Daniel Cremers Technische Universtitat München The reconstruction and understanding of 3D shape from images is among the central challenges in computer vision. In my presentation, I will focus on algorithms for computing correspondence between two 3D shapes. Specifically I will discuss advantages and drawbacks of combinatorial solutions versus direct solutions. Whereas combinatorial approaches aim at convexifying the combinatorial matching challenge and thereby help to avoid local minima in the correspondence estimation, the latter approaches are often significantly faster and are more easily generalized to tackle related challenges like shape interpolation and extrapolation.