A COMPARISON OF WAVELET-BASED AND RIDGELET-

BASED TEXTURE CLASSIFICATION OF TISSUES IN

COMPUTED TOMOGRAPHY

Lindsay Semler and Lucia Dettori

Intelligent Multimedia Processing Laboratory

School of Computer Scienve, Telecommunications and Information Systems

DePaul University, Chicago IL, 60604, USA

Keywords: Multi-Resolution Analysis, Texture Classification, Wavelet, Ridgelet, Computed Tomography.

Abstract: The research presented in this article is aimed at developing an automated imaging system for classification

of tissues in medical images obtained from Computed Tomography (CT) scans. The article focuses on using

multi-resolution texture analysis, specifically: the Haar wavelet, Daubechies wavelet, Coiflet wavelet, and

the ridgelet. The algorithm consists of two steps: automatic extraction of the most discriminative texture

features of regions of interest and creation of a classifier that automatically identifies the various tissues.

The classification step is implemented using a cross-validation Classification and Regression Tree approach.

A comparison of wavelet-based and ridgelet-based algorithms is presented. Tests on a large set of chest and

abdomen CT images indicate that, among the three wavelet-based algorithms, the one using texture features

derived from the Haar wavelet transform clearly outperforms the one based on Daubechies and Coiflet

transform. The tests also show that the ridgelet-based algorithm is significantly more effective and that

texture features based on the ridgelet transform are better suited for texture classification in CT medical

images.

1 INTRODUCTION

The research presented in this article is part of an

ongoing project (Xu et al. 2005), (Channin et al.

2004), and (Semler, Dettori, & Furst 2005) aimed at

developing an automated imaging system for

classification of tissues in medical images obtained

by Computed Tomography (CT) scans.

Classification of human organs in CT scans using

shape or grey level information is particularly

challenging due to the changing shape of organs in a

stack of slices in 3D medical images and the grey

level intensity overlap in soft tissues. However,

healthy organs are expected to have a consistent

texture within tissues across multiple slices. This

research focuses on using multi-resolution texture

analysis for the classification of tissues from normal

chest and abdomen CT scans. The approach consists

of two steps: extraction of the most discriminative

texture features of regions of interest and creation of

a classifier that automatically identifies the various

tissues. Four forms of multi-resolution analysis were

carried on and texture features vectors were created

from image transformations based on: the Haar

wavelet, the Daubechies wavelet, the Coiflet

wavelet, and the ridgelet. The classification step is

implemented through a decision tree classifier based

on the cross-validation Classification and Regression

Tree (C&RT) approach. Multi-resolution analysis

has been successfully used in image processing, and

a number of applications to texture classification

have been proposed over the past few years. Several

studies have investigated the discriminating power

of wavelet-based features applied to various

domains, examples can be found in (Dara & Watsuji

2003) and (Mulcahy 1997). Recently, the finite

ridgelet transform has emerged as a new multi-

resolution analysis tool. Applications of ridgelet

transforms to image contrast enhancement and

image denoising have been developed in recent

years as in (Do, & Vetterli 2003), however, to the

authors’ knowledge, applications to texture

classification have only been investigated in the

context of natural images (LeBorgne & O’Connor

2005).

Texture is a commonly used feature in the analysis

and interpretation of images. It can be characterized

285

Semler L. and Dettori L. (2006).

A COMPARISON OF WAVELET-BASED AND RIDGELET- BASED TEXTURE CLASSIFICATION OF TISSUES IN COMPUTED TOMOGRAPHY.

In Proceedings of the First International Conference on Computer Vision Theory and Applications, pages 285-289

DOI: 10.5220/0001365702850289

Copyright

c

SciTePress

by a set of local statistical properties of the pixel

grey level intensity. Statistical, structural, or spectral

techniques commonly used are: wavelets, run-length

statistics, spectral measures, fractal dimensions,

statistical moments, and co-occurrence matrices.

The discrete wavelet transform decomposes the

image into several directional details obtaining low-

pass bands that capture horizontal, vertical and

diagonal activity. First and second order statistics of

the wavelet detail coefficients provide texture

descriptors that can discriminate contrasting

intensity properties spatially distributed throughout

the image, according to various levels of resolution.

Wavelets have been an area of research in many

texture classification applications and have been

useful in capturing texture information and edge

detection in natural images

(Li, Jun 2003), such as

detecting the vertical outline of a skyscraper.

However, they are not able to capture enough

directional information in noisy images, such as

medical CT scans.

A better approach to texture classification for this

type of images is to apply a ridgelet transform

instead of a Wavelet transform. Ridgelets, like

wavelets, capture directional information of an

image, however, they are not limited to vertical,

horizontal, and diagonal directions. Structural

information derived from the ridgelet transform of

an image is based on multiple radial directions in the

frequency domain. For ridgelets, first order statistics

can be calculated on the directional detail

coefficients, providing texture descriptors that can

be used in the classification of texture. Our tests

confirm that the multi-directional capabilities of the

ridgelet transform provide better texture information

and prove to be more effective in the texture

classification in medical images.

The article is organized as follows. Section 2

describes the data set, the wavelet and ridgelet

transforms and the texture feature extraction process.

The classification algorithm is detailed in Section 3.

Tests and a comparison of wavelet-based and

ridgelet-based features are presented in Section 4.

2 TEXTURE FEATURES

The texture classification algorithm proposed in this

article consists of four main steps: segmentation of

regions of interest (organs), application of the

discrete wavelet or ridgelet transform, extraction of

texture features, and creation of a classifier. In this

article, we analyze and compare texture

classification techniques based on four different

multi-resolution approaches: Haar (H) wavelet,

Daubechies 4 (D4) wavelet, Coiflet (C6) wavelet,

and the ridgelet.

A wavelet is a mathematical function that filters a

signal or an image with a series of averaging and

differencing calculations see for example (Mulcahy

1997). Wavelets are typically used in image

decomposition and compression. Wavelets can be

calculated according to various levels of resolution

(or blurring) depending on how many levels of

averages are calculated. They are sensitive to the

spatial distribution of grey level pixels, but are also

able to differentiate and preserve details at various

scales or resolutions.

The ridgelet transform is an application of a multi-

resolution wavelet to a radon transform. A radon

transform is able to provide directional information

in the frequency domain. Thus, ridgelets capture

several directions, in addition to the horizontal,

vertical and diagonal offered by the wavelet. The

ridgelet gives rotation invariant structural

information on multiple directions and scales.

2.1 The Data Set

The texture classification algorithms were tested on

3D data extracted from two normal chest and

abdomen CT studies from Northwestern Memorial

Hospital. The data consisted of 340 2D DICOM

consecutives slices, each slice being 512 x 512 and

having 12-bit grey level resolution. Using an Active

Contour Models (“Snake”) algorithm, five organs

were segmented from the initial data: heart, liver,

spleen, kidney, and backbone (Xu et al. 2005). The

segmentation process generated 140 Backbone

slices, 52 Heart, 58 Liver, 54 Kidney, and 40 Spleen.

Both wavelets and ridgelets are extremely

sensitive to contrast in the grey level intensity,

therefore, in order to use wavelet-based or ridgelet-

based texture description it was necessary to

eliminate all background pixels to avoid mistaking

the edge between the artificial background and the

organ as a texture feature. Each slice was therefore

further cropped, and only square sub-images fully

contained in the interior of the segmented area were

generated. These images were of sizes 31 x 31 (for

ridgelets) or 32 x 32 (for wavelets), resulting in

2,091 slices of “pure” single-organ tissue (363

Backbone, 446 Heart, 506 Liver, 411 Kidney, 364

Spleen). These images were cropped to the

respective size because of the requirements of an

image of size 2

n

for wavelets and a prime image size

for ridgelets.

VISAPP 2006 - IMAGE ANALYSIS

286

2.2 Feature Extraction

Once the medical images have been segmented, the

wavelet and ridgelet discrete transforms are applied.

Several texture features are then extracted from the

wavelet and ridgelet coefficients generated by these

transforms. First, the three different families of

wavelets were investigated to determine which

would yield a higher discriminating power. Haar,

Daubechies and Coiflet wavelet filters were applied

to each of the images, using two levels of resolution.

At each resolution level, three detail coefficient

matrices were calculated capturing the vertical,

horizontal and diagonal structures of the image.

The following first order statistics were

calculated on each of the directional matrices: Mean

and Standard Deviation. Also calculated from these

matrices were 4-directional co-occurrence matrices

on which the following second order statistics were

calculated: Energy, Entropy, Contrast,

Homogeneity Sum-mean, Variance, Maximum

Probability, Inverse Difference Moment, and Cluster

Tendency (Haralick, Shanmugame, & Dinstein

1973). This generated a 264-element texture

descriptor vector per image. To avoid problems of

overfitting for the decision trees the resulting feature

vector was reduced to 22 features (using only two

levels of resolution and averaging over wavelet

details and co-occurrence directions). Further details

on feature vector reduction and more in-depth

analysis of the various wavelet-based texture

features are provided in (Semler, Dettori, & Furst

2005).

The Finite Ridgelet Transform as presented in

(Do & Vetterli 2003), was also applied. This was

computed by: first calculating a discrete radon

transform, and then applying a one-dimensional

wavelet transform. The radon transform was

computed by: first calculating the 2-dimensional fast

Fourier transform of the image, and then applying a

1-dimensional inverse Fourier transform on each of

the 32 radial directions of the radon projection. A

one-dimensional Haar wavelet was applied to each

of the radial directions, for two levels of resolution.

The following texture descriptors were then

calculated for each radial direction and resolution

level of the wavelet details: mean, standard

deviation, energy and entropy. Entropy texture

descriptors were determined to yield the highest

discriminating power; further details are presented in

(Semler, Dettori & Kerr 2006). Several different

combinations of resolution levels were also

investigated, and two levels of resolution were

determined best for both ridgelets and wavelets. The

numbers of features extracted were limited since

each descriptor is calculated over two resolution

levels and for 32 directions, yielding 64 descriptors.

Although the ridgelet-based features contain

more descriptors, it should not be assumed they

would perform better than the wavelet-based

features because of the increase in number of

descriptors. In (Semler, Dettori, & Furst 2005), it

was found that a wavelet-based feature vector of 33

descriptors outperformed another same-family

wavelet-based feature vector of 99 descriptors.

3 TEXTURE CLASSIFICATION

The classification step was carried out using a

decision tree classifier based on the Classification

and Regression Tree (C&RT) approach (Channin et

al. 2004). A decision tree predicts the class of an

object (organ) from values of predictor variables

(texture descriptors). The most relevant texture

descriptors are found for each specific organ, and

based on those selected descriptors, a set of decision

rules are generated. These set of rules are then used

for the classification of the each region. Using the

C&RT cross-validation approach, each tree’s

parameter was optimized, including depth of tree,

number of parent nodes, and number of child nodes.

To evaluate the performance of each classifier,

specificity, sensitivity, precision, and accuracy rates

were calculated from each of the misclassification

matrices.

A misclassification matrix is a table that lists each

organ and its true positives, true negatives, false

positives and false negatives. The number of true

positives is the number of organs that are correctly

classified as that organ. The number of true

negatives is the number of other organs that are

correctly classified as other organs. The number of

false positives is the number of organs that are

incorrectly classified as that organ. The number of

false negatives is the number of organs that are

incorrectly classified as other organ. From the

misclassification matrix specificity, sensitivity,

precision, and accuracy statistics were computed.

Table 1: Measures of classification performance.

Measure Definition

Sensitivity True Positive / Total Positive

Specificity True Negative / Total Negatives

Precision True Positive / (True Positive + False Positives)

Accuracy (True Positives + True Negatives) / Total Sample

A COMPARISON OF WAVELET-BASED AND RIDGELET-BASED TEXTURE CLASSIFICATION OF TISSUES IN

COMPUTED TOMOGRAPHY

287

Specificity measures the accuracy among

positive instances, and is calculated by dividing the

true negatives by the number of all other organ

slices. Sensitivity measures the accuracy among

negative instances, and is calculated by dividing the

number of true positives by the total number of that

specific organ slices. Precision measures show how

consistent the results can be reproduced. Accuracy

reflects the overall correctness of the classifier, and

is calculated by adding the true positives and

negatives together and dividing by the entire number

of organ slices.

4 WAVELET - RIDGELET

COMPARISON

Tables 2-5 in the Appendix show a comparison of

accuracy, precision, specificity, and sensitivity

results, for each tissue of interest for the three

wavelet-based texture features and the ridgelet-based

texture features respectively. Within all the

wavelets, the Haar wavelet outperformed all others

for most organs and performance measures. The

only exception is the backbone, for which the

Daubechies and Coiflet wavelets produce slightly

better results. The performance for the Haar-based

descriptors in all other organs was significantly

higher, thus indicating that these descriptors yield

the highest discriminating power among the

wavelet-based features.

The results also show that the ridgelet-based

texture features outperform all wavelet-based

descriptors. Accuracy rates for Wavelet-based

texture descriptors range between 85 - 93%, while

ridgelet-based accuracy rates are in the 91 - 97%

range. Precision rates for the wavelets are between

55 - 91%, compared to 73 - 93% for ridgelets.

Specificity rates for the wavelets are in the 82-97%

range, while specificity for the ridgelet descriptors is

in the 92-98% range. Furthermore, sensitivity rates

for the wavelets are in the 35-87% range, whereas

ridgelets are between 72-94%. The lower bound of

the sensitivity range for wavelets is due to the poor

performance of those descriptors (especially Coiflets

and Daubechies) for Heart and Spleen. The texture

of the images for these two organs is quite similar

and the classifier often mistakes the two organs for

one another. Further investigation is needed to

determine the underlying cause for the poor

performance of the Heart and Spleen.

Overall, the ridgelet-based descriptors have

significantly higher performance measures, with

accuracy rates approximately four percent higher

than any other feature set for all individual organs.

This was expected due to the fact that the ridgelet

transform is able to capture multi-directional

features, as opposed to the wavelet transform which

focuses mainly on horizontal, vertical, and diagonal

features, which are not dominant in medical CT scan

images. One of the limitations of using ridgelet-

based descriptors is the fact that ridgelets are most

effective in detecting linear radial structures, which

are not the main component of medical images. A

recent extension of ridgelets is the curvelet

transform. Curvelets have been proven to be

particularly effective at detecting image activity

along curves instead of radial directions (Starck

Donoho & Candes 1999). We are currently

investigating the use of curvelet-based texture

descriptors and we expect this to further improve the

ability of our classifier to successfully classify each

tissue sample.

REFERENCES

Xu, D., Lee, J., Raicu, D.S., Furst, J.D., & Channin, D.

(2005). Texture Classification of Normal Tissues in

Computed Tomography. The 2005 Annual Meeting of

the Society for Computer Applications in Radiology.

Channin, D., Raicu, D.S., Furst, J.D., Xu, D.H., Lilly, L.,

& Limpsangsri, C. (2004). Classification of Tissues in

Computed Tomography using Decision Trees. Poster

and Demo. The 90

th

Scientific Assembly and Annual

Meeting of Radiology Society of North America.

Semler, L., Dettori, L., & Furst, J. (2005). Wavelet-Based

Texture Classification of Tissues in Computed

Tomography. Proceedings of the 18th IEEE

International Symposium on Computer-Based Medical

Systems, 265-270.

Do, M.N., & Vetterli, M. (2003) The Finite Ridgelet

Transform for Image Representation. IEEE

Transactions on Image Processing, 12, 16 - 28.

LeBorgne, H.L., & O’Connor, N. (2005). Natural Scene

Classification and Retrieval Using Ridgelet-based

Image Signatures. Advanced Concepts for Intelligent

Vision Systems, 20-23.

Starck, J.L., Donoho, D.L., & Candes, E.J. (1999).

Astronomical Image Representation by the Curvelet

Transform. Astronomy &Astrophysics, 398, 785-800.

Semler, L., Dettori, L., & Kerr, B. (2006). Ridgelet-Based

Texture Classification in Computed Tomography,

submitted to IEEE Computer Society Conference on

Computer Vision and Pattern Recognition.

Dara, B & Watsuji, N. (2003). Using Wavelets for Texture

Classification. IJCI Proceedings of International

Conference on Signal Processing, ISN 1304-2386.

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Mulcahy, C. (1997). Image Compression Using the Haar

Wavelet Transform. Spelman Science & Math

Journal, 1, 22-31.

Li, Jun. (2003). A Wavelet Approach to Edge Detection,

Master of Science thesis, Sam Houston State

University. Huntsville, Texas.

Do, M., & Vetterli, M. (2003). Image Denoising Using

Orthonormal Finite Ridgelet Transform. Proceedings

of SPIE: Wavelet Applications in Signal and Image

Processing, 4119, 831-842.

Haralick, R. M., Shanmugam, D., & Dinstein, I. (1973).

Texture Features for Image Classification. IEEE

Transactions on Systems, Man, and Cybernetics, 3, 6,

610 – 621.

APPENDIX

Table 2: Wavelet-Ridgelet accuracy rates comparison.

Accuracy

Feature Set Backbone Heart Liver Kidney Spleen Average

Haar 93.7 85.0 88.6 92.8 89.5 89.9

Daubechies 93.6 84.0 88.0 83.6 88.2 87.5

Coiflets 93.1 85.3 88.3 85.8 88.6 88.2

Ridgelet 97.3 93.6 92.7 92.7 91.7 93.6

Table 3: Wavelet-Ridgelet precision rates comparison.

Precision

Feature Set Backbone Heart Liver Kidney Spleen Average

Haar 82.6 67.0 69.9 82.6 69.7 74.4

Daubechies 91.6 57.4 55.7 64.9 64.3 66.8

Coiflets 90.7 58.9 56.7 70.6 70.8 69.5

Ridgelet 93.5 90.8 79.4 88.5 72.9 85.0

Table 4: Wavelet-Ridgelet specificity rates comparison.

Specificity

Feature Set Backbone Heart Liver Kidney Spleen Average

Haar 96.1 92.1 91.4 94.4 94.3 93.7

Daubechies 97.3 91.8 92.0 82.9 96.2 92.0

Coiflets 96.8 89.4 92.2 87.4 97.6 92.7

Ridgelet 98.7 97.9 92.3 97.67 93.4 96.0

Table 5: Wavelet-Ridgelet sensitivity rates comparison.

Sensitivity

Feature Set Backbone Heart Liver Kidney Spleen Average

Haar 82.6 59.0 77.7 87.3 65.5 74.4

Daubechies 83.5 49.1 63.2 85.4 40.2 64.2

Coiflets 85.9 67.1 64.3 81.6 35.2 66.8

Ridgelet 90.9 77.8 94.2 72.5 83.8 83.8

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