Texture Segmentation Using Separable and Non-Separable Wavelet Frames (Special Section on Digital Signal Processing)

In this paper, a new feature which is characterized by the extrema density of 2-D wavelet frames estimated at the output of the corresponding filter bank is proposed for texture segmentation. With and without feature selection, the discrimination ability of features based on pyramidal and treestructured decompositions are comparatively studied using the extrema density, energy, and entropy as features, respectively. These comparisons are demonstrated with separable and nonseparable wavelets. With the three-, four-, and five-category textured images from Brodatz album, it is observed that most performances with feature selection improve significantly than those without feature selection. In addition, the experimental results show that the extrema density-based measure performs best among the three types of features investigated. A MinMin method based on genetic algorithms, which is a novel approach with the spatial separation criterion (SPC) as the evaluation function is presented to evaluate the segmentation performance of each subset of selected features. In this work, the SPC is defined as the Euclidean distance within class divided by the Euclidean distance between classes in the spatial domain. It is shown that with feature selection the tree-structured wavelet decomposition based on non-separable wavelet frames has better performances than the tree-structured wavelet decomposition based on separable wavelet frames and pyramidal decomposition based on separable and non-separable wavelet frames in the experiments. Finally, we compare to the segmentation results evaluated with the templates of the textured images and verify the effectiveness of the proposed criterion. Moreover, it is proved that the discriminatory characteristics of features do spread over all subbands from the feature selection vector. key words: extrema density, wavelet frames, texture segmentation, feature selection, Min-Min method, genetic algorithms, spatial separation criterion (SPC)

[1]  Thomas Marill,et al.  On the effectiveness of receptors in recognition systems , 1963, IEEE Trans. Inf. Theory.

[2]  Josef Kittler,et al.  An analysis of the Max-Min approach to feature selection and ordering , 1993, Pattern Recognit. Lett..

[3]  Jan M. Van Campenhout,et al.  On the Possible Orderings in the Measurement Selection Problem , 1977, IEEE Transactions on Systems, Man, and Cybernetics.

[4]  Maria Petrou,et al.  Performance Evaluation of Texture Segmentation Algorithms based on Wavelets , 1996 .

[5]  Eero P. Simoncelli,et al.  Non-separable extensions of quadrature mirror filters to multiple dimensions , 1990, Proc. IEEE.

[6]  Kenneth A. De Jong,et al.  Genetic algorithms as a tool for feature selection in machine learning , 1992, Proceedings Fourth International Conference on Tools with Artificial Intelligence TAI '92.

[7]  M.,et al.  Statistical and Structural Approaches to Texture , 2022 .

[8]  C.-C. Jay Kuo,et al.  Texture analysis and classification with tree-structured wavelet transform , 1993, IEEE Trans. Image Process..

[9]  John S. Baras,et al.  Properties of the multiscale maxima and zero-crossings representations , 1993, IEEE Trans. Signal Process..

[10]  Michael Unser,et al.  Texture classification and segmentation using wavelet frames , 1995, IEEE Trans. Image Process..

[11]  Philippe Andrey,et al.  Unsupervised image segmentation using a distributed genetic algorithm , 1994, Pattern Recognit..

[12]  Keinosuke Fukunaga,et al.  A Branch and Bound Algorithm for Feature Subset Selection , 1977, IEEE Transactions on Computers.

[13]  Stéphane Mallat,et al.  Singularity detection and processing with wavelets , 1992, IEEE Trans. Inf. Theory.

[14]  Michal Haindl,et al.  Unsupervised Texture Segmentation , 1998, SSPR/SPR.

[15]  4 - Analyse multirésolution pour les images avec un facteur de résolution √2 , 1990 .

[16]  Anil K. Jain,et al.  Unsupervised texture segmentation using Gabor filters , 1990, 1990 IEEE International Conference on Systems, Man, and Cybernetics Conference Proceedings.

[17]  Jack Sklansky,et al.  A note on genetic algorithms for large-scale feature selection , 1989, Pattern Recognit. Lett..

[18]  Jelena Kovacevic,et al.  Nonseparable multidimensional perfect reconstruction filter banks and wavelet bases for Rn , 1992, IEEE Trans. Inf. Theory.

[19]  Josef Bigün,et al.  Unsupervised feature reduction in image segmentation by local transforms , 1993, Pattern Recognit. Lett..

[20]  Martin D. Levine,et al.  Geometric Primitive Extraction Using a Genetic Algorithm , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[21]  Wilson S. Geisler,et al.  Multichannel Texture Analysis Using Localized Spatial Filters , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[22]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[23]  Kenneth I. Laws,et al.  Rapid Texture Identification , 1980, Optics & Photonics.

[24]  Jian Fan,et al.  Texture Classification by Wavelet Packet Signatures , 1993, MVA.

[25]  Michel Barlaud,et al.  Pyramidal lattice vector quantization for multiscale image coding , 1994, IEEE Trans. Image Process..

[26]  A. Wayne Whitney,et al.  A Direct Method of Nonparametric Measurement Selection , 1971, IEEE Transactions on Computers.

[27]  Jack Sklansky,et al.  A note on genetic algorithms for large-scale feature selection , 1989, Pattern Recognition Letters.

[28]  Bedrich J. Hosticka,et al.  An unsupervised texture segmentation algorithm with feature space reduction and knowledge feedback , 1998, IEEE Trans. Image Process..

[29]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[30]  A. W. M. van den Enden,et al.  Discrete Time Signal Processing , 1989 .

[31]  Aleksandra Mojsilovic,et al.  Texture analysis and classification with the nonseparable wavelet transform , 1997, Proceedings of International Conference on Image Processing.