Spaces of Curves, Dynamical Contours and Localization in Computer Vision

Using techniques from computational differential geometry, we present a new approach to the algorithmic study of planar curves, with applications to shape and image analysis. The main idea is to construct spaces of curves satisfying constraints suited to specific problems and exploit the geometric structure of these spaces to quantify and analyze properties of contours and solve optimization and inference problems. Applications include: (i) new geometric algorithms for the estimation of contours and appearances of partially occluded objects in images; (ii) the development of a novel multi-resolution, algorithmic approach to statistical shape analysis using progressive localization in the frequency domain; (iii) algorithms for computing planar elasticae with enhanced performance and speed.