Global optimization for alignment of generalized shapes

In this paper, we introduce a novel algorithm to solve global shape registration problems. We use gray-scale “images” to represent source shapes, and propose a novel two-component Gaussian Mixtures (GM) distance map representation for target shapes. Based on this flexible asymmetric image-based representation, a new energy function is defined. It proves to be a more robust shape dissimilarity metric that can be computed efficiently. Such high efficiency is essential for global optimization methods. We adopt one of them, the Particle Swarm Optimization (PSO), to effectively estimate the global optimum of the new energy function. Experiments and comparison performed on generalized shape data including continuous shapes, unstructured sparse point sets, and gradient maps, demonstrate the robustness and effectiveness of the algorithm.