Are multifractal multipermuted multinomial measures good enough for unsupervised image segmentation?

By extending multinomial measures, a new class of self-similar multifractal measures is developed for texture representation. Two multifractal features have been shown to be suitable for texture discrimination and classification. Their use within a supervised segmentation framework provides us with satisfactory results. In this paper we complete the survey on these features by showing their rotation invariant property and their scaling behaviour. Both properties are particularly important for analyzing aerial images because the geographical elements can appear in different orientations and scales. Then, an automatic clustering algorithm based on a watershed technique is used for the segmentation of real world images. The experimental results are encouraging.

[1]  L. Devroye,et al.  Nonparametric Density Estimation: The L 1 View. , 1985 .

[2]  James M. Keller,et al.  Texture description and segmentation through fractal geometry , 1989, Comput. Vis. Graph. Image Process..

[3]  D. W. Scott,et al.  Multivariate Density Estimation, Theory, Practice and Visualization , 1992 .

[4]  Bidyut Baran Chaudhuri,et al.  Texture Segmentation Using Fractal Dimension , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[5]  Koichiro Deguchi,et al.  Texture Characterization and Texture-Based Image Partitioning Using Two-Dimensional Linear Estimation Techniques , 1978, IEEE Transactions on Computers.

[6]  Jean-Paul Berroir,et al.  Texture and multifractals : new tools for image analysis , 1992 .

[7]  P. Martinez,et al.  Texture analysis by universal multifractal features in a polarimetric SAR image , 1996, IGARSS '96. 1996 International Geoscience and Remote Sensing Symposium.

[8]  Hkansson,et al.  Finite-size effects on the characterization of fractal sets: f( alpha ) construction via box counting on a finite two-scaled Cantor set. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[9]  F. G. Peet,et al.  Surface Curvature as a Measure of Image Texture , 1985, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[10]  David W. Scott,et al.  Multivariate Density Estimation: Theory, Practice, and Visualization , 1992, Wiley Series in Probability and Statistics.

[11]  K. Falconer Techniques in fractal geometry , 1997 .

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

[13]  J. L. Véhel,et al.  MULTIFRACTAL SEGMENTATION OF IMAGES , 1994 .

[14]  Tohru Ishizaka,et al.  Integration of local fractal dimension and boundary edge in segmenting natural images , 1996, Proceedings of 3rd IEEE International Conference on Image Processing.

[15]  Serge Beucher,et al.  Use of watersheds in contour detection , 1979 .

[16]  Sylvie Philipp-Foliguet,et al.  Approximation of granular textures by quadric surfaces , 1994, Pattern Recognit..

[17]  James M. Keller,et al.  Local fractal geometric features for image segmentation , 1990, Int. J. Imaging Syst. Technol..

[18]  Alex Pentland,et al.  Fractal-Based Description of Natural Scenes , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[19]  Brian Everitt,et al.  Cluster analysis , 1974 .

[20]  L. Devroye The double kernel method in density estimation , 1989 .

[21]  Bidyut Baran Chaudhuri,et al.  Multifractal and generalized dimensions of gray-tone digital images , 1995, Signal Process..

[22]  Luc Devroye,et al.  Nonparametric Density Estimation , 1985 .

[23]  Robert M. Haralick,et al.  Textural Features for Image Classification , 1973, IEEE Trans. Syst. Man Cybern..

[24]  Jean Serra,et al.  Image Analysis and Mathematical Morphology , 1983 .