On the validity of fractal dimension measurements in image analysis

Journal of Visual Communication and Image Representation

Volumn 7, Issue 3, 1996, Pages 217-229

  Soille, Pierre ^a   Rivest, Jean Françoise ^b  

^a PSL RESEARCH UNIVERSITY   (France)

^b UNIVERSITY OF OTTAWA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; FRACTALS; IMAGE SEGMENTATION; MATHEMATICAL TRANSFORMATIONS;

FLAT STRUCTURING ELEMENT METHOD; POWER SPECTRUM METHOD; VARIOGRAM METHOD;

IMAGE ANALYSIS;

EID: 0030244617     PISSN: 10473203     EISSN: None     Source Type: Journal    
DOI: 10.1006/jvci.1996.0020     Document Type: Article

References (35)

1. S. Beucher, Segmentation d'images et morphologie mathématique. Ph.D. Thesis, Ecole des Mines de Paris, June 1990.
2. G. Bouligand, Ensembles impropres et nombre dimensionnel, Bull. Sci. Math. II-52, II-53, 1928, 1929.
3. R. Brammer, Unified image computing based on fractals and chaos model techniques, Opt. Eng. 28(7), 1989, 726-834.
4. M. Carlotto, Toward the unsupervised interpretation of outdoor imagery, J. Visual Comm. Image Represent. 1(2), November 1990, 158-175.
5. J. Carr and W. Benzer, On the practice of estimating fractal dimension, Math. Geol. 23(7), 1991, 945-958.
6. S. Chen, M. Keller, and R. Crownover, On the calculation of fractal features from images, IEEE Trans. Pattern Anal. Mach. Intell. 15(10), October 1993, 1087-1090.
7. K. Clarke, Computation of the fractal dimension of topographic surfaces using the triangular prism surface area method, Comput. Geosci. 12(5), 1986, 713-722.
8. R. Creutzburg and E. Ivanov, Fast algorithm for computing fractal dimensions of image segments, Lecture Notes in Comput. Sci. 399, 1989, 42-51.
9. B. Dubuc, J.-F. Quiniou, C. Roques-Carmes, C. Tricot, and S. Zucker, Evaluating the fractal dimension of profiles, Phys. Rev. A 39(3), February 1989, 1500-1512.
10. J. Garding, Properties of fractal intensities surfaces, Pattern Recognition Lett. 8, December 1988, 319-324.
11. J. Keller, S. Chen, and R. Crownover, Texture description and segmentation through fractal geometry, Comput. Vision Graphics Image Process. 45, 1989, 150-166.
12. P. Kube and A. Pentland, On the imaging of fractal surfaces, IEEE Trans. Pattern Anal. Mach. Intell. 10(5), September 1988, 704-707.
13. B. Mandelbrot, Les objets fractals: forme, hasard et dimension. Flammarion, Paris, 1975.
14. B. Mandelbrot, The Fractal Geometry of Nature. Freemann, New York, 1983.
15. B. Mandelbrot, Self-affine fractals and fractal dimension, Phys. Scripta 32, 1985, 257-260.
16. P. Maragos, Fractal signal analysis using mathematical morphology, in Advances in Electronics and Electron Physics (P. Hawkes and B. Kazan, Eds.). Academic Press, San Diego, 1993.
17. P. Maragos and F.-K. Sun, Measuring the fractal dimension of signals: morphological covers and iterative optimization, IEEE Trans. Signal Process. 41(1), January 1993, 108-121.
18. G. Matheron, Eléments pour une théorie des milieux poreux. Masson, Paris, 1967.
19. H. Minkowski, Über die Begriffe Länge, Oberfläche, und Volumen, Jahresbericht der Deutschen Mathematiker Vereinigung, 9, 1901, 115-121.
20. S. Peleg, J. Naor, R. Hartley, and D. Avnir, Multiple resolution texture analysis and classification, IEEE Trans. Pattern Anal. Mach. Intell. 6(4), July 1984, 518-523.
21. A. Pentland, Fractal-based description of natural scenes, IEEE Trans. Pattern Anal. Mach. Intell. 6(6), November 1984, 661-674.
22. A. Pentland, Shading into texture, Artificial Intell. 29, 1986, 147-170.
23. W. Press, B. Flannery, S. Teukolsky, and W. Vetterling, Numerical Recipes in C. The Art of Scientific Computing. Cambridge Univ. Press, Cambridge, UK, 1988.
24. A. Rao, A Taxonomy for Texture Description and Identification. Springer-Verlag, New York, 1990.
25. J.-P. Rigaut, Automated image segmentation by mathematical morphology and fractal geometry, J. Microsc. 150(Pt. 1), April 1988, 21-30.
26. J.-F. Rivest, J. Serra, and P. Soille, Dimensionality in image analysis, J. Visual Comm. Image Represent. 3(2), 1992, 137-146.
27. J.-F. Rivest, P. Soille, and S. Beucher, Morphological gradients, J. Electronic Imaging, 2(4), October 1993, 326-336.
28. D. Saupe, Algorithms for random fractals, in The Science of Fractal Images (H. Peitgen and D. Saupe, Eds.). Springer-Verlag, New York, 1988.
29. J. Serra, Image Analysis and Mathematical Morphology. Academic Press, London, 1982.
30. P. Soille, Morphologie mathématique: du relief à la dimensionalité -Algorithmes et méthodes -. Ph.D. thesis, Université catholique de Louvain, Louvain-la-Neuve, Belgium, February 1992.
31. P. Soille and J.-F. Rivest, Dimensionality of morphological operators and cluster analysis, in Image Algebra and Morphological Image Process IV (E. Dougherty, P. Gader, and J. Serra, Eds.), Vol. SPIE-2030, pp. 43-53. July 1993.
32. P. Soille, J. Serra, and J.-F. Rivest, Dimensional measurements and operators in mathematical morphology, in Nonlinear Image Processing III (E. Dougherty, J. Astola, and G. Boncelet, Eds.), Vol. SPIE-1658, pp. 127-138. February 1992.
33. B. Super and A. Bovik, Localized measurements of image fractal dimension using Gabor filters, J. Visual Comm. Image Represent. 2(2), June 1991, 114-128.
34. R. Voss, Random fractals: Characterization and measurement, in Scaling Phenomena in Disordered Systems (R. Pynn and A. Skjeltorp, Eds.), Chap. 1, pp. 1-12. Plenum, New York, 1986.
35. R. Voss, Fractals in nature: from characterization to simulation, in The Science of Fractal Images (H. Peitgen and D. Saupe, Eds.), Chap. 1, pp. 21-70. Springer-Verlag, New York, 1988.