Boundary Detection in Piecewise Homogeneous Textured Images

1 I n t r o d u c t i o n The problem of texture analysis (recognition and segmentation) has traditionally been approached by computing locally defined vector-valued "descriptors" of each region in the image. The texture recognition problem is thus reduced to a conventional classification problem, and boundary detection may be performed by locating areas of rapid change in the descriptor vectors, or, dually, by clustering regions with similar descriptors. Constraints on texture analysis algorithms come from the physics and the geometry of image formation: often one would like to ensure invariance with respect to changes in illumination, scaling and rotation, sometimes also to tilt and slant. The search for good local descriptors has been the focus of much work with two main classes of descriptors being favored in the more recent literature: (a) linear filters followed by elementary nonlinearities and smoothing (e.g. [1, 2, 3, 4]), and (b) different statistics of brightness computed on image patches (e.g. [5, 6, 7]). The filtering framework has natural characteristics for addressing the scaleand rotation-invariance issues: if each filter category is present at multiple scales and orientations, and if the discretization is fine enough, the representation of image properties given by the filter outputs is roughly scale and rotation-invariant. A number of important issues having to do with scale selection and response normalization have remained virtually unanswered: What are the basic regularity hypotheses that a texture has to satisfy for the local descriptor approach to work? How does one identify automatically the proper scale for analyzing a texture, and how does one choose the thresholds for declaring a boundary? In this paper we make explicit and formalize a general assumption about texture regularity. We show how this assumption can be used to find texture boundaries and we * Research supported by Airforce grant AFOSR-89-0276-C and ARC) grant DAAL03-86-K-0171, Center for Intelligent Control Systems