Curvelet-based snake for multiscale detection and tracking of geophysical fluids

Detection and target tracking have an application to many scientific problems. The approach developed in this paper is motivated by the applications of detection and tracking characteristic deformable structures in geophysical fluids. We develop an integrated detection and tracking method of geophysical fluids based on a discrete curvelet representation of the information characterizing the targets. Curvelets are in some sense geometric wavelets, allowing an optimal sparse representation of two-dimensional piecewise continuous objects with C²-singularities. The proposed approach first identifies a consistent vortex by a curvelet-based gradient-vector-flow snake and then establishes the motion correspondence of the snaxels between successive time frames by a constructed so-called semi-T or comp-T multiscale motion-estimation method based on the geometric wavelets. Furthermore, a combination of total-variation regularization and cycle-spinning techniques effectively removes false matches and improves significantly the estimation. Numerical experiments at each stage demonstrate the performance of the proposed tracking methodology for temporal oceanographic satellite image sequences corrupted by noise, with weak edges and submitted to large deformations, in comparison to conventional methods.