Texture description and segmentation through fractal geometry

Abstract Fractal geometry is receiving increased attention as a model for natural phenomena. In this paper we first present a new method for estimating the fractal dimension from image surfaces and show that it performs better at describing and segmenting generated fractal sets. Since the fractal dimension alone is not sufficient to characterize natural textures, we define a new class of texture measures based on the concept of lacunarity and use them, together with the fractal dimension, to describe and segment natural texture images.

[1]  Alex Pentland,et al.  Fractal-Based Description , 1983, IJCAI.

[2]  Mary M. Galloway,et al.  Texture analysis using gray level run lengths , 1974 .

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

[4]  A. Rosenfeld,et al.  Mosaic Models for Textures , 1981, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[5]  Joseph Naor,et al.  Multiple Resolution Texture Analysis and Classification , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[6]  Haluk Derin,et al.  Modeling and Segmentation of Noisy and Textured Images Using Gibbs Random Fields , 1987, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[7]  L. S. Davis.  Image Texture Analysis Techniques - a Survey , 1980 .

[8]  Clifford A. Pickover,et al.  Fractal characterization of speech waveform graphs , 1986, Comput. Graph..

[9]  W. Richards,et al.  Visual texture discrimination using random-dot patterns. , 1977, Journal of the Optical Society of America.

[10]  Alex Pentland,et al.  Shading into Texture , 1984, Artif. Intell..

[11]  King-Sun Fu,et al.  Stochastic tree grammar inference for texture synthesis and discrimination , 1979 .

[12]  R. Voss.  Random Fractals: characterization and measurement , 1991 .

[13]  Peter de Souza,et al.  Texture recognition via autoregression , 1982, Pattern Recognit..

[14]  B. Mandelbrot,et al.  Fractional Brownian Motions, Fractional Noises and Applications , 1968 .

[15]  Ruzena Bajcsy,et al.  Computer Description of Textured Surfaces , 1973, IJCAI.

[16]  S. Zucker.  Toward a model of texture , 1976 .

[17]  Richard W. Conners,et al.  Toward a Structural Textural Analyzer Based on Statistical Methods , 1980 .

[18]  Azriel Rosenfeld,et al.  A Comparative Study of Texture Measures for Terrain Classification , 1975, IEEE Transactions on Systems, Man, and Cybernetics.

[19]  Olivier D. Faugeras,et al.  Decorrelation Methods of Texture Feature Extraction , 1980, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[20]  James M. Keller,et al.  Characteristics of Natural Scenes Related to the Fractal Dimension , 1987, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[21]  Ramakant Nevatia,et al.  Structural Analysis of Natural Textures , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[22]  Rangasami L. Kashyap,et al.  A Model-Based Method for Rotation Invariant Texture Classification , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[23]  Luigia Carlucci,et al.  A formal system for texture languages , 1972, Pattern Recognit..

[24]  Larry S. Davis.  Computing the spatial structures of cellular textures , 1979 .

[25]  B Julesz,et al.  Experiments in the visual perception of texture. , 1975, Scientific American.

[26]  B. Mandelbrot.  Fractal Geometry of Nature , 1984 .

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