Optimization Methods for 3D Reconstruction : Depth Sensors, Distance Functions and Low-Rank Models

Sammanfattning: This thesis explores methods for estimating 3D models using depth sensors andfinding low-rank approximations of matrices. In the first part we focus on how toestimate 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 3Dmodels using the images obtained from the camera. We present algorithms thatare both accurate, robust and in addition, fast enough for online 3D reconstructionin real-time. The frame rate varies between about 5-20 Hz. It is shown inexperiments that these algorithms are viable for several different applications suchas autonomous quadrocopter navigation and object reconstruction.In the second part we study the problem of finding a low-rank approximationof a given matrix. This has several applications in computer vision such as rigidand non-rigid Structure from Motion, denoising, photometric stereo and so on.Two convex relaxations which take both the rank function and a data term intoaccount are introduced and analyzed together with a non-convex relaxation. It isshown that these methods often avoid shrinkage bias and give better results thanthe common heuristic of replacing the rank function with the nuclear norm.