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Local Linear Transforms for Texture Analysis

M. Unser

Proceedings of the Seventh IEEE International Conference on Pattern Recognition (ICPR'84), Montréal QC, Canada, July 30-August 2, 1984, vol. II, pp. 1206-1208.



Conventional first-order statistics are known to carry little textural information. The author shows how it is possible, by local linear transformation of the pixels in a given neighborhood, to perform a change of coordinate system in which first-order statistics will be strongly affected by the structure of the texture. Estimates of the first-order statistics of the transformed coefficients are used for texture characterization. It is shown that the optimum change of coordinates, in the sense that the variances along the axes are as different as possible, is the local Karhunen-Loève transform. An entropic efficiency measure of the rotation in the case of an energy preserving transform is introduced. This quantity is minimal in the initial coordinate system and maximal in the optimum Karhunen-Loève basis. Experiments on real textures demonstrate that the local discrete sine- and cosine-transform perform closely to the KL-transform. Various transforms are applied to texture classification and lead to encouraging results.


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