDGE(rL3,'sobel');
WED3 == sum(sum(BWLR3));
[BWLR2,thLR2] == EDGE(rL2,'sobel');
WED2 == sum(sum(BWLR2);
[BWLRl,thLRl] == EDGE(rLl,'sobel');
WEDI = sum(sum(BWLRl));
77
%Calculation ofvariance
VarA5=var(A5);
VarA4=var(A4);
VarA3=var(A3);
VarA2=var(A2);
VarAl =var(Al);
VarH5=var(H5);
VarH4=var(H4);
VarH3=var(H3);
VarH2=var(H2);
VarH1=var(H1);
VarV5=var(V5);
VarV4=var(V4);
VarV3=var(V3);
VarV2=var(V2);
VarVl =var(Vl);
VarD5=var(D5);
VarD4=var(D4);
VarD3=var(D3);
VarD2=var(D2);
VarD1==var(D 1);
%Calculation ofskewness
SKA5=skewness(A5);
SKA4=skewness(A4);
SKA3==skewness(A3);
SKA2==skewness(A2);
SKAI==skewness(AI);
SKH5=skewness(H5);
SKH4==skewness(H4);
SKH3==skewness(H3);
SKH2==skewness(H2);
SKHI==skewness(HI);
SKY5==skewness(V5);
SKY4=skewness(V4);
SKV3==skewness(V3);
SKV2==skewness(V2);
SKVl=skewness(VI);
SKD5==skewness(D5);
78
SKD4=skewness(D4);
SKD3=skewness(D3);
SKD2=skewness(D2);
SKD1==skewness(D l);
%Calculation ofkurtosis
KA5==kurtosis(A5);
KA4==kurtosis(A4);
KA3==kurtosis(A3);
KA2==kurtosis(A2);
KAl==kurtosis(Al);
KH5=kurtosis(H5);
KH4==kurtosis(H4);
KH3==kurtosis(H3);
KH2==kurtosis(H2);
KHl==kurtosis(Hl);
KV5==kurtosis(V5);
KV4==kurtosis(V4);
KV3==kurtosis(V3);
KV2==kurtosis(V2);
KVl==kurtosis(Vl);
KD5==kurtosis(D5);
KD4==kurtosis(D4);
KD3==kurtosis(D3);
KD2==kurtosis(D2);
KD1==kurtosis(D 1);
% Spacing and tabs for writing data on the text file created by (jopen JJ
fprintf(feat,'%d\t%9 .2f\t%9.2f\t%9.2f\t%9.2f\t%9.2f\t%9.2f\t%9.2f\to/09.2f\t%9.2f\t%
9.2f\1%9.2f\t%9.2f\t%9.2£\t%9.2f\t%9.2f\t%9.2f\t%9.2f\t%9.2f\t%9.2f\t%9.2f\t%9.2f
\to/09.2£\t%9.2f\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%
9.2f\t%9.2f\1%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2f\t%9.2f
\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\1%9.2f\t%9.2f\t%9.2f\t%9.2£\t%
9.2f\t%9.2£\t%9.2f\t%9.2f\1%9.2£\1%9.2£\1%9.2£\1%9.2f\1%9.2£\1%9.2£\1%9.2£\t%9.2f
\t%9.2£\.t%9.2f\t%9.2f\t%9.2f\t%9.2f\t%9.2£\t%9.2£\t%9.2f\n',filenuffi,EA5,EA4,EA3
,EA2,EA1,EH5,EH4,EH3,EH2,EH1,EV5,EV4,EV3,EV2,EV1,ED5,ED4,ED3,ED2,E
Dl,EL5,EL4,EL3,EL2,ELl,WED5,WED4,WED3,WED2,WEDl,VarA5,VarA4,Var
A3,VarA2,VarAl,VarH5,VarH4,VarH3,VarH2,VarHl,VarV5,VarV4,VarV3,VarV2,
VarVl,VarD5,VarD4,VarD3,VarD2,VarDI,SKA5,SKA4,SKA3,SKA2,SKAl,SKH5,
SKH4,SKH3,SKH2,SKHl ,SKD5,SKD4,SKD3,SKD2,SKD1,SKV5,SKV4,SKV3,SK
V2,SKVl,KA5,KA4,KA3,KA2,KAl,KH5,KH4,KH3,KH2,KHI,KV5,KV4,KV3,KV
2,KV1,KD5,KD4,KD3,KD2,KD1);
79
filenum
end
fclose('all')
toc;
3. Function program for calculating GLDH-based features (Jeyamkondan et aI.,
2001)
function texture == gldh (Image, teta)
I == double (Image);
[h, w] == size (I);
Irv == reshape (I, h*w, 1);
len == length (Irv);
switch (teta)
%Calculating textural features at angle of0° and distance of1 pixel
case 0,
srv (1: len-480) == Irv (1: len-480) + Irv (481 : len);
srv (len-479: len) == Irv (len-479: len);
drv (1: len-480) == Irv (1: len-480) - lrv (481 : len);
drv (len-479: len) == Irv (len-479: len);
%Calculating textural features at angle of45° and distance of1 pixel
case 45,
srv (1: len - 481) == Irv (1: len - 481) + Irv (482 : len);
srv (len - 480: len) == Irv (len - 480: len);
drY (1: len - 481) == Irv (1: len - 481) - lrv (482: len);
drY (len.- 480: len) == Irv (len - 480: len);
%Calculating texturalfeatures at angle 0/90° and distance ofI pixel
case 90,
srv (1: len-I) == Irv (1 :len-I) + lrv (2:len);
srv (len) == Irv(len);
drY (1: len-I) == lrv (1 :len-I) - Irv (2:len);
80
dry (len) == Irv(len);
%Calculating textural features at angle of1350 and distance of1 pixel
case 135,
srv(1) == Irv (1);
srv (2: len- 480) == Irv (2: len-480) + Irv (481 : len-I);
srv (len-479: len) == Irv (len-479: len);
drv( 1) == Irv (1);
dry (2: len- 480) == Irv (2: len-480) - Irv (481 : len-I);
dry (len-479: len) == Irv (len-479: len);
end
sbin == 0:510;
hsrv == hist (srv, sbin);
dbin == -255:255;
hdrv == hist (drv , dbin);
psrv == hsrv/len;
pdrv == hdrv/len;
Gmean == mean(Irv);
sbin == sbin+1;
aI == sum(psrv. *(sbin-2*Gmean):'\2);
bI == sum(pdrv.*(dbin.1\2));
%Calculating correlation
corr == 0.5* (aI-b I);
texture(4) == corr;
%Calculating contrast
contrast == b1;
texture(5) == contrast;
%Calculating entropy
entropy == - sum (psrv.*log10(psrv+1)) - sum (pdrv.* log10(pdrv+1));
texture(6) == entropy* 100;
%Calculating homogeneity
homogeneity == sum ((1.11 +dbin.1\2). *pdrv);
texture(7) = homogeneity;
%Calculating cluster shade
clshade == sum (((sbin - 2*Gmean).1\3). *psrv);
texture(8) == clshade/l000;
81
%Calculating cluster prominence
clprom == sum (((sbin - 2*Gmean)/'4).*psrv);
texture(9) == clprom/1000000;
4. Program for extracting GLDH-based features from wavelet decomposition images
(Jeyamkondan et aI., 2001)
%Creating a file for writing data
wavegdh== fopen('GLDH-Rspace.txt','w');
pref=='OB1C';
path==[pwd '\'];
tic;
for filenum==1:186
file==strcat(pref,num2str(filenum),'. tir);
I == (imread([path file],'tif));
%R color band ofthe RGB color space
x1==1(:,:,1);
%G color band ofthe RGB color space
x2==I(:,:,2);
%B color band o/the RGB color space
x3==1( :,:,3);
%CIE L*a *b * color space calculation by calling the function program
[L, a, b] == rgb2Lab (I);
%Wavelet decomposition using Haar wavelet in R, G, and B color bands, each band
calculated separately
[C,S]==wavedec2(x1,5,'haar');
[C,S]==wavedec2(x2,5,'haar');
[C,S]==wavedec2(x3,5,'haar');
%Wavelet decomposition using Haar wavelet in R, G, and B color bands, each band
calcula~edseparately
[C,S]==wavedec2(L,5,'haar');
[C,S]==wavedec2(a,5,'haar');
[C,S]==wavedec2(b,5,'haar');
%Wavelet decomposition using Daubechies wavelet in R, G, and B color bands, each
band calculated separately
[C,S]==wavedec2(x1,5,'db2');
82
[C,S]==wavedec2(x2,5,'db2');
[C,S]==wavedec2(x3,5,'db2');
%Wavelet decomposition using Daubechies wavelet in R, G, and B color bands, each
band calculated separately
[C,S]==wavedec2(L,5,'db2');
[C,S]==wavedec2(a,5,'db2');
[C,S]==wavedec2(b,5,'db2');
%Wavelet decompositionfor contrast stretched images in R,G,and B color bands
//Contrast stretching operation
j==imadjust(xl, stretchlim(xi ),[]);
j==imadjust(x2, stretchlim(x2),[]);
j==imadjust(x3, stretchlim(x3),[]);
j==doubleG);
[C,S]==wavedec2G,5,'haar');
[C,S]==wavedec2G,5,'db2');
% Extracting wavelet coefficients from all levels
cA2 == appcoef2(C,S,'db2',5);
[cH5,cV5,cD5] == detcoef2('all',C,S,5);
[cH4,cV4,cD4] == detcoef2('all',C,S,4);
[cH3,cV3,cD3] == detcoef2('all',C,S,3);
[cH2,cV2,cD2] == detcoef2('all',C,S,2);
[cHI,cVI,cDI] == detcoef2('all',C,S,I);
%Reconstructing approximation coefficients from I to 5
A5 == wrcoef2('a',C"S 'db2'"5)-
A4 == wrcoef2('a',C"S 'db2'"4)-
A3 == wrcoef2('a',C"S 'db2'"3)-
A2 == wrcoef2('a',C"S 'db2'"2)-
Al == wrcoef2('a',C"S 'db2'"1)-
% Reconstructing horizontal coefficients from I to 5
H5 == wrcoef2('h',C"S 'db2'"5)-
H4 == wrcoef2('h',C,S,'db2',4);
H3 == wrcoef2('h',C,S,'db2',3);
H2 == wrcoef2('h',C,S,'db2',2);
HI == wrcoef2('h',C,S,'db2',1);
%Reconstructing diagonal coefficients from 1 to 5
D5 == wrcoef2('d',C,S,'db2',5);
D4 == wrcoef2('d',C,S,'db2',4);
D3 == wrcoef2('d',C,S,'db2',3);
83
D2 == wrcoef2('d',C"S 'db2'"2)"
D1 == wrcoef2('d',C"S 'db2'"I)"
%Reconstructing vertical coefficients from 1 to 5
V5 = wrcoef2('v',C"S 'db2'"5)"
V4 = wrcoef2('v',C"S 'db2'"4)"
V3 = wrcoef2('v',C"S 'db2'"3)"
V2 == wrcoef2('v',C"S 'db2'"2)"
VI == wrcoef2('v',C"S 'db2'"I)"
% Reshaping the approximation levels from 1 to 5
A5 == reshape (A5, [prod(size(A2)) 1]);
A4 == reshape (A4, [prod(size(A2)) 1]);
A3 = reshape (A3, [prod(size(A2)) 1]);
A2 == reshape (A2, [prod(size(A2)) 1]);
Al == reshape (AI, [prod(size(A2)) 1]);
% Reshaping the horizontal levels from 1 to 5
H5 == reshape (H5, [prod(size(H2)) 1]);
H4 == reshape (H4, [prod(size(H2)) 1]);
H3 == reshape (H3, [prod(size(H2)) 1]);
H2 = reshape (H2, [prod(size(H2)) 1]);
HI == reshape (H1, [prod(size(H1)) 1]);
% Reshaping the diagonal levels from 1 to 5
D5 = reshape (D5, [prod(size(D2)) 1]);
D4 == reshape (D4, [prod(size(D2)) 1]);
D3 == reshape (D3, [prod(size(D2)) 1]);
D2 == reshape (D2, [prod(size(D2)) 1]);
D1 == reshape (D1, [prod(size(D1)) 1]);
% Reshaping the vertical levels from 1 to 5
V5 == reshape (V5, [prod(size(V2)) 1]);
V4 == reshape (V4, [prod(size(V2)) 1]);
V3 = reshape (V3, [prod(size(V2)) 1]);
V2 = reshape (V2, [prod(size(V2)) 1]);
VI == reshape (V1, [prod(size(V 1)) 1]);
%Calculating GLDH-basedfeatures for the approximation level) for 0°
texA5 == gdlh(A5,O);
texA4 = gldh(A4,O);
texA3 = gldh(A3,O);
texA2 == gldh(A2,O);
texAl == gldh(AI,O);
84
%Calculating GLDH-basedfeatures for the horizontal level, for 0°
texH5 == gldh(H5,O);
texH4 == gldh(H4,O);
texH3 == gldh(H3,O);
texH2 == gldh(H2,O);
texHl == gldh(Hl,O);
%Calculating GLDH-basedfeatures for the vertical level, for 0°
texV5 == gldh(V5,O);
texV4 == gldh(V4,O);
texV3 == gldh(V3,O);
texV2 == gldh(V2,O);
texVl == gldh(Vl,O);
%Calculating GLDH-basedfeatures for the diagonal level, for 0°
texD5 == gldh(D5,O);
texD4 == gldh(D4,O);
texD3 == gldh(D3,O);
texD2 == gldh(D2,O);
texDl == gldh(DI,O);
% Spacing and tabs for writing data on the text file created by (Jopen"
fprintf(wavegdh,'%d\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\to/09.2£\t%9.2£\t%9.2£\t%9.
2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t
%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\to/09.
2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t
%9.2£\t%9.2£\t%9.2£\t%9.2f\t%9.2£\t%9.2£\t%9.2f\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.
2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t
%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.
2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t
%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2f\t%9.2£\t%9.2£\t%9.2f\t%9.2£\t%9.2£\t%9.2£\t%9.
2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\to/09.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t
%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\t%9.2£\n',filenum,texA5(1),
texA5(2), texA5(3), texA5(4), texA5(5), texA5(6), texA4(1), texA4(2), texA4(3),
texA4(4), texA4(5), texA4(6), texA3(1), texA3(2), texA3(3), texA3(4), texA3(5),
texA3(6), texA2(I), texA2(2), texA2(3), texA2(4), texA2(5), texA2(6), texAl(l),
texAl(2), texAl(3), texAl(4), texAl(5), texAI(6), texH5(1), texH5(2), texH5(3),
texH5(4), texH5(5), texH5(6), texH4(1), texH4(2), texH4(3), texH4(4), texH4(5),
texH4(6), texH3(1), texH3(2), texH3(3), texH3(4), texH3(5), texH3(6), texH2(1),
texH2(2), texH2(3), texH2(4), texH2(5), texH2(6), texHI(I), texHI(2), texHI(3),
texHI(4), texHI(5), texHI(6), texV5(1), texV5(2), texV5(3), texV5(4), texV5(5),
texV5(6), texV4(1), texV4(2), texV4(3), texV4(4), texV4(5), texV4(6), texV3(1),
texV3(2), texV3(3), texV3(4), texV3(5), texV3(6), texV2(1), texV2(2), texV2(3),
texV2(4), texV2(5), texV2(6), texVl(I), texVl(2), texVI(3), texVI(4), texVI(5),
texVI(6), texD5(1), texD5(2), texD5(3), texD5(4), texD5(5), texD5(6), texD4(1),
85
texD4(2), texD4(3), texD4(4), texD4(5), texD4(6), texD3(1), texD3(2), texD3(3),
texD3(4), texD3(5), texD3(6), texD2(1), texD2(2), texD2(3), texD2(4) texA2(5)
texA2(6), texV1(1), texV1(2), texV1(3), texV1(4), texV1(5) texVl(6));
filenum
end
fclose('all')
toe;
5. Program for predicting WBS scores using BPNN with Bayesian regularization
p=[ WT- or GLDH-based textural features ];
tc==[ WBS scores obtainedfrom Department ofAnimal Science Meat Laboratory]';
t == tc(l ,:);
% Normalizing the data
[pn,meanp,stdp,tn,meant,stdt] = prestd(p,t);
% Principal component analysis
[ptrans,transMat] = prepca(pn,O.Ol);
[R,Q] = size(ptrans);
%Test Set
iitst == 2:4:Q;
%Training Set
iitr == [1 :4:Q 3:4:Q 4:4:Q];
test.P == ptrans(:,iitst); test.T == tn(:,iitst);
ptr == ptrans(:,iitr); ttr == tn(:,iitr);
%Creating a feed-forward BPNN with bayesian regularization training. One output
neuron, with linear transfer function and 10 and 20 neurons in the hidden layer, with
logsigmoid and tansigmoid transferfunctions
net == newff(minmax(ptr),[lO 20 l],{'logsig' 'tansig' 'purelin'},'trainbr');
net.trainParam.show == 10;
net.trainParam.epochs = 50;
%Training the network
[net,tr]=train(net,ptr,ttr);
antr = sim(net,ptrans(:,iitr));
86
% Un-normalizing the output which had been normalized by PRESTD.
atr == poststd(antr,meant,stdt);
%Post-processing the network training set by performing a linear regression between
one element ofthe network response and the corresponding target
[m,b,r] == postreg(atr,t(:,iitr));
antst == sim(net,ptrans(:,iitst));
atst == poststd(antst,meant,stdt);
(m,b,r] == postreg(atst,t(:,iitst));
87
VITA ~
Anand Lakshmikanth
Candidate for the Degree of
Master of Science
Thesis: PREDICTING TENDERNESS OF BEEF USING MACHINE VISION
Major Field: Biosystems Engineering
Biographical:
Personal: Born in Karur, Tamilnadu, India on May 10th 1974, the son of
P.R. Lakshmikanthan and S. Visalakshi.
Education: Graduated from D.T.E.A. Senior Secondary School, New Delhi,
India in May 1992; received Bachelor of Engineering Degree in
Agriculture from College of Agricultural Engineering, Tamil Nadu
Agricultural University (TNAU), Kumulur, Tamilnadu, India in June
1998. Completed the requirements for Master of Science degree with a
major in Biosystems Engineering at Oklahoma State University in
December 2002.
Experience: Employed by Oklahoma State University as Graduate Research
Assistant in the Department of Biosystems and Agricultural Engineering
from July 2000 to present.
Professional Memberships: American Society of Agricultural Engineers.