Implicit higher order polynomials for motion estimation and tracking

In this technical report, we propose a novel technique to address motion estimation and tracking. Such technique represents the motion field using a regular grid of thin-plate splines, and the moving objects using an implicit function on the image plane that is a cubic interpolation of a ”level set function” defined on this grid. Optical flow is determined through the deformation of the grid and consequently of the underlying image structures towards satisfying the constant brightness constraint. Tracking is performed in similar fashion through the consistent recovery in the temporal domain of the zero iso-surfaces of a level set that is the projection of the FFD implicit function according to the cubic spline formulation. Such an approach is a compromise between dense motion estimation and parametric motion models, introduces smoothness in an implicit fashion, is intrinsic, and can cope with important object deformations. Promising results demonstrate the potentials of our approach.