Abstract

The recognition of objects from their projected two-dimensional shapes is a challenging problem owing to the spectrum of possible variations reflected in the image domain, e.g., those caused by movement of parts, changes in viewing geometry, occlusion, etc. This motivates a need for quantitative as well as qualitative descriptions of shape in terms of structural relations between components; the latter remain largely invariant under the above changes. In this paper we confront the theoretical and practical difficulties of computing such a representation, based on the detection of shocks or singularities that arise as a shape is deformed, as organized in two stages. First, we develop subpixel local detectors for the detection of shocks and a classification of them into four types. Second, we show that shock patterns are not arbitrary, but obey the rules of a grammar which limits the possible shock combinations. In addition, shock patterns satisfy specific topological and geometric constraints. We develop this shock grammar and exploit the topological and geometric constraints to enforce global consistency: shock hypotheses that violate the grammar or are topologically or geometrically invalid are pruned, and survivors are organized into higher level structures. The result is a computational method for the detection, classification, and grouping of shocks. This leads to a description of shape as a hierarchical graph of shock groups. The graph is computed in the reaction-diffusion space, where diffusion plays a role of regularization to determine the significance of each shock-group. The representation is stable with rotations, scale changes, occlusion, movement of parts, noise and other variations, even at very low resolutions. We illustrate the suitability of this repres...

Citations