@phdthesis{dissertation, author = {Kolev, Kalin}, title = {Convexity in Image-Based 3D Surface Reconstruction}, year = {2012}, school = {Technische Universität München}, pages = {162}, language = {en}, abstract = {The reconstruction of three-dimensional geometry from images is one of the fundamental problems in computer vision and has been exposed to an intensive exploration in recent years. While many of the existing methods manifest considerable accuracy, they suffer from lacking robustness due to the absence of any globality guarantees of the computed result. In this work, we present convex optimization as a powerful tool for shape estimation and demonstrate its applicability to the image-based reconstruction problem. In particular, we show how different paradigms like shape-from-silhouettes, multiview stereo or the integration of silhouettes and stereo can be cast as convex optimization problems. In all cases, the obtained solution is a globally optimal one with respect to the underlying model or lies within an energetic bound of the optimal one. The practical value of convex formulations in this context is additionally emphasized by a quantitative comparison to established discrete graph cut methods. It turns out that continuous convex models prove superior to discrete counterparts in terms of metrication accuracy, potential for parallel computing and memory requirements. }, keywords = {convex optimization, image-based modeling, 3D segmentation}, note = {}, url = {https://mediatum.ub.tum.de/1079897}, }