The Scale of Geometric Texture

  • Geoffrey Oxholm
  • Prabin Bariya
  • Ko Nishino
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7572)


The most defining characteristic of texture is its underlying geometry. Although the appearance of texture is as dynamic as its illumination and viewing conditions, its geometry remains constant. In this work, we study the fundamental characteristic properties of texture geometry—self similarity and scale variability—and exploit them to perform surface normal estimation, and geometric texture classification. Textures, whether they are regular or stochastic, exhibit some form of repetition in their underlying geometry. We use this property to derive a photometric stereo method uniquely tailored to utilize the redundancy in geometric texture. Using basic observations about the scale variability of texture geometry, we derive a compact, rotation invariant, scale-space representation of geometric texture. To evaluate this representation we introduce an extensive new texture database that contains multiple distances as well as in-plane and out-of plane rotations. The high accuracy of the classification results indicate the descriptive yet compact nature of our texture representation, and demonstrates the importance of geometric texture analysis, pointing the way towards improvements in appearance modeling and synthesis.


Visibility Function Surface Orientation Scale Variability Photometric Stereo Query Texture 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bariya, P., Novatnack, J., Schwartz, G., Nishino, K.: 3D Geometric Scale Variability in Range Images: Features and Descriptors. Int’l Journal of Computer Vision 99, 232–255 (2012)CrossRefGoogle Scholar
  2. 2.
    Barsky, S., Petrou, M.: Classification of 3D Rough Surfaces Using Color and Gradient Information Recovered by Color Photometric Stereo. In: SPIE Conf. on Visualization and Optimization Techniques (2001)Google Scholar
  3. 3.
    Barsky, S., Petrou, M.: The 4-Source Photometric Stereo Technique For Three-Dimensional Surfaces in the Presence of Highlights and Shadows. IEEE Trans. on Pattern Analysis and Machine Intelligence 25(10), 1239–1252 (2003)CrossRefGoogle Scholar
  4. 4.
    Boykov, Y., Kolmogorov, V.: An Experimental Comparison of Min-Cut/Max-Flow Algorithms for Energy Minimization in Vision. IEEE Trans. on Pattern Analysis and Machine Intelligence 26(9), 1124–1137 (2004)CrossRefGoogle Scholar
  5. 5.
    Chandraker, M., Agarwal, S.: ShadowCuts: Photometric Stereo with Shadows. In: IEEE Int’l Conf. on Computer Vision and Pattern Recognition, pp. 1–8 (2007)Google Scholar
  6. 6.
    Chantler, M., Schmidt, M., Petrou, M., McGunnigle, G.: The Effect of Illuminant Rotation on Texture Filters: Lissajous’s Ellipses. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002, Part III. LNCS, vol. 2352, pp. 289–303. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  7. 7.
    Cohen, F., Fan, Z., Patel, M.: Classification of Rotated and Scaled Textured Images Using Gaussian Markov Random Field Models. IEEE Trans. on Pattern Analysis and Machine Intelligence 13(2), 192–202 (1991)CrossRefGoogle Scholar
  8. 8.
    Dana, K.J., Nayar, S.K.: 3D Textured Surface Modeling. In: IEEE Workshop on the Integration of Appearance and Geometric Methods in Object Recognition, pp. 44–56 (1999)Google Scholar
  9. 9.
    Fountain, S.R., Tan, T.N., Baker, K.D.: A Comparative Study of Rotation Invariant Classification and Retrieval of Texture Images. In: British Machine Vision Conference, pp. 266–275 (1998)Google Scholar
  10. 10.
    Kim, J., Zabih, R.: Factorial Markov Random Fields. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002, Part III. LNCS, vol. 2352, pp. 321–334. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  11. 11.
    Koppal, S., Narasimhan, S.: Clustering appearance for scene analysis. In: IEEE Int’l Conf. on Computer Vision and Pattern Recognition, vol. 2, pp. 1323–1330 (2006)Google Scholar
  12. 12.
    Lazebnik, S., Schmid, C., Ponce, J.: Affine-Invariant Local Descriptors and Neighborhood Statistics for Texture Recognition. In: IEEE Int’l Conf. on Computer Vision (2003)Google Scholar
  13. 13.
    Leung, T., Malik, J.: Recognizing Surfaces Using Three-Dimensional Textons. In: IEEE Int’l Conf. on Computer Vision, pp. 1010–1017 (1999)Google Scholar
  14. 14.
    Lin, J.: Divergence Measures Based on the Shannon Entropy. IEEE Trans. on Information Theory 37(1), 145–151 (1991)zbMATHCrossRefGoogle Scholar
  15. 15.
    McGunnigle, G., Chantler, M.: Rough Surface Classification Using Point Statistics from Photometric Stereo. Pattern Recognition Letters 21, 593–604 (2000)CrossRefGoogle Scholar
  16. 16.
    Nayar, S., Ikeuchi, K., Kanade, T.: Shape from Interreflections. Int’l Journal of Computer Vision 6(3), 173–195 (1991)CrossRefGoogle Scholar
  17. 17.
    Nayar, S., Krishnan, G., Grossberg, M.D., Raskar, R.: Fast Separation of Direct and Global Components of a Scene using High Frequency Illumination. ACM Trans. on Graphics 25(3), 935–944 (2006)CrossRefGoogle Scholar
  18. 18.
    Novatnack, J., Nishino, K.: Scale-Dependent 3D Geometric Features. In: IEEE Int’l Conf. on Computer Vision, pp. 1–8 (2007)Google Scholar
  19. 19.
    Penirschke, A., Chantler, M., Petrou, M.: Illuminant Rotation Invariant Classification of 3D Surface Textures Using Lissajous’s Ellipses. In: Intl. Workshop on Texture Analysis and Synthesis (2002)Google Scholar
  20. 20.
    Smith, M.: The analysis of surface texture using photometric stereo acquisition and gradient space domain mapping. Image and Vision Computing 17(14), 1009–1019 (1999)CrossRefGoogle Scholar
  21. 21.
    Sunkavalli, K., Zickler, T., Pfister, H.: Visibility Subspaces: Uncalibrated Photometric Stereo with Shadows. In: Daniilidis, K., Maragos, P., Paragios, N. (eds.) ECCV 2010, Part II. LNCS, vol. 6312, pp. 251–264. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  22. 22.
    Varma, M., Zisserman, A.: Classifying Images of Materials: Achieving Viewpoint and Illumination Independence. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002, Part III. LNCS, vol. 2352, pp. 255–271. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  23. 23.
    Woodham, R.J.: Photometric Method for Determining Surface Orientation from Multiple Images. Optical Engineering 19(1), 139–144 (1980)Google Scholar
  24. 24.
    Wu, T.-P., Tang, C.-K.: Photometric Stereo Via Expectation Maximization. IEEE Trans. on Pattern Analysis and Machine Intelligence 32(3), 546–560 (2010)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Geoffrey Oxholm
    • 1
  • Prabin Bariya
    • 1
  • Ko Nishino
    • 1
  1. 1.Department of Computer ScienceDrexel UniversityPhiladelphiaUSA

Personalised recommendations