PARAFAC CLASSIFICATION OF LAMB CARCASS SOFT

TISSUES IN COMPUTER TOMOGRAPHY (CT) IMAGE STACKS

Jørgen Kongsro

Animalia – Norwegian Meat Research Centre, P.O. Box 396 Økern, N-0513 Oslo, Norway

Keywords: Lamb carcass, Tissue, PARAFAC, Multi-Way Analysis, Computer Tomography, Classification, Image,

Stacks.

Abstract: Computer Tomography is shown to be an efficient and cost-effective tool for classification and

segmentation of soft tissues in animal carcasses. By using 15 fixed anatomical sites based on vertebra

columns, 120 lamb carcasses were CT scanned in Norway during autumn of 2005. Frequency distributions

of CT values (HU [-200,200]) of soft tissues from each image were obtained. This yielded a 3-way data set

(120 samples * 400 CT values * 15 anatomical sites). The classification of the soft tissues was done by

multi way Parallel Factor Analysis (PARAFAC), which resulted in 3 components or soft tissues classified

from the images; fat, marbled and lean muscle tissue.

1 INTRODUCTION

Computer Tomography is based on the attenuation

of X-ray through a body. There is high correlation

between the density of the body or body

components, and the X-ray attenuation measured.

This relationship is used to estimate the body

composition, volume or weight of a biological

sample. The attenuation of X-rays is visualized by

reconstruction of 360

rotation of X-ray tube in a CT

tomogram or CT image. Image data from Computer

Tomography can be orientated in different ways.

Single slice tomograms can be handled like 2-way

(rows*columns) data arrays. Stacks of tomograms

from 3D samples are often orientated as multi-way

data arrays (rows*columns*stack). Combining CT

data with other types of data, like MRI etc., can also

yield multi-modal data arrays which can be handled

either in a multi-dimensional fashion or be unfolded

prior to analysis. Unfolding of multi-way data may

sometimes lead to poor estimation and

interpretability of variation between the different

stacks or batches in a multi-way data array.

There are two primary ways to perform

classification. Supervised classification (1), where

classes are known in advance (a priori), and un-

supervised classification (2), where classes are not

known in advance. For classification of soft tissues

from CT images of lamb carcasses, it can be difficult

to obtain solid a priori knowledge or reference data

of classes. Traditionally, reference data has been

collected by using destructive dissection. This

procedure is both expensive and not very accurate

due to differences operators / butchers (Nissen et al.

2006). The accuracy of classification of tissues may

be influenced the accuracy of the reference method

used, i.e. for calibration purposes or detection of

false negatives or positives. By using non-supervised

classification, validation techniques can ensure that

the model works for new data and finds the optimal

or true number of classes in the model. The non-

supervised approach will not be affected by

reference or a priori error.

Parallel Factor Analysis (PARAFAC) is one

method designed to analyze and decompose multi-

way data, and was introduced by Harshman in 1971

for Psychometrics. The PARAFAC method can be

used as a non-supervised classification tool to

classify soft tissues in CT image stacks sampled

from whole lamb carcasses.

The main purpose of this study is to apply

PARAFAC decomposition of multi-way CT image

data array as a classification tool of different lamb

carcass soft tissues.

2 MATERIALS & METHODS

2.1 Sampled Animals

120 lambs from a single Norwegian abattoir were

sampled according to an experimental design from

242

Kongsro J. (2008).

PARAFAC CLASSIFICATION OF LAMB CARCASS SOFT TISSUES IN COMPUTER TOMOGRAPHY (CT) IMAGE STACKS.

In Proceedings of the First International Conference on Bio-inspired Systems and Signal Processing, pages 242-248

DOI: 10.5220/0001062202420248

 SciTePress

August to September in 2005. The design was set up

to cover the variation in all levels of fatness in the

carcasses, and the principle of over-sampling at the

extremes was applied (Engel et al. 2003): The

carcasses were sampled in three groups; low,

intermediate and high level of fatness. Selection was

made using fatness score from the EUROP carcass

grading system for lamb in Norway. Low fatness

equals –2 standard deviations (st.dev.) and below

mean value. High fatness + 2 std and above mean

value (Kirton et al., 1995). Intermediate between

high and low (table 1). 40% of the samples were

selected for each of the groups low and high fatness

and 20% selected for intermediate fatness (Tab. 1),

yielding a 40-20-40 grouping of the designed

samples. In addition, two subsets of equal size (50-

50) were constructed for validation by split-half-

analysis.

Table 1: Sampling and experimental design.

n = 120 Low Mid High

% n % n % n

Design

40 48 20 24 40 48

Subset 1

38 23 20 12 42 25

Subset 2

38 23 20 12 42 25

1 40-20-40 design for sampling

2 Data subsets for Split-half analysis

2.2 Computer Tomography

2.2.1 Settings

The lambs were scanned at the Norwegian

University of Life Sciences using a Siemens

Somaton Emotion CT Scanner. Two persons were

involved in the scanning of lamb carcasses: one

operation the scanner, and the other preparing and

entering the carcasses into the machine. The

capacity of this procedure was approximately 8-10

carcasses per hour. The protocol for CT scanning is

described in Table 2.

Table 2: CT protocol used for scanning of lamb carcasses.

Topogram Sequence

100 mA

130 kV

Slice width: 2.0 mm

Length: 1024 mm

Tube position: AP

Direction: Caudiocranial

Kernel: T80s (sharp)

Window: 256-64

170 mAs

130 kV

Scan time: 0.8s

Slice width: 3 mm

Number of scans: 15

Direction: Caudiocranial

Kernel: B50M

Window: 100-50

Field of view (FOV): 400

2.2.2 Anatomical Sites

Figure 1: Scanning sites CT, lamb carcass.

Fifteen (15) anatomical scanning sites spanning the

entire carcass were selected from a topogram using

spine vertebras as fixing points (Fig. 1). A topogram

is a survey picture produced by the CT-scanner. It is

obtained by fixation of the X-ray tube in the upper

position and moving the object at constant speed

through the gantry. Each colour of the lines

represents anatomical sections of the carcass

(cervical, thoracic, lumbar, sacral and caudal). The

anatomical sites were selected to span the entire

variation of the carcass, but the number of images

was limited due to capacity. High X-ray dose (170

mAs) was selected to increase the resolution of the

tomograms. The anatomical sites collected from the

mid-section of the carcass, were selected using

literature reference sites for grading of lamb

carcasses (Berg et al. 1997;Bruwer et al.

1987;Chandraratne et al. 2006;Chandraratne,

Kulasiri, & Samarasinghe 2007;Cunha et al.

2004;Jones et al. 1992;Kirton et al. 1995). In

addition to literature reference sites, additional sites

on the leg and shoulder were added using spine

vertebras as fixing points.

2.2.3 Import and Pre-processing of Images

The CT scanner generated images in DICOM

format, which is a common medical image format.

The images were imported into MATLAB using the

Image Processing Toolbox routine dicomread.

Figure 2: Raw image, Binary image for arithmetic

extraction and processed image after extraction.

In the raw CT images, the couch material (non-

carcass component) was visible (Fig. 2). This was

removed using arithmetic extraction in MATLAB.

The extraction was performed using image array

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STACKS

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multiplication, subtracting the couch material from

the raw image using a binary image (Fig. 2)

containing zeros and ones to remove the couch area

(zeros) of the image. The lamb area of the image

was now extracted and ready for further analysis

(fig.3).

2.2.4 Frequency Distribution of Pixel Values

(HU)

Figure 3: 15 pre-processed CT images from all scanning

sites, from neck (1) to knee joint of leg (15).

A frequency distribution of the signal intensities

(pixels) was generated for each anatomical site

(Dobrowolski et al., 2004) (Fig. 5) from each of the

pre-processed images (Fig. 5) using the frequency of

Hounsfield Units [HU] in the interval [-200,200].

HU is related to density of biological tissues, where

0 is regarded as the HU of pure water. The interval

of 400 HU is expected to cover the soft animal

tissues (fat and muscle) in the CT images

(Dobrowolski et al. 2004;Romvari et al. 2002). Each

image was represented as a frequency distribution 2-

way array [1 x 400]. For each sample, 15 images

were generated, generating a 3-way array [1 x 400 x

15], giving a [120 x 400 x 15] data array for the

entire samples.

2.3 PARAFAC

PARAFAC is a generalization of Principal

Component Analysis (PCA) to higher order arrays

(Bro 1997). Decomposition of the data array is made

into triads or trilinear components (Fig. 4), but

instead of one score vector and one loading vector as

in bilinear PCA, each component consist of one

score vector and two loading vectors (trilinear).

PARAFAC is regarded as a “strong” multi-way

method utilizing the multi-mode structure for

modelling without unfolding, and providing other

attractive features (Huang et al. 2003).

Figure 4: PARAFAC decomposition of a 3-way data

array.

In this study, PARAFAC is used to decompose

the landscapes of the frequency distributions and

anatomical positions into a number of trilinear

components (f).

∑

ijkkfjfifijk

ecbaX

The element x

ijk

represent the landscape of

histogram spectra and anatomical positions of the

lamb carcass sample i, frequency distribution j,

anatomical position k. The landscapes are

decomposed into sample scores a

, frequency

distribution loadings b

and anatomical position

loadings c

for each factor f or PARAFAC

component f. The residuals e

ijk

, contains variation

not explained by the model.

The PARAFAC components will be estimates of

the CT histogram signals from the individual

chemical components (fat & lean) if the data are

approximately low-rank trilinear and when the

correct number of components is used. If the optimal

case is found, the scores for each of the components

represent the relative content of carcass soft tissues.

The number of components will represent the non-

supervised classes of soft tissues suggested by the

validated PARAFAC model.

PARAFAC models of CT image histogram

landscapes were estimated with 1 to 4 components.

The models were mean-centred since this has proven

to yield the best result and interpretation of the

figures. Since each component is expected to

represent a single peaked frequency distribution (one

local maxima) of a soft tissue, unimodality

constraints was imposed on the model (Johansen et

al. 2006). When calibrating PARAFAC models of

CT images against a dissection reference,

unimodality constraints seemed to yield the most

accurate results (Johansen, Egelandsdal, Røe, Kvaal,

& Aastveit 2006).

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The correct number of components was selected

using core consistency and split-half analysis (Bro

1997) as validation tools. The split was done using a

50-50 split of the actual designed (table 1) samples,

estimating independent PARAFAC models for both

split data subsets. Due to the uniqueness of the

PARAFAC model, the same loadings will be

obtained from different samples if the samples

reflect the same CT histogram variables, when the

correct number of components is chosen and enough

data are available in each of the split data subsets

(Andersen & Bro 2003).

All the models were constructed using the

PLS_Toolbox 4.0, August 10, 2006, Copyright

Eigenvector Research, Inc. 1995-2006 for

MATLAB, the Image Processing Toolbox V5.3

(R2006b) for MATLAB and MATLAB 7.3.0.267

MathWorks Inc.

3 RESULTS & DISCUSSION

3.1 Landscapes

Figure 5: 3D CT histogram landscape of one sample, raw

data.

From the landscape, a distinctive frequency

distribution that appears between different

anatomical sites is revealed (Fig. 5). There are two

peaks identified as the shoulder site and the leg

anatomical site. These sites are the “muscular” parts

of the carcass (leg muscles), and therefore provide a

high response or histogram intensity (number of

pixels). There are two ridges in the landscapes, one

larger than the other. The large ridge is identified as

the lean tissue, and the small ridge as the fat tissue

part. When comparing very fat animals with very

lean animals, the fat ridge is almost absent in the

very lean animals. These observations will be further

investigated in the PARAFAC analysis.

3.2 PARAFAC

Table 3: PARAFAC diagnostics. Full model (n=120). # of

components, explained variance, core consistency, number

of iterations and computation time (s).

# Expl. Var.

(%)

Core cons. # iter Time

(s)

1 50.06 100 5 6

2 66.36 95 11 12

3 73.18 78 18 20

4 76.80 0 23 28

The results from the PARAFAC models are shown

in Table 3. Three components seem to yield a

consistent model, with relatively low number of

iterations and computation time.

In order to validate the appropriate number of

components in the model, the results from the split-

half analysis is shown in Figure 6. The figure shows

the frequency distribution loadings for 1 to 4

components, were subset 1 has solid lines, and

subset two dashed lines. Due to the uniqueness of

the PARAFAC model, the same loadings should be

obtained if the samples reflect the same CT

histogram and anatomical site pattern when the

optimal number of components is chosen. The solid

and dashed lines seem to be correlated for the 1-, 2-

and 3-component models, while for the 4-component

model; the solid and dashed lines do not correlate.

Thus, the model seems to be valid with 3

components.

The PARAFAC decomposition of the CT

histogram landscapes is shown in Figure 7, were the

raw landscape in Figure 5 is decomposed into three

PARAFAC components. The 1st component seems

to model the fat tissue in the frequency distribution,

and the 2nd seem to model muscle tissue. The 3

component seems to model very lean muscle tissue.

Component 2 and 3 seem to be two types of muscle

tissue, “marbled” or muscle tissue with higher fat

content (# 2) and lean muscle tissue (# 3)

For practical purposes, the PARAFAC models

yields a better understanding of the uniqueness and

nature of the CT value (HU) frequency distribution.

From the images in Figure 8, the PARAFAC

loadings were applied to a test image from a lamb

carcass belly. Loadings above a manually set

baseline (0.02) were selected to ease interpretation

of the test images. The first image from left

represents the total area of soft tissue. The 2

image

PARAFAC CLASSIFICATION OF LAMB CARCASS SOFT TISSUES IN COMPUTER TOMOGRAPHY (CT) IMAGE

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Figure 6: Validation of PARAFAC components (split-half analysis). 1 to 4 component PARAFAC models. 1 –and 2 –

component model (top), 3- and 4- component model (bottom).

Figure 7: PARAFAC decomposition of a 3D CT frequency distribution. 3 components or classes identified. # 1 represent fat

tissue, # 2 muscle tissue with marbling fat and the 3

lean muscle tissue.

-100

100

Anatomy

Comp.1

-100

100

Anatomy

Comp.2

-100

100

Anatomy

Comp.3

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Figure 8; PARAFAC CT value frequency loadings > 0.02 applied on CT image from belly. From left, soft tissue HU= [-

200, 200], # 1, # 2, # 3.

represents component 1, the 3

component 2 and 4

(right) component 3. When inspecting the images

visually, # 1 represent fat tissue, # 2 muscle tissue

with marbling fat and the 3

lean muscle tissue.

PARAFAC yields a consistent decomposition of the

3D frequency distribution of the CT images, and

selected 3 unique soft tissue components

representing fat, and two types of muscle tissue.

4 CONCLUSIONS

This paper presents modelling and decomposition of

multi-way array CT image data, using PARAFAC as

a non-supervised classification tool for different

lamb carcass soft tissues. Multi-way modelling

applying PARAFAC did yield sensible interpretation

of the 3D CT value frequency distribution. Three

components or classes of soft tissues were extracted

from the model; fat, marbled and lean muscle.

ACKNOWLEDGEMENTS

This study was sponsored by grant 162188 of the

Research Council of Norway, as part of a Ph.D.

study program. I am grateful for the assistance from

Prof. Rasmus Bro at the Faculty of Life Sciences,

University of Copenhagen.

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