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

Erik Bylow

Research output: ThesisDoctoral Thesis (compilation)

475 Downloads (Pure)


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.
Original languageEnglish
  • Olsson, Carl, Supervisor
  • Kahl, Fredrik, Supervisor
  • Andersson, Fredrik, Supervisor
ISBN (Print)978-91-7753-622-2
ISBN (electronic) 978-91-7753-623-9
Publication statusPublished - 2018

Bibliographical note

Defence details
Date: 2018-04-20
Time: 13:15
Place: lecture hall MH:Hörmandersalen, Centre for Mathematical Sciences, Sölvegatan 18, Lund University, Faculty of Engineering LTH, Lund
External reviewer
Name: Zach, Christopher
Title: Doctor
Affiliation: Toshiba Research Cambridge, UK

Subject classification (UKÄ)

  • Computer Vision and Robotics (Autonomous Systems)

Free keywords

  • Computer Vision
  • 3D Reconstruction


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