Optimization for Motion Estimation

Motion cues are an integral part of our visual experience, and therefore it is not surprising that the recovery of motion information from image sequences is a prominent problem in computer vision. Such motion estimates can, e.g., be obtained using nonparametric variational techniques, but while these techniques yield accurate results on a diverse range of image sequences, there are still a number of open problems. In this thesis, we address two of those open problems: (i) the common practice of regularizing the flow gradient induces a bias towards fronto-parallel flows (a.k.a. staircasing), which is particularly pronounced when using robust penalty functions like the Total Variation, and (ii) variational models are typically minimized by applying local optimization schemes, which are prone to get stuck in local minima. To address problem (i), we introduce a robust regularization approach based on decorrelated second-order derivatives, derive an efficient numerical solution scheme, and demonstrate that this regularizer does not induce staircasing artifacts. We also propose an optimization strategy that facilitates large moves in the solution space of variational models by constructing and solving a series of auxiliary binary problems, thereby outlining one potential solution for problem (ii). Furthermore, we develop a global flow estimation technique that accommodates any positive concave, monotonic regularizer, e.g. truncated Total Variation or generalized Laplacian, and almost arbitrary data terms. Despite this flexibility, the resulting optimization problem remains convex and therefore its globally optimal solution can be computed in polynomial time. We conclude with an extensive evaluation on the challenging Middlebury optical flow data sets, demonstrating the viability of the proposed solutions. In spite of our focus on motion estimation, the presented secondorder regularizer as well as the optimization strategies are applicable to other problems in computer vision, e.g. denoising, inpainting, and other correspondence problems.