Robust Modeling and Estimation of Optical Flow with Overlapped Basis Functions

摘要

Computation of optical flow has been formulated as nonlinear optimization of acost function comprising a gradient constraint term and a field smoothness factor. Results obtained using these techniques are often erroneous, highly sensitive to numerical precision, and determined sparsely, and they carry with them all the pitfalls of nonlinear optimization. In this paper, we regularize the gradient constraint equation by modeling optical flow as a linear combination of an overlapped set of basis functions. We develop a theory for estimating model parameters robustly and reliably. We prove that the extended least squares solution proposed here is unbiased and robust to small perturbations in the estimates of gradients and to mild deviations from the gradient constraint. The solution is obtained by a numerically stable sparse matrix inversion, giving a reliable flow field estimate over the entire frame. Experimental results of our scheme are surprisingly accurate and consistent across a variety of images, in comparison with the standard optical flow algorithms. We argue that our flow field model offers higher accuracy and robustness than conventional optical flow techniques, and is better suited for image stabilization, mosaicking and video compression.