Mathematical optimization is fundamental in computational imaging, where problems often center on minimizing an objective function under various constraints. An important class of optimization problems involves minimal partitioning, which aims to segment data into partitions which meet certain criteria, such as photometric or geometric similarity. This class of problems is computationally demanding as it is has a NP-Hard complexity, which means that the computational effort required to estimate a solution increases exponentially with the size of the data. Consequently, finding (nearly) optimal solutions within a reasonable amount of time is often infeasible. This dissertation presents an analysis of the efficient and effective utilization of minimal partitioning techniques in RGB-D image processing. This is achieved by constraining the underlying optimization problems with the L0 “norm”, which enforces piecewise constant solutions. The first case study analyses the utilization of the L0 “norm” for scene flow estimation, where 3D motions are modeled as rigid transformations and constrained to be piece-wise constant. By substituting the L0 “norm” with the truncated quadratic “norm”, this approach achieves both high accuracy as well as real-time performance. The next focus is on the estimation of geometric models on RGB-D images, specifically to obtain denoised depth and normal values. The novel geometric model definition along with the Cut Pursuit optimization leads to a higher accuracy compared to other model based methods. The third and final enhancement addresses the high computational demands of the preceding Cut Pursuit based method by introducing a stochastic optimization technique. It improves the convergence rate and also the overall runtime efficiency.
Andreas Görlitz (Wed,) studied this question.