Solving Quadratically Constrained Geometrical Problems using Lagrangian Duality

Carl Olsson, Anders P Eriksson

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

Abstract

In this paper we consider the problem of solving different pose and registration problems under rotational constraints. Traditionally, methods such as the iterative closest point algorithm have been used to solve these problems. They may however get stuck in local minima due to the non-convexity of the problem. In recent years methods for finding the global optimum, based on Branch and Bound and convex under-estimators, have been developed. These methods are provably optimal, however since they are based on global optimization methods they are in general more time consuming than local methods. In this paper we adopt a dual approach. Rather than trying to find the globally optimal solution we investigate the quality of the solutions obtained using Lagrange duality. Our approach allows its to formulate a single convex semidefinite program that approximates the original problem well.
Original languageEnglish
Title of host publication19th International Conference on Pattern Recognition, 2008. ICPR 2008.
PublisherIEEE - Institute of Electrical and Electronics Engineers Inc.
Pages2469-2473
ISBN (Print)978-1-4244-2174-9
DOIs
Publication statusPublished - 2008
Event19th International Conference on Pattern Recognition (ICPR 2008) - Tampa, FL, Tampa, FL
Duration: 2008 Dec 82008 Dec 11

Publication series

Name
ISSN (Print)1051-4651

Conference

Conference19th International Conference on Pattern Recognition (ICPR 2008)
CityTampa, FL
Period2008/12/082008/12/11

Subject classification (UKÄ)

  • Mathematics

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