Approximately global optimization for robust alignment of generalized shapes

In this paper, we introduce a novel method to solve shape alignment problems. We use gray-scale "images" to represent source shapes, and propose a novel two-component Gaussian Mixture (GM) distance map representation for target shapes. This asymmetric representation is a flexible image-based representation which is able to represent different kinds of shape data, including continuous contours, unstructured sparse point sets, edge maps, and even gray-scale gradient maps. Using this representation, a new energy function based on a novel two-component Gaussian Mixture distance model is proposed. The new energy function was empirically evaluated to be a more robust shape dissimilarity metric that can be computed efficiently. Such high efficiency is essential for global optimization methods. We adopt and modify one of them, the Particle Swarm Optimization (PSO), to effectively estimate the global optimum of the new energy function. Differently from the original PSO, several new strategies were employed to make the optimization more robust and prevent it from converging prematurely. The overall performance of the proposed framework as well as the properties of each algorithmic component were evaluated and compared with those of some state-of-the-art methods. Extensive experiments and comparison performed on generalized 2D and 3D shape data demonstrate the robustness and effectiveness of the method.