Globally Optimal Least Squares Solutions for Quasiconvex 1D Vision Problems

Carl Olsson, Martin Byröd, Fredrik Kahl

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceedingpeer-review

2 Citations (SciVal)

Abstract

Solutions to non-linear least squares problems play an essential role in structure and motion problems in computer vision. The predominant approach for solving these problems is a Newton like scheme which uses the: hessian of the function to iteratively find a, local solution. Although fast, this strategy inevitably leeds to issues with poor local minima, and missed global minima. In this paper rather than trying to develop all algorithm that is guaranteed to always work, we show that it is often possible to verify that a local solution is in fact; also global. We present a simple test that verifies optimality of a solution using only a few linear programs. We show oil both synthetic and real data that for the vast majority of cases we are able to verify optimality. Further more we show even if the above test fails it is still often possible to verify that the local solution is global with high probability.
Original languageEnglish
Title of host publicationImage Analysis, Proceedings
PublisherSpringer
Pages686-695
Volume5575
Publication statusPublished - 2009
Event16th Scandinavian Conference on Image Analysis - Oslo, Norway
Duration: 2009 Jun 152009 Jun 18

Publication series

Name
Volume5575
ISSN (Print)1611-3349
ISSN (Electronic)0302-9743

Conference

Conference16th Scandinavian Conference on Image Analysis
Country/TerritoryNorway
CityOslo
Period2009/06/152009/06/18

Subject classification (UKÄ)

  • Mathematics

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