Texture description and segmentation through fractal geometry

Automatic identification of angiogenesis in double stained images of liver tissue

BACKGROUND

To grow beyond certain size and reach oxygen and other essential nutrients, solid tumors trigger angiogenesis (neovascularization) by secreting various growth factors. Based on this fact, several researches proposed that density of newly formed vessels correlate with tumor malignancy. Vessel density is known as a true prognostic indicator for several types of cancer. However, automated quantification of angiogenesis is still in its primitive stage, and deserves more intelligent methods by taking advantages accruing from novel computer algorithms.

RESULTS

The newly introduced characteristics of subimages performed well in identification of region-of-angiogenesis. The proposed technique was tested on 522 samples collected from two high-resolution tissues. Having 0.90 overall f-measure, the results obtained with Support Vector Machines show significant agreement between automated framework and manual assessment of microvessels.

CONCLUSION

This study introduces a new framework to identify angiogenesis to measure microvessel density (MVD) in digitalized images of liver cancer tissues. The objective is to recognize all subimages having new vessel formations. In addition to region based characteristics, a set of morphological features are proposed to differentiate positive and negative incidences.

Automatic classification for pathological prostate images based on fractal analysis

Accurate grading for prostatic carcinoma in pathological images is important to prognosis and treatment planning. Since human grading is always time-consuming and subjective, this paper presents a computer-aided system to automatically grade pathological images according to Gleason grading system which is the most widespread method for histological grading of prostate tissues. We proposed two feature extraction methods based on fractal dimension to analyze variations of intensity and texture complexity in regions of interest. Each image can be classified into an appropriate grade by using Bayesian, k-NN, and support vector machine (SVM) classifiers, respectively. Leave-one-out and k-fold cross-validation procedures were used to estimate the correct classification rates (CCR). Experimental results show that 91.2%, 93.7%, and 93.7% CCR can be achieved by Bayesian, k-NN, and SVM classifiers, respectively, for a set of 205 pathological prostate images. If our fractal-based feature set is optimized by the sequential floating forward selection method, the CCR can be promoted up to 94.6%, 94.2%, and 94.6%, respectively, using each of the above three classifiers. Experimental results also show that our feature set is better than the feature sets extracted from multiwavelets, Gabor filters, and gray-level co-occurrence matrix methods because it has a much smaller size and still keeps the most powerful discriminating capability in grading prostate images.

Characterization and classification of tumor lesions using computerized fractal-based texture analysis and support vector machines in digital mammograms

OBJECTIVE

This paper presents a detailed study of fractal-based methods for texture characterization of mammographic mass lesions and architectural distortion. The purpose of this study is to explore the use of fractal and lacunarity analysis for the characterization and classification of both tumor lesions and normal breast parenchyma in mammography.

MATERIALS AND METHODS

We conducted comparative evaluations of five popular fractal dimension estimation methods for the characterization of the texture of mass lesions and architectural distortion. We applied the concept of lacunarity to the description of the spatial distribution of the pixel intensities in mammographic images. These methods were tested with a set of 57 breast masses and 60 normal breast parenchyma (dataset1), and with another set of 19 architectural distortions and 41 normal breast parenchyma (dataset2). Support vector machines (SVM) were used as a pattern classification method for tumor classification.

RESULTS

Experimental results showed that the fractal dimension of region of interest (ROIs) depicting mass lesions and architectural distortion was statistically significantly lower than that of normal breast parenchyma for all five methods. Receiver operating characteristic (ROC) analysis showed that fractional Brownian motion (FBM) method generated the highest area under ROC curve (A ( z ) = 0.839 for dataset1, 0.828 for dataset2, respectively) among five methods for both datasets. Lacunarity analysis showed that the ROIs depicting mass lesions and architectural distortion had higher lacunarities than those of ROIs depicting normal breast parenchyma. The combination of FBM fractal dimension and lacunarity yielded the highest A ( z ) value (0.903 and 0.875, respectively) than those based on single feature alone for both given datasets. The application of the SVM improved the performance of the fractal-based features in differentiating tumor lesions from normal breast parenchyma by generating higher A ( z ) value.

CONCLUSION

FBM texture model is the most appropriate model for characterizing mammographic images due to self-affinity assumption of the method being a better approximation. Lacunarity is an effective counterpart measure of the fractal dimension in texture feature extraction in mammographic images. The classification results obtained in this work suggest that the SVM is an effective method with great potential for classification in mammographic image analysis.

Fractal analysis of surface electromyography signals: a novel power spectrum-based method

This paper presents a novel power spectrum-based method for fractal analysis of surface electromyography signals. This method, named the bi-phase power spectrum method, provides a bi-phase power-law which represents a multi-scale statistically self-affine signal. This form of statistical self-affinity provides an accurate approximation for stochastic signals originating from a strong non-linear combination of a number of similar distributions, such as surface electromyography signals which are formed by the summation of a number of single muscle fiber action potentials. This power-law is characterized by a set of spectral indicators, which are related to distributional and geometrical characteristics of the electromyography signal's interference pattern. These novel spectral indicators are capable of sensing the effects of motor units' recruitment and shape separately by exploiting the geometry of the interference pattern. The bi-phase power spectrum method is compared to geometrical techniques and the 1/f(alpha) approach for fractal analysis of electromyography signals. The extracted indicators using the bi-phase power spectrum method are evaluated in the context of force and joint angle and the results of a human study are presented. Results demonstrate that the bi-phase power spectrum method provides reliable information, consisting of components capable of sensing force and joint angle effects separately, which could be used as complementary information for confounded conventional measures.

Texture analysis of aggressive and nonaggressive lung tumor CE CT images

This paper presents the potential for fractal analysis of time sequence contrast-enhanced (CE) computed tomography (CT) images to differentiate between aggressive and nonaggressive malignant lung tumors (i.e., high and low metabolic tumors). The aim is to enhance CT tumor staging prediction accuracy through identifying malignant aggressiveness of lung tumors. As branching of blood vessels can be considered a fractal process, the research examines vascularized tumor regions that exhibit strong fractal characteristics. The analysis is performed after injecting 15 patients with a contrast agent and transforming at least 11 time sequence CE CT images from each patient to the fractal dimension and determining corresponding lacunarity. The fractal texture features were averaged over the tumor region and quantitative classification showed up to 83.3% accuracy in distinction between advanced (aggressive) and early-stage (nonaggressive) malignant tumors. Also, it showed strong correlation with corresponding lung tumor stage and standardized tumor uptake value of fluorodeoxyglucose as determined by positron emission tomography. These results indicate that fractal analysis of time sequence CE CT images of malignant lung tumors could provide additional information about likely tumor aggression that could potentially impact on clinical management decisions in choosing the appropriate treatment procedure.

Texture analysis of multiple sclerosis: a comparative study

The difficulty of using magnetic resonance imaging (MRI) to support early diagnosis of multiple sclerosis (MS) stems from the subtle pathological changes in the central nervous system (CNS). In this study, texture analysis was performed on MR images of MS patients and normal controls and a combined set of texture features were explored in order to better discriminate tissues between MS lesions, normal appearing white matter (NAWM) and normal white matter (NWM). Features were extracted from gradient matrix, run-length (RL) matrix, gray level co-occurrence matrix (GLCM), autoregressive (AR) model and wavelet analysis, and were selected based on greatest difference between different tissue types. The results of the combined set of texture features were compared with our previous results of GLCM-based features alone. The results of this study demonstrated that (1) with the combined set of texture features, classification was perfect (100%) between MS lesions and NAWM (or NWM), less successful (88.89%) among the three tissue types and worst (58.33%) between NAWM and NWM; (2) compared with GLCM-based features, the combined set of texture features were better at discriminating MS lesions and NWM, equally good at discriminating MS lesions and NAWM and at all three tissue types, but less effective in classification between NAWM and NWM. This study suggested that texture analysis with the combined set of texture features may be equally good or more advantageous than the commonly used GLCM-based features alone in discriminating MS lesions and NWM/NAWM and in supporting early diagnosis of MS.

Fractal feature extraction of marrow cell images

An algorithm based on the cell image center of gravity and its scaleless range (as scale-invariant) is proposed to estimate the fractal dimension of the marrow cell images. Since the texture of a color image contains not only certain statistical similarity on the structure but also the color distributions, two color parameters are extracted from the color images of marrow cells for the fractal dimension calculation. An efficient approach is described for the discrimination between different marrow cells with the combination of the fractal dimension.

Fractal Analysis of the Maternal Surface of the Placenta: Preliminary Report

AIMS

The objective of this study was to determine whether the maternal surface of the placenta is fractal, and whether the mean fractal dimension differs according to the gestational age and clinically or pathologically different conditions.

METHODS

Using digitized images of the maternal surface of 75 placentas, fractal dimensions were measured with a fractal analysis software.

RESULTS

The mean fractal dimension of the maternal surface of the placentas significantly exceeded the topological dimension of a surface (= 2). This means that the morphological pattern of the maternal surface fulfills the mathematical definition of fractal structures. Among the three different groups of gestational age, the mean fractal dimension in 22-29 weeks was significantly lower than that in 30-36 and 37-41 weeks (p = 0.022 and 0.014, respectively). Although not significantly different (p = 0.149), in 30-36 weeks the mean fractal dimension of the placentas complicated by pregnancy-induced hypertension (PIH) was greater than that without PIH.

CONCLUSION

Fractal geometry, a vocabulary of irregular shapes, can be useful for describing quantitatively the architecture of the maternal surface of the placenta and become a useful tool for analyzing physiological and pathological placental formation mathematically.

Volumetric texture segmentation by discriminant feature selection and multiresolution classification

In this paper, a multiresolution volumetric texture segmentation (M-VTS) algorithm is presented. The method extracts textural measurements from the Fourier domain of the data via subband filtering using an orientation pyramid (Wilson and Spann, 1988). A novel Bhattacharyya space, based on the Bhattacharyya distance, is proposed for selecting the most discriminant measurements and producing a compact feature space. An oct tree is built of the multivariate features space and a chosen level at a lower spatial resolution is first classified. The classified voxel labels are then projected to lower levels of the tree where a boundary refinement procedure is performed with a three-dimensional (3-D) equivalent of butterfly filters. The algorithm was tested with 3-D artificial data and three magnetic resonance imaging sets of human knees with encouraging results. The regions segmented from the knees correspond to anatomical structures that can be used as a starting point for other measurements such as cartilage extraction.

Use of color texture in determining the nature of melanocytic skin lesions—a qualitative and quantitative approach

Melanocytic nevi are recognized as precursors of melanoma. Aiding in early recognition of melanoma, we estimated color texture parameters, fractal dimension and lacunarity of melanoma and other melanocytic nevi. Digital images of the lesions were processed. Graphic three-dimensional pseudoelevation images of the lesions and surrounding skin were produced to identify irregularities in color texture within the lesions. Estimation of lacunarity and fractal dimension followed in order to produce a numerical estimate of the coarseness of color texture. Clinicians readily perceive the resulting "geographical" images. Irregularity in the anaglyph, which might veil malignancy, is effortlessly identified through these images, and therefore an early excision of a suspect lesion is indicated.

Self-similar random field models in discrete space

Self-similar random fields are of interest in various areas of image processing since they fit certain types of natural patterns and textures. Current treatments of self-similarity in continuous two-dimensional (2-D) space use a definition that is a direct extension of the one-dimensional definition, which requires invariance of the statistics of a random process to time scaling. Current discrete-space 2-D approaches do not consider scaling, but, instead, are based on ad hoc formulations, such as digitizing continuous random fields. In this paper, we show that the current statistical self-similarity definition in continuous space is restrictive and provide an alternative, more general definition. We also provide a formalism for discrete-space statistical self-similarity that relies on a new scaling operator for discrete images. Within the new framework, it is possible to synthesize a wider class of discrete-space self-similar random fields and texture images.

Fractal analysis of surface growth patterns in endometrioid endometrial adenocarcinoma

OBJECTIVE

A fractal is a shape made of parts similar to the whole in some way. The objective of this study was to determine whether surface growth patterns in endometrioid endometrial adenocarcinoma are fractal, and the mean fractal dimension differs according to histologic grades and depth of myometrial invasion.

METHODS

After the images of photographs of 120 resected uteri with endometrial cancers were digitized, the fractal dimensions of surface of tumors were measured using a fractal analysis software.

RESULTS

The mean fractal dimensions of surface growth patterns in G1, G2, and G3 adenocarcinoma were 2.318, 2.303, and 2.383, respectively. These values were significantly greater than the topological dimension of a surface (= 2). The value was significantly higher in G3 than in G2 (p = 0.03). And although not statistically significant, the value of G3 was greater than G1 (p = 0.10) and than (G1 and G2) group (p = 0.06). No significant difference nor tendency was found in the fractal dimension of the surface of the tumor according to depth of invasion.

CONCLUSION

This study shows that the surface of endometrioid endometrial adenocarcinoma has a fractal structure, and the mean fractal dimension may differ according to histologic grades. Our report proposes a new way of looking at endometrial cancer pathology. We believe that fractal geometry gives insights into tumor morphology and becomes a useful tool for analyzing complex and irregular tumor growth patterns mathematically.

Ultrasonic liver tissues classification by fractal feature vector based on M-band wavelet transform

This paper describes the feasibility of selecting fractal feature vector based on M-band wavelet transform to classify ultrasonic liver images-normal liver, cirrhosis, and hepatoma. The proposed feature extraction algorithm is based on the spatial-frequency decomposition and fractal geometry. Various classification algorithms based on respective texture measurements and filter banks are presented and tested. Classifications for the three sets of ultrasonic liver images reveal that the fractal feature vector based on M-band wavelet transform is trustworthy. A hierarchical classifier, which is based on the proposed feature extraction algorithm is at least 96.7% accurate in the distinction between normal and abnormal liver images and is at least 93.6% accurate in the distinction between cirrhosis and hepatoma liver images. Additionally, the criterion for feature selection is specified and employed for performance comparisons herein.

Volumetric Texture Description and Discriminant Feature Selection for MRI

This paper considers the problem of classification of Magnetic Resonance Images using 2D and 3D texture measures. Joint statistics such as co-occurrence matrices are common for analysing texture in 2D since they are simple and effective to implement. However, the computational complexity can be prohibitive especially in 3D. In this work, we develop a texture classification strategy by a sub-band filtering technique that can be extended to 3D. We further propose a feature selection technique based on the Bhattacharyya distance measure that reduces the number of features required for the classification by selecting a set of discriminant features conditioned on a set training texture samples. We describe and illustrate the methodology by quantitatively analysing a series of images: 2D synthetic phantom, 2D natural textures, and MRI of human knees.

Fetal lung maturity analysis using ultrasound image features

This pilot study was carried out to find the feasibility of analyzing the maturity of the fetal lung using ultrasound images. Data were collected from normal pregnant women at intervals of two weeks from the gestation age of 24 to 38 weeks. Images were acquired at two centers located at different geographical locations. The total data acquired consisted of 750 images of immature and 250 images of mature class. A region of interest of 64 x 64 pixels was used for extracting the features. Various textural features were computed from the fetal lung and liver images. The ratios of fetal lung to liver feature values were investigated as possible indexes for classifying the images into those from mature (reduced pulmonary risk) and immature (possible pulmonary risk) lung. The features used are fractal dimension, lacunarity, and features derived from the histogram of the images. The following classifiers were used to classify the fetal lung images as belonging to mature or immature lung: nearest neighbor, k-nearest neighbor, modified k-nearest neighbor, multilayer perceptron, radial basis function network, and support vector machines. The classification accuracy obtained for the testing set ranges from 73% to 96%.

Texture feature coding method for classification of liver sonography

This paper introduces a new texture analysis method called texture feature coding method (TFCM) for classification of ultrasonic liver images. The TFCM transforms a gray-level image into a feature image in which each pixel is represented by a texture feature number (TFN) coded by TFCM. The TFNs obtained are used to generate a TFN histogram and a TFN co-occurrence matrix (CM), which produces texture feature descriptors for classification. Four conventional texture analysis methods that are gray-level CM, texture spectrum, statistical feature matrix and fractal dimension, are used also to classify liver sonography for comparison. The supervised maximum likelihood (ML) classifiers implemented by different type texture features are applied to discriminate ultrasonic liver images into three disease states that are normal liver, liver hepatitis and cirrhosis. The 30 liver sample images proven by needle biopsy are used to train the ML system that classify on a set of 90 test sample images. Experimental results show that the ML classifier together with TFCM texture features outperforms one with the four conventional methods with respect to classification accuracy.

A textural approach based on Gabor functions for texture edge detection in ultrasound images

Edge detection is an important, but difficult, step in quantitative ultrasound (US) image analysis. In this paper, we present a new textural approach for detecting a class of edges in US images; namely, the texture edges with a weak regional mean gray-level difference (RMGD) between adjacent regions. The proposed approach comprises a vision model-based texture edge detector using Gabor functions and a new texture-enhancement scheme. The experimental results on the synthetic edge images have shown that the performances of the four tested textural and nontextural edge detectors are about 20%-95% worse than that of the proposed approach. Moreover, the texture enhancement may improve the performance of the proposed texture edge detector by as much as 40%. The experiments on 20 clinical US images have shown that the proposed approach can find reasonable edges for real objects of interest with the performance of 0.4 +/- 0.08 in terms of the Pratt's figure.

An investigation into the feasibility of fetal lung maturity prediction using statistical textural features

Fetal lung and liver tissues were examined by ultrasound in 240 subjects during 24 to 38 weeks of gestational age in order to investigate the feasibility of predicting the maturity of the lung from the textural features of sonograms. A region of interest of 64 x 64 pixels is used for extracting textural features. Since the histological properties of the liver are claimed to remain constant with respect to gestational age, features obtained from the lung region are compared with those from liver. Though the mean values of some of the features show a specific trend with respect to gestation age, the variance is too high to guarantee definite prediction of the gestational age. Thus, we restricted our purview to an investigation into the feasibility of fetal lung maturity prediction using statistical textural features. Out of 64 features extracted, those features that are correlated with gestation age and less computationally intensive are selected. The results of our study show that the sonographic features hold some promise in determining whether the fetal lung is mature or immature.

The vocabulary and grammar of color patterns

We determine the basic categories and the hierarchy of rules used by humans in judging similarity and matching of color patterns. The categories are: (1) overall color; (2) directionality and orientation; (3) regularity and placement; (4) color purity; (5) complexity and heaviness. These categories form the pattern vocabulary which is governed by the grammar rules. Both the vocabulary and the grammar were obtained as a result of a subjective experiment. Experimental data were interpreted using multidimensional scaling techniques yielding the vocabulary and the hierarchical clustering analysis, yielding the grammar rules. Finally, we give a short overview of the existing techniques that can be used to extract and measure the elements of the vocabulary.

A simple unsupervised MRF model based image segmentation approach

A simple technique has been suggested to obtain optimal segmentation based on tonal and textural characteristics of an image using the Markov random field (MRF) model. The technique takes an initially over segmented image as well as the original image as its inputs and defines an MRF over the region adjacency graph (RAG) of the initially segmented regions. A tonal-region based segmentation technique due to Kartikeyan and Sarkar (1989) has been used for initial segmentation. The energy function has been defined over the first order cliques of the MRF. The essence of this approach is primarily based on quantitative values of the second order statistics, on region characteristics and consequently deciding upon the action of merging neighboring regions using the F-statistic. The effectiveness of our approach is demonstrated with wide variety of real life examples viz., indoor, outdoor and satellite and a comparison of its output with that of a previous work in the literature has been provided.

A pattern classification approach to characterizing solitary pulmonary nodules imaged on high resolution CT: preliminary results

The purpose of this research is to characterize solitary pulmonary nodules as benign or malignant based on quantitative measures extracted from high resolution CT (HRCT) images. High resolution CT images of 31 patients with solitary pulmonary nodules and definitive diagnoses were obtained. The diagnoses of these 31 cases (14 benign and 17 malignant) were determined from either radiologic follow-up or pathological specimens. Software tools were developed to perform the classification task. On the HRCT images, solitary nodules were identified using semiautomated contouring techniques. From the resulting contours, several quantitative measures were extracted related to each nodule's size, shape, attenuation, distribution of attenuation, and texture. A stepwise discriminant analysis was performed to determine which combination of measures were best able to discriminate between the benign and malignant nodules. A linear discriminant analysis was then performed using selected features to evaluate the ability of these features to predict the classification for each nodule. A jackknifed procedure was performed to provide a less biased estimate of the linear discriminator's performance. The preliminary discriminant analysis identified two different texture measures--correlation and difference entropy--as the top features in discriminating between benign and malignant nodules. The linear discriminant analysis using these features correctly classified 28/31 cases (90.3%) of the training set. A less biased estimate, using jackknifed training and testing, yielded the same results (90.3% correct). The preliminary results of this approach are very promising in characterizing solitary nodules using quantitative measures extracted from HRCT images. Future work involves including contrast enhancement and three-dimensional measures extracted from volumetric CT scans, as well as the use of several pattern classifiers.

Extended fractal analysis for texture classification and segmentation

The Hurst parameter for two-dimensional (2-D) fractional Brownian motion (fBm) provides a single number that completely characterizes isotropic textured surfaces whose roughness is scale-invariant. Extended self-similar (ESS) processes were previously introduced in order to provide a generalization of fBm. These new processes are described by a number of multiscale Hurst parameters. In contrast to the single Hurst parameter, the extended parameters are able to characterize a greater variety of natural textures where the roughness of these textures is not necessarily scale-invariant. In this work, we evaluate the effectiveness of multiscale Hurst parameters as features for texture classification and segmentation. For texture classification, the performance of the generalized Hurst features is compared to traditional Hurst and Gabor features. Our experiments show that classification accuracy for the generalized Hurst and Gabor features are comparable even though the generalized Hurst features lower the dimensionality by a factor of five. Next, the segmentation accuracy using generalized and standard Hurst features is evaluated on images of texture mosaics. For these experiments, the performance is evaluated with and without supplemental contrast and average grayscale features. Finally, we investigate the effectiveness of the Hurst features to segment real synthetic aperture radar (SAR) imagery.

An automatic diagnostic system for CT liver image classification

Computed tomography (CT) images have been widely used for liver disease diagnosis. Designing and developing computer-assisted image processing techniques to help doctors improve their diagnosis has received considerable interests over the past years. In this paper, a CT liver image diagnostic classification system is presented which will automatically find, extract the CT liver boundary and further classify liver diseases. The system comprises a detect-before-extract (DBE) system which automatically finds the liver boundary and a neural network liver classifier which uses specially designed feature descriptors to distinguish normal liver, two types of liver tumors, hepatoma and hemageoma. The DBE system applies the concept of the normalized fractional Brownian motion model to find an initial liver boundary and then uses a deformable contour model to precisely delineate the liver boundary. The neural network is included to classify liver tumors into hepatoma and hemageoma. It is implemented by a modified probabilistic neural network (PNN) [MPNN] in conjunction with feature descriptors which are generated by fractal feature information and the gray-level co-occurrence matrix. The proposed system was evaluated by 30 liver cases and shown to be efficient and very effective.

A two-component model of texture for analysis and synthesis

A model of natural texture based on a structural component that uses affine coordinate transformations and a stochastic residual component is presented. It is argued that the selection of an appropriate analysis scale can be formulated in terms of a tradeoff between the rate at which parameters are generated and the distortion resulting from the approximation by the structural component. An efficient algorithm for identifying the parameters of the structural model is described and its utility demonstrated on a number of synthetic and natural textures.

Wavelet image extension for analysis and classification of infarcted myocardial tissue

Some computer applications for tissue characterization in medicine and biology, such as analysis of the myocardium or cancer recognition, operate with tissue samples taken from very small areas of interest. In order to perform texture characterization in such an application, only a few texture operators can be employed: the operators should be insensitive to noise and image distortion and yet be reliable in order to estimate texture quality from the small number of image points available. In order to describe the quality of infarcted myocardial tissue, we propose a new wavelet-based approach for analysis and classification of texture samples with small dimensions. The main idea of this method is to decompose the given image with a filter bank derived from an orthonormal wavelet basis and to form an image approximation with higher resolution. Texture energy measures calculated at each output of the filter bank as well as energies of synthesized images are used as texture features in a classification procedure. We propose an unsupervised classification technique based on a modified statistical t-test. The method is tested with clinical data, and the classification results obtained are very promising. The performance of the new method is compared with the performance of several other transform-based methods. The new algorithm has advantages in classification of small and noisy input samples, and it represents a step toward structural analysis of weak textures.

Characterisation of structural changes in the arterial elastic matrix by a new fractal feature: directional fractal curve

A new fractal feature, the Directional Fractal Curve (DFC), defined over an arc of 180 and composed of 90 fractal dimensions determined at intervals of arc of 2, is developed to account for the anisotropic property of a fractal texture. The DFC algorithm is first applied to two images with different textural patterns, one without directional preference and one with a well-organised texture. The DFC of these images shows different patterns. The technique is then applied to quantify the structure of the elastic texture in the arterial wall where the elastic network was imaged by scanning electron microscopy following selective tissue digestion. The results suggest: (i) that images of the elastin matrix of the arterial wall exhibit fractal properties with directional preference, (ii) the DFC gives quantitative parameters which allow characterisation of structural changes in the elastin matrix of the arterial wall in terms of disorganisation and fragmentation of elastin fibres-conditions which are associated with medial degeneration due to normal ageing or presence of arterial disease.

A new approach for subset 2-D AR model identification for describing textures

This paper addresses the problem of identification of appropriate autoregressive (AR) components to describe textural regions of digital images by a general class of two-dimensional (2-D) AR models. In analogy with univariate time series, the proposed technique first selects a neighborhood set of 2-D lag variables corresponding to the significant multiple partial auto-correlation coefficients. A matrix is then suitably formed from these 2-D lag variables. Using singular value decomposition (SVD) and orthonormal with column pivoting factorization (QRcp) techniques, the prime information of this matrix corresponding to different pseudoranks is obtained. Schwarz's (1978) information criterion (SIG) is then used to obtain the optimum set of 2-D lag variables, which are the appropriate autoregressive components of the model for a given textural image. A four-class texture classification scheme is illustrated with such models and a comparison of the technique with the work of Chellappa and Chatterjee (1985) is provided.

Segmentation of Gabor-filtered textures using deterministic relaxation

A supervised texture segmentation scheme is proposed in this article. The texture features are extracted by filtering the given image using a filter bank consisting of a number of Gabor filters with different frequencies, resolutions, and orientations. The segmentation model consists of feature formation, partition, and competition processes. In the feature formation process, the texture features from the Gabor filter bank are modeled as a Gaussian distribution. The image partition is represented as a noncausal Markov random field (MRF) by means of the partition process. The competition process constrains the overall system to have a single label for each pixel. Using these three random processes, the a posteriori probability of each pixel label is expressed as a Gibbs distribution. The corresponding Gibbs energy function is implemented as a set of constraints on each pixel by using a neural network model based on Hopfield network. A deterministic relaxation strategy is used to evolve the minimum energy state of the network, corresponding to a maximum a posteriori (MAP) probability. This results in an optimal segmentation of the textured image. The performance of the scheme is demonstrated on a variety of images including images from remote sensing.