On the use of interval arithmetic in geometric branch and bound algorithms

Authors:
T. M. Breuel
Affiliations:
Palo Alto Research Center, Palo Alto, CA
Venue:
Pattern Recognition Letters
Year:
2003

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Abstract

Branch and bound methods have become established methods for geometric matching over the last decade. This paper presents techniques that improve on previous branch and bound methods in two important ways: they guarantee reliable solutions even in the presence of numerical roundoff error, and they eliminate the need to derive bounding functions manually. These new techniques are compared experimentally with recognition-by-alignment and previous branch and bound techniques on geometric matching problems. Novel methods for non-linear baseline finding and globally optimal robust linear regression using these techniques are described.