Abstract
We investigate the maximum likelihood metameres of local pure 2nd order structure in natural images. Using the shape index, we re-parameterise the 2nd order structure and gain a one-parameter index which offers a qualitative description of local pure 2nd order image structure. Inspired by Koenderink and previous work within Geometric Texton Theory the maximum likelihood metameres are calculated for a quantised version of the shape index. Results are presented and discussed for natural images, Gaussian noise images, and Brownian or pink noise images. Furthermore, we present statistics for the shape index, principal direction, and curvedness of natural images. Finally, the results are discussed in the terms of their applicability to Geometric Texton Theory.
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References
Canny, J.: A computational approach to edge detection. IEEE Transactions on Pattern Analysis and Machine Intelligence 8(6), 679–698 (1986)
Casorati, F.: Nuova definitione della curvatura delle superficie e suo confronto con quella di gauss. Rend. Maem. Accd. Lomb. (1867/1868)
Daugman, J.G.: Uncertainty relations for resolution in space, spatial frequency, and orientation optimized by two-demensional visual cortical filters. Journal of the Optical Society of America A, 1160–1169 (1985)
Field, D.J.: Relations between the statistics of natural images and the response proporties of cortical cells. J. Optic. Soc. Am. 4(12), 2379–2394 (1987)
Florack, L.M.J., et al.: Cartesian differential invariants in scale-space. Journal of Mathematical Imaging and Vision 3(4), 327–348 (1993)
Griffin, L.D., Lillholm, M.: The 2nd order local-image-structure solid. IEEE Transactions on Pattern Analysis and Machine Intelligence (In Press)
Lillholm, M., Griffin, L.D.: Image Features and the 1-D, 2nd Order Gaussian Derivative Jet. In: Kimmel, R., Sochen, N.A., Weickert, J. (eds.) Scale-Space 2005. LNCS, vol. 3459, pp. 26–37. Springer, Heidelberg (2005)
Griffin, L.D., Lillholm, M.: Hypotheses for image features, icons and textons. International Journal of Computer Vision 70(3), 213–230 (2006)
Griffin, L.D., Lillholm, M., Nielsen, M.: Natural image profiles are most likely to be step edges. Vision Research 44(4), 407–421 (2004)
Harris, C., Stephens, M.J.: A combined corner and edge detector. In: Alvey’88, pp. 147–152 (1988)
Hubel, D.H., Wiesel, T.N.: Receptive fields and functional architecture of monkey striate cortex. Journal of Physiology 195, 215–243 (1968)
Jones, J.P., Palmer, L.A.: The two-dimensional spatial structure of simple receptive fields in cat striate cortex. Journal of Neurophysiology 58(6), 1233–1258 (1987)
Koenderink, J.J.: The structure of images. Biological Cybernetics 50, 363–370 (1984)
Koenderink, J.J.: What is a feature? Journal of Intelligent Systems 3(1), 49–82 (1993)
Koenderink, J.J., van Doorn, A.J.: Receptive field assembly specificity. Journal of Visual Communication and Image Representation 3(1), 1–12 (1992)
Koenderink, J.J., van Doorn, A.J.: Metamerism in complete sets of image operators. In: Advances in Image Understading ’96, pp. 113–129 (1996)
Koenderink, J.J., van Doorn, A.J.: Local image operators and iconic structure. In: Sommer, G. (ed.) AFPAC 1997. LNCS, vol. 1315, pp. 66–93. Springer, Heidelberg (1997)
Koenderink, J.J., van Doorn, A.J.: Receptive-field families. Biological Cybernetics 63(4), 291–297 (1990)
Koenderink, J.J., van Doorn, A.J.: Local Structure of Gaussian Texture. IEICE Transactions on Information and Systems 86(7), 1165–1171 (2003)
Leung, T., Malik, J.: Representing and Recognizing the Visual Appearance of Materials using Three-dimensional Textons. International Journal of Computer Vision 43(1), 29–44 (2001)
Lillholm, M., Nielsen, M., Griffin, L.D.: Feature-based image analysis. International Journal of Computer Vision 52(2-3), 73–95 (2003)
Lindeberg, T.: Feature detection with automatic scale selection. International Journal of Computer Vision 30(2), 79–116 (1998)
Liu, X., Wang, D.L.: A spectral histogram model for texton modeling and texture discrimination. Vision Research 42(23), 2617–2634 (2002)
Marr, D.: Vision: A computational investigation into the human representation and processing of visual information. W.H. Freeman, New York (1982)
Nasrallah, A.J., Griffin, L.D.: Gradient direction dependencies in natural images. Spatial Vision, Accepted (Oct. 2006)
Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D, 259–268 (1992)
van Hateren, J.H., van der Schaaf, A.: Independent components filters of natural images compared with simple cells in primary visual cortex. Proc. R. Soc., London Series B 265, 359–366 (1998)
Varma, M., Zisserman, A.: A Statistical Approach to Texture Classification from Single Images. International Journal of Computer Vision 62(1), 61–81 (2005)
Young, R.A.: The gaussian derivative theory of spatial vision: Analysis of cortical receptive field line-weighting profiles. Gen. Motors Res. Tech. Rep, GMR-4920 (1985)
Zhu, S.C., et al.: What are Textons? International Journal of Computer Vision 62(1), 121–143 (2005)
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Lillholm, M., Griffin, L.D. (2007). Maximum Likelihood Metameres for Local 2nd Order Image Structure of Natural Images. In: Sgallari, F., Murli, A., Paragios, N. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2007. Lecture Notes in Computer Science, vol 4485. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72823-8_34
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DOI: https://doi.org/10.1007/978-3-540-72823-8_34
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