Continuous curve matching with scale-space curvature and extrema-based scale selection

We extend a symmetric parametric curve matching algorithm designed for recognition and morphometry by incorporating Gaussian smoothing and curvature scale-space. A general statement of the matching theory and the properties of the associated algorithm is given. Gaussian smoothing is used to assist in approximating the continuous solution from the discrete solution given by dynamic programming. The method is then investigated in a multi-scale framework, which has the advantage of reducing the effects of noise and occlusion. A novel scale-space derived energy functional that incorporates geometric information from many scales at once is proposed. The related issue of selecting a smoothing kernel for a given matching problem is also explored, resulting in a topologically based method of scale-selection. This application requires estimating the matching between the fine and coarse scale versions of the same curve. We provide a tool for finding this inter-scale, intra-curve correspondence, based on tracking curvature extrema through scales. These novel algorithms are demonstrated on both 2D and 3D data.