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.
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