Abstract
We present a novel approach to the weighted graph-matching problem in computer vision, based on a convex relaxation of the underlying combinatorial optimization problem. The approach always computes a lower bound of the objective function, which is a favorable property in the context of exact search algorithms. Furthermore, no tuning parameters have to be selected by the user, due to the convexity of the relaxed problem formulation.
For comparison, we implemented a recently published deterministic annealing approach and conducted numerous experiments for both established benchmark experiments from combinatorial mathematics, and for random ground-truth experiments using computer-generated graphs. Our results show similar performance for both approaches. In contrast to the convex approach, however, four parameters have to be determined by hand for the annealing algorithm to become competitive.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M. Herbert, J. Ponce, T. Boult, and A. Gross, editors. Object Representation in Computer Vision, volume 994 of Lect. Not. Comp. Sci. Springer-Verlag, 1995.
H.H. Bültho and S. Edelman. Psychophysical support for a two-dimensional view interpolation theory of object recognition. Proc. Nat. Acad. Science,, 92:60–64, 1992.
S. Umeyama. An eigendecomposition approach to weighted graph matching problems. IEEE Trans. Patt. Anal. Mach. Intell., 10(5):695–703, 1988.
G. Vosselmann. Relational matching, volume 628 of Lect. Not. Comp. Sci. Springer, 1992.
W.K. Konen, T. Maurer, and C. von der Malsburg. A fast dynamic link matching algorithm for invariant pattern recognition. Neural Networks, 7(6/7):1019–1030, 1994.
S. Gold and A. Rangarajan. A graduated assignment algorithm for graph matching. IEEE Trans. Patt. Anal. Mach. Intell., 18(4):377–388, 1996.
A.D.J. Cross, R.C. Wilson, and E.R. Hancock. Inexact graph matching using genetic search. Pattern Recog., 30(6):953–970, 1997.
A.D.J. Cross and E.R. Hancock. Graph-matching with a dual-step em algorithm. IEEE Trans. Patt. Anal. Mach. Intell., 20(11):1236–1253, 1998.
W. Förstner. A framework for low level feature extraction. In J.O. Eklundh, editor, Computer Vision-ECCV’ 94, volume 801 of Lect. Not. Comp. Sci., pages 61–70. Springer-Verlag, 1994.
S. Ishii and M. Sato. Doubly constrained network for combinatorial optimization. Neurocomputing, 2001. to appear.
G. Finke, R.E. Burkard, and F. Rendl. Quadratic assignment problems. Annals of Discrete Mathematics, 31:61–82, 1987.
K.M. Anstreicher and N.W. Brixius. A new bound for the quadratic assignment problem based on convex quadratic programming. Technical report, Dept. of Management Sciences, University of Iowa, 1999.
R.E. Burkard, S. Karisch, and F. Rendl. Qaplib ‐ a quadratic assignment problem library. J. Global Optimization, 10:391–403, 1997.
H. Bunke. Error correcting graph matching: On the in uence of the underlying cost function. IEEE Trans. Patt. Anal. Mach. Intell., 21(9):917–922, 1999.
A. Rangarajan, A. Yuille, and E. Mjolsness. Convergence properties of the softassign quadratic assignment algorithm. Neural Computation, 11(6):1455–1474, 1999.
C. Schellewald, S. Roth, and C. Schnörr. Evaluation of spectral and convex relaxations to the quadratic assignment of relational object views. Comp. science series, technical report, Dept. Math. and Comp. Science, University of Mannheim, Germany, 2001. in preparation.
S.W. Hadley, F. Rendl, and H. Wolkowicz. A new lower bound via projection for the quadratic assignment problem. Math. of Operations Research,, 17:727–739, 1992.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Schellewald, C., Roth, S., Schnörr, C. (2001). Evaluation of Convex Optimization Techniques for the Weighted Graph-Matching Problem in Computer Vision. In: Radig, B., Florczyk, S. (eds) Pattern Recognition. DAGM 2001. Lecture Notes in Computer Science, vol 2191. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45404-7_48
Download citation
DOI: https://doi.org/10.1007/3-540-45404-7_48
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42596-0
Online ISBN: 978-3-540-45404-5
eBook Packages: Springer Book Archive