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

Bylow, Erik LU (2018)
Abstract
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... (More)
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. (Less)
Please use this url to cite or link to this publication:
author
supervisor
opponent
  • Doctor Zach, Christopher, Toshiba Research Cambridge, UK
organization
publishing date
type
Thesis
publication status
published
subject
keywords
Computer Vision, 3D Reconstruction
publisher
Department of Mathematics, Lund University
defense location
lecture hall MH:Hörmandersalen, Centre for Mathematical Sciences, Sölvegatan 18, Lund University, Faculty of Engineering LTH, Lund
defense date
2018-04-20 13:15:00
ISBN
978-91-7753-623-9
978-91-7753-622-2
language
English
LU publication?
yes
id
a8a053ef-58da-42f5-b05d-69491b07c787
date added to LUP
2018-03-26 13:15:41
date last changed
2018-11-21 21:38:53
@phdthesis{a8a053ef-58da-42f5-b05d-69491b07c787,
  abstract     = {This thesis explores methods for estimating 3D models using depth sensors and<br/>finding low-rank approximations of matrices. In the first part we focus on how to<br/>estimate the movement of a depth camera and creating a 3D model of the scene.<br/>Given an accurate estimation of the camera position, we can produce dense 3D<br/>models using the images obtained from the camera. We present algorithms that<br/>are both accurate, robust and in addition, fast enough for online 3D reconstruction<br/>in real-time. The frame rate varies between about 5-20 Hz. It is shown in<br/>experiments that these algorithms are viable for several different applications such<br/>as autonomous quadrocopter navigation and object reconstruction.<br/><br/>In the second part we study the problem of finding a low-rank approximation<br/>of a given matrix. This has several applications in computer vision such as rigid<br/>and non-rigid Structure from Motion, denoising, photometric stereo and so on.<br/>Two convex relaxations which take both the rank function and a data term into<br/>account are introduced and analyzed together with a non-convex relaxation. It is<br/>shown that these methods often avoid shrinkage bias and give better results than<br/>the common heuristic of replacing the rank function with the nuclear norm.},
  author       = {Bylow, Erik},
  isbn         = {978-91-7753-623-9},
  language     = {eng},
  publisher    = {Department of Mathematics, Lund University},
  school       = {Lund University},
  title        = {Optimization Methods for 3D Reconstruction : Depth Sensors, Distance Functions and Low-Rank Models},
  url          = {https://lup.lub.lu.se/search/files/40457796/Erik_Bylow_inkl_omslag.pdf},
  year         = {2018},
}