Advertisement

Texture analysis

  • Pierre Soille
Chapter

Abstract

An informal definition of the notion of texture is ‘the characteristic physical structure given to an object by the size, shape, arrangement, and proportions of its parts’ (Anonymous, 1994). The goal of texture analysis in image processing is to map the image of a textured object into a set of quantitative measurements revealing its very nature. The success of this mapping can be assessed by determining whether the resulting vectors are discriminant: measurement vectors of similar textures should form a cluster in the associated feature space and should be well separated from measurement vectors corresponding to different textures. In addition, the dimensionality of the vectors should be as small as possible for efficiency considerations. In this sense, texture analysis can be considered as a pattern recognition/classification problem.

Keywords

Line Segment Texture Analysis Mathematical Morphology Texture Segmentation Catchment Basin 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. Adams. Radial decomposition of discs and spheres. Computer Vision, Graphics, and Image Processing: Graphical Models and Image Processing, 55 (5): 325–332, September 1993.CrossRefGoogle Scholar
  2. Anonymous. Webster’s Encyclopedic Unabridged Dictionary. Gramercy Books, New York, 1994.Google Scholar
  3. A. Aubert, D. Jeulin, and R. Hashimoto. Surface texture classification from morphological transformations. In J. Goutsias, L. Vincent, and D. Bloomberg, editors, Mathematical Morphology and its Applications to Image and Signal Processing, pages 253–262, Boston, 2000. Kluwer Academic Publishers.Google Scholar
  4. P. Brodatz. Textures: a Photographic Album for Artists and Designers. Dover Publications, New York, 1966.Google Scholar
  5. J. Carr and W. Benzer. On the practice of estimating fractal dimension. Mathematical Geology, 23 (7): 945–958, 1991.CrossRefGoogle Scholar
  6. Y. Chen and E. Dougherty. Gray-scale morphological granulometric texture classification. Optical Engineering, 33 (8): 2713–2722, August 1994.CrossRefGoogle Scholar
  7. Y. Chen, E. Dougherty, S. Totterman, and J. Hornak. Classification of trabecular structure in magnetic resonance images based on morphological granulometries. Magnetic Resonance in Medicine, 29: 358–370, 1993.CrossRefGoogle Scholar
  8. M. Dominguez and L. Torres. Analysis and synthesis of textures through the inference of Boolean functions. Signal Processing, 59 (1): 1–16, 1997.MATHCrossRefGoogle Scholar
  9. E. Dougherty and J. Pelz. Morphological granulometric analysis of electrophotographic images — size distribution statistics for process control. Optical Engineering, 30 (4): 438–445, 1991.CrossRefGoogle Scholar
  10. E. Dougherty, J. Pelz, F. Sand, and A. Lent. Morphological image segmentation by local granulometric size distributions. Journal of Electronic Imaging, 1 (1): 40–60, January 1992.CrossRefGoogle Scholar
  11. B. Dubuc, J.-F. Quiniou, C. Roques-Carmes, C. Tricot, and S. Zucker. Evaluating the fractal dimension of profiles. Physical Review A, 39 (3): 1500–1512, February 1989.MathSciNetCrossRefGoogle Scholar
  12. D. Jeulin. Morphological modeling of images by sequential random functions. Signal Processing, 16: 403–431, 1989.MathSciNetCrossRefGoogle Scholar
  13. D. Jeulin. Random models for the morphological analysis of powders. Journal of Microscopy, 172 (Part 1): 13–21, October 1993.CrossRefGoogle Scholar
  14. D. Jeulin and M. Kurdy. Directional mathematical morphology for oriented image restoration and segmentation. Acta Stereologica, 11: 545–550, 1992.Google Scholar
  15. D. Jeulin and P. Laurenge. Simulation of rough surfaces by morphological random functions. Journal of Electronic Imaging, 6 (1): 16–30, January 1997.CrossRefGoogle Scholar
  16. R. Jones and P. Soille. Periodic lines: definition, cascades, and application to granulometries. Pattern Recognition Letters, 17 (10): 1057–1063, September 1996.CrossRefGoogle Scholar
  17. A. Knoll, A. Horvat, K. Lyakhova, G. Krausch, G. Sevink, A. Zvelindovsky, and R. Magerle. Phase behavior in thin films of cylinder-forming block copolymers. Physical Review Letters,89(3): 035501, June 2002. URL http://dx.doi.org/ 10.1103/PhysRevLett.89.035501.Google Scholar
  18. M. Köppen, J. Ruiz-del-Solar, and P. Soille. Texture segmentation by biologically-inspired use of neural networks and mathematical morphology. In M. Heiss, editor, NC’98, International ICSC/IFAC Symposium on Neural Computation,pages 267–272, Wien, September 1998. ICSC Academic Press. URL http:// www.vision.fhg.de/ipk/publikationen/pdf/nc98.pdf. Google Scholar
  19. B. Laÿ. Recursive algorithms in mathematical morphology. Acta Stereologica, 6 (3): 691–696, September 1987.Google Scholar
  20. W. Li, V. Haese-Coat, and J. Ronsin. Residues of morphological filtering by reconstruction for texture classification. Pattern Recognition, 30 (7): 1081–1093, 1997.CrossRefGoogle Scholar
  21. R. Magerle. Nanotomography: real-space volume imaging with scanning probe microscopy. Lecture Notes in Physics, 600: 93–106, 2002.CrossRefGoogle Scholar
  22. B. Mandelbrot. How long is the coast of Great-Britain? Statistical self-similarity and fractional dimension. Science, 155: 636–638, 1967.CrossRefGoogle Scholar
  23. B. Mandelbrot. The Fractal Geometry of Nature. W.H. Freemann and Company, New York, 1983.Google Scholar
  24. P. Maragos. Pattern spectrum and multiscale shape representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11 (7): 701–716, July 1989.MATHGoogle Scholar
  25. P. Maragos. Fractal signal analysis using mathematical morphology. In P. Hawkes and B. Kazan, editors, Advances in Electronics and Electron Physics, volume 88, pages 199–246. Academic Press, 1994.Google Scholar
  26. P. Maragos and F.-K. Sun. Measuring the fractal dimension of signals: morphological covers and iterative optimization. IEEE Transactions on Signal Processing, 41 (1): 108–121, January 1993.MATHCrossRefGoogle Scholar
  27. G. Matheron. Eléments pour une Théorie des Milieux Poreux. Masson, Paris, 1967.Google Scholar
  28. G. Matheron. Random Sets and Integral Geometry. Wiley, New York, 1975.MATHGoogle Scholar
  29. J. Mattioli and M. Schmitt. On information contained in the erosion curve. In Y.-L. O, A. Toet, D. Foster, H. Heijmans, and P. Meer, editors, Shape in Picture: Mathematical Description of Shape in Grey-level Images, pages 177–195. Springer-Verlag, 1994.Google Scholar
  30. A. Mauricio and C. Figueiredo. Texture analysis of grey-tone images by mathematical morphology: a nondestructive tool for the quantitative assessment of stone decay. Mathematical Geology, 32 (5): 619–642, 2000.CrossRefGoogle Scholar
  31. H. Minkowski. Über die Begriffe Länge, Oberfläche und Volumen. Jahresbericht der Deutschen Mathematiker Vereinigung, 9: 115–121, 1901.MATHGoogle Scholar
  32. P. Nacken. Chamfer metrics, the medial axis and mathematical morphology. Journal of Mathematical Imaging and Vision, 6 (2/3): 235–248, 1996.MathSciNetCrossRefGoogle Scholar
  33. S. Peleg, J. Naor, R. Hartley, and D. Avnir. Multiple resolution texture analysis and classification. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6 (4): 518–523, July 1984.CrossRefGoogle Scholar
  34. A. Rao. A Taxonomy for Texture Description and Identification. Springer-Verlag, New York, 1990.MATHGoogle Scholar
  35. T. Reed and J. du Buf. A review of recent texture segmentation and feature extraction techniques. Computer Vision and Image Understanding,57(3):359372, May 1993.Google Scholar
  36. J.-P. Rigaut. Automated image segmentation by mathematical morphology and fractal geometry. Journal of Microscopy, 150(Pt 1 ): 21–30, April 1988.CrossRefGoogle Scholar
  37. J. Serra. The Boolean model and random sets. Computer Vision, Graphics, and Image Processing, 12: 99–126, 1980.Google Scholar
  38. J. Serra. Image Analysis and Mathematical Morphology. Academic Press, London, 1982.MATHGoogle Scholar
  39. J. Serra. Boolean random functions. Journal of Microscopy, 156: 41–63, 1989.CrossRefGoogle Scholar
  40. K. Sivakumar and J. Goutsias. Discrete morphological size distributions and densities: estimation techniques and applications. Journal of Electronic Imaging, 6 (1): 31–53, January 1997.CrossRefGoogle Scholar
  41. K. Sivakumar and J. Goutsias. Morphologically constrained GRFs: applications to texture synthesis and analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence, 21 (2): 99–113, 1999.CrossRefGoogle Scholar
  42. P. Soille. Advances in the analysis of topographic features on discrete images. Lecture Notes in Computer Science, 2301: 175–186, March 2002a.MathSciNetCrossRefGoogle Scholar
  43. P. Soille. Morphological texture analysis: an introduction. Lecture Notes in Physics, 600: 215–237, 2002b.CrossRefGoogle Scholar
  44. P. Soille and J.-F. Rivest. On the validity of fractal dimension measurements in image analysis. Journal of Visual Communication and Image Representation, 7 (3): 217–229, September 1996.CrossRefGoogle Scholar
  45. P. Soille and H. Talbot. Directional morphological filtering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 23 (11): 1313–1329, November 2001.CrossRefGoogle Scholar
  46. D. Stoyan and H. Stoyan. Fractals, Random Shapes, and Point Fields. John Wiley & Sons, Chichester, 1994.MATHGoogle Scholar
  47. M. Vanrell and J. Vitrià. Mathematical morphology, granulometries, and texture perception. In E. Dougherty, P. Gader, and J. Serra, editors, Image Algebra and Morphological Image Processing IV, volume SPIE-2030, pages 152–161, July 1993.Google Scholar
  48. L. Vincent. Fast grayscale granulornetry algorithms. In J. Serra and P. Soille, editors, Mathematical Morphology and its Applications to Image Processing, pages 265–272. Kluwer Academic Publishers, 1994.Google Scholar
  49. L. Vincent. Granulometries and opening trees. Fundamenta Informaticae, 41 (1–2): 57–90, 2000.MathSciNetMATHGoogle Scholar
  50. P. Wagner. Texture analysis. In B. Jähne, H. Haußecker, and P. Geißler, editors, Handbook of Computer Vision and Applications, volume 2, chapter 12, pages 275–308. Academic Press, San Diego, 1999.Google Scholar
  51. D. Wang, V. Haese-Coat, A. Bruno, and J. Ronsin. Texture classification and segmentation based on iterative morphological decomposition. Journal of Visual Communication and Image Representation, 4 (3): 197–214, September 1993.CrossRefGoogle Scholar
  52. M. Werman and S. Peleg. Min-max operators in texture analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence, 7 (6): 730–733, November 1985.CrossRefGoogle Scholar
  53. X. Zheng, P. Gong, and M. Strome. Characterizing spatial structure of tree canopy using colour photographs and mathematical morphology. Canadian Journal of Remote Sensing, 21 (4): 420–428, 1995.Google Scholar
  54. Z. Zhou and A. Venetsanopoulos. Analysis and implementation of morphological skeleton transforms. Circuits Systems Signal Process, 11 (1): 253–280, 1992.MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Pierre Soille
    • 1
  1. 1.EC Joint Research CentreIspra (Va)Italy

Personalised recommendations