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

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.

[1]  Thomas M. Breuel.  A Comparison of Search Strategies for Geometric Branch and Bound Algorithms , 2002, ECCV.

[2]  Luc Jaulin,et al.  Applied Interval Analysis , 2001, Springer London.

[3]  David M. Mount,et al.  Efficient algorithms for robust feature matching , 1999, Pattern Recognit..

[4]  E. Hansen,et al.  An interval Newton method , 1983 .

[5]  Eldon Hansen,et al.  Global optimization using interval analysis , 1992, Pure and applied mathematics.

[6]  William M. Wells,et al.  Statistical Approaches to Feature-Based Object Recognition , 2004, International Journal of Computer Vision.

[7]  Remco C. Veltkamp,et al.  Reliable and Efficient Pattern Matching Using an Affine Invariant Metric , 1999, International Journal of Computer Vision.

[8]  Thomas M. Breuel,et al.  Finding lines under bounded error , 1996, Pattern Recognit..

[9]  David M. Mount,et al.  Ecient Algorithms for Robust Feature Matching , 1998 .

[10]  Daniel P. Huttenlocher,et al.  Comparing Images Using the Hausdorff Distance , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[11]  William Grimson,et al.  Object recognition by computer - the role of geometric constraints , 1991 .

[12]  H. Baird.  Model-Based Image Matching Using Location , 1985 .

[13]  M. H. van Emden,et al.  Interval arithmetic: From principles to implementation , 2001, JACM.

[14]  Thomas M. Breuel.  Robust least-square-baseline finding using a branch and bound algorithm , 2001, IS&T/SPIE Electronic Imaging.

[15]  Clark F. Olson,et al.  Locating geometric primitives by pruning the parameter space , 2001, Pattern Recognit..

[16]  Frédéric Jurie,et al.  Solution of the Simultaneous Pose and Correspondence Problem Using Gaussian Error Model , 1999, Comput. Vis. Image Underst..

[17]  Thomas M. Breuel,et al.  Fast recognition using adaptive subdivisions of transformation space , 1992, Proceedings 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.