A Framework for Non-rigid Matching and Correspondence

Matching feature point sets lies at the core of many approaches to object recognition. We present a framework for non-rigid matching that begins with a skeleton module, affine point matching, and then integrates multiple features to improve correspondence and develops an object representation based on spatial regions to model local transformations. The algorithm for feature matching iteratively updates the transformation parameters and the correspondence solution, each in turn. The affine mapping is solved in closed form, which permits its use for data of any dimension. The correspondence is set via a method for two-way constraint satisfaction, called softassign, which has recently emerged from the neural network/statistical physics realm. The complexity of the non-rigid matching algorithm with multiple features is the same as that of the affine point matching algorithm. Results for synthetic and real world data are provided for point sets in 2D and 3D, and for 2D data with multiple types of features and parts.