On Wednesday 18th of April 2018 Erik Bylow has nailed his PhD Theses with title "Optimization Methods for 3D Reconstruction: Depth Sensors, Distance Functions and Low-Rank Models"
This thesis explores methods for estimating 3D models using depth sensors and finding low-rank approximations of matrices. In
the first part we focus on how to estimate the movement of a depth camera and creating a 3D model of the scene. Given an
accurate estimation of the camera position, we can produce dense 3D models using the images obtained from the camera. We
present algorithms that are both accurate, robust and in addition, fast enough for online 3D reconstruction in real-time. The
frame rate varies between about 5-20 Hz. It is shown in experiments that these algorithms are viable for several different
applications such as autonomous quadrocopter navigation and object reconstruction.
In the second part we study the problem of finding a low-rank approximation of a given matrix. This has several applications in
computer vision such as rigid and non-rigid Structure from Motion, denoising, photometric stereo and so on. Two convex relaxations which take both the rank function and a data term into account are introduced and analyzed together with a non-
convex relaxation. It is shown that these methods often avoid shrinkage bias and give better results than the common heuristic of replacing the rank function with the nuclear norm.