Generalized Thin-Plate SplineWarps

Thin-plate spline warps have been shown to be very effective as a parameterized model of the optic flow field between images of various deforming surfaces. Examples include a sheet of paper being manually handled. Recent work has used such warps for images of smooth rigid surfaces. Standard thin-plate spline warps are not rigid, in the sense that they do not satisfy the epipolar geometry constraint, and are intrinsically affine, in the sense of the affine camera model. We propose three types of warps based on the thin-plate spline. The first one is a flexible rigid warp. It describes the optic flow field induced by a smooth rigid surface, and satisfies the affine epipolar geometry constraint. The second and third ones extend the standard thin-plate spline and the proposed rigid flexible warp to the perspective camera model. The properties of these warps are studied in details, and a hierarchy is defined. Experimental results on simulated and real data are reported, showing that the proposed warps outperform the standard one in several cases of interest.