The analysis and recognition of real-world textures in three dimensions

The observed image texture for a rough surface has a complex dependence on the illumination and viewing angles due to effects such as foreshortening, local shading, interreflections, and the shadowing and occlusion of surface elements. We introduce the dimensionality surface as a representation for the visual complexity of a material sample. The dimensionality surface defines the number of basis textures that are required to represent the observed textures for a sample as a function of ranges of illumination and viewing angles. Basis textures are represented using multiband correlation functions that consider both within and between color band correlations. We examine properties of the dimensionality surface for real materials using the Columbia Utrecht Reflectance and Texture (CUReT) database. The analysis shows that the dependence of the dimensionality surface on ranges of illumination and viewing angles is approximately linear with a slope that depends on the complexity of the sample. We extend the analysis to consider the problem of recognizing rough surfaces in color images obtained under unknown illumination and viewing geometry. We show, using a set of 12,505 images from 61 material samples, that the information captured by the multiband correlation model allows surfaces to be recognized over a wide range of conditions. We also show that the use of color information provides significant advantages for three-dimensional texture recognition.