Spaces of Curves, Dynamical Contours and Localization in Computer Vision
W. Mio, A. Srivastava, X. Liu
Using techniques from computational differential geometry, we develop a new approach to the algorithmic study of planar curves, with applications to shape and image analysis. We construct spaces of curves and exploit their geometric structure 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 multi-resolution, algorithmic approach to statistical shape analysis using progressive localization in the frequency domain; (iii) algorithms for computing planar elasticae with enhanced speed and performance.