The Scale of Geometric Texture

Abstract. The most defining characteristic of texture is its underlying geometry. Although the appearance of texture is as dynamic as its illumination and view-ing conditions, its geometry remains constant. In this work, we study the fun-damental characteristic properties of texture geometry—self similarity and scale variability—and exploit them to perform surface normal estimation, and geomet-ric 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 tex-ture 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 improve-ments in appearance modeling and synthesis.

The 4-Source Photometric Stereo Under General Unknown Lighting

Abstract. Many previous works on photometric stereo have shown how to recover the shape and reflectance properties of an object using multiple images taken under a fixed viewpoint and variable lighting conditions. However, most of them only dealt with a single point light source in each image. In this paper, we show how to perform photometric stereo with four images which are taken under distant but general lighting conditions. Our method is based on the representation that uses low-order spherical harmonics for Lambertian objects. Attached shadows are considered in this representation. We show that the lighting conditions can be estimated regardless of object shape and reflectance properties. The estimated illumination conditions can then help to recover the shape and reflectance properties.