Mapping Image Regularities into Shape Constraints: Skewed Symmetry, Affine-Transformable Patterns, and the Shape-from-Texture Paradigm

Abstract

Certain image properties, such as parallelisms, symmetries, and repeated patterns, provide cues for perceiving the 3-D shape from a 2-D picture. This paper demonstrates how we can map those image properties into 3-D shape constraints by associating appropriate assumptions with them and by using appropriate computational and representational tools. We begin with the exploration of how one specific image property, "skewed symmetry", can be defined and formulated to serve as a cue to the determination of surface orientations. Then we will discuss the issue from two new, broader viewpoints. One is the class of Affine-transformable patterns. It has various interesting properties, and includes skewed symmetry as a special case. The other is the computational paradigm of shape-from-texture. Skewed symmetry is derived in a second, independent way, as an instance of the application of the paradigm. This paper further claims that the ideas and techniques presented here are applicable to many other properties, under the general framework of the shape-from-texture paradigm, with the underlying meta-heuristic of non-accidental image properties.