Methods for Optimal Model Fitting and Sensor Calibration

Erik Ask

Research output: ThesisDoctoral Thesis (monograph)

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Abstract

The problem of fitting models to measured data has been studied extensively, not least in the field of computer vision. A central problem in this field is the difficulty in reliably find corresponding structures and points in different images, resulting in outlier data. This thesis presents theoretical results improving the understanding of the connection between model parameter estimation and possible outlier-inlier partitions of data point sets. Using these results a multitude of applications can be analyzed in respects to optimal outlier inlier partitions, optimal norm fitting, and not least in truncated norm sense. Practical polynomial time optimal solvers are derived for several applications, including but not limited to multi-view triangulation and image registration.

In this thesis the problem of sensor network self calibration is investigated. Sensor networks play an increasingly important role with the increased availability of mobile, antenna equipped, devices. The application areas can be extended with knowledge of the different sensors relative or absolute positions. We study this problem in the context of bipartite sensor networks. We identify requirements of solvability for several configurations, and present a framework for how such problems can be approached. Further we utilize this framework to derive several solvers, which we show in both synthetic and real examples functions as desired.

In both these types of model estimation, as well as in the classical random samples based approaches minimal cases of polynomial systems play a central role. A majority of the problems tackled in this thesis will have solvers based on recent techniques pertaining to action matrix solvers. New application specific polynomial equation sets are constructed and elimination templates designed for them. In addition a general improvement to the method is suggested for a large class of polynomial systems. The method is shown to improve the computational speed by significant reductions in the size of elimination templates as well as in the size of the action matrices. In addition the methodology on average improves the numerical stability of the solvers.
Original languageEnglish
QualificationDoctor
Awarding Institution
  • Mathematics (Faculty of Engineering)
Supervisors/Advisors
  • Åström, Kalle, Supervisor
  • Enqvist, Olof, Supervisor
  • Oskarsson, Magnus, Supervisor
Award date2014 Oct 10
Publisher
Print ISBNs978-91-7623-097-8, 978-91-7623-096-1
Publication statusPublished - 2014

Bibliographical note

Defence details

Date: 2014-10-10
Time: 13:15
Place: Lecture hall MH:C, Centre for Mathematical Sciences, Sölvegatan 18, Lund University Faculty of Engineering

External reviewer(s)

Name: Björkman, Mårten
Title: Associate Prof.
Affiliation: The Royal Institute of Technology (KTH), Stockholm, Sweden

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Subject classification (UKÄ)

  • Mathematics
  • Computer Vision and Robotics (Autonomous Systems)

Keywords

  • Model Fitting
  • Sensor Networks
  • Computer Vision
  • Polynomial Equations
  • Action Matrix Methods

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