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Comparing Images Using the Hausdorff Distance
September 1993 (vol. 15 no. 9)
pp. 850-863

The Hausdorff distance measures the extent to which each point of a model set lies near some point of an image set and vice versa. Thus, this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another. Efficient algorithms for computing the Hausdorff distance between all possible relative positions of a binary image and a model are presented. The focus is primarily on the case in which the model is only allowed to translate with respect to the image. The techniques are extended to rigid motion. The Hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived. The method is quite tolerant of small position errors such as those that occur with edge detectors and other feature extraction methods. It is shown that the method extends naturally to the problem of comparing a portion of a model against an image.

[1] A. Aho, J. Hopcroft, and J. Ullman,Data Structures and Algorithms. Reading, MA: Addison-Wesley, 1983.
[2] H. Alt, B. Behrends, and J. Blomer, "Measuring the resemblance of polygonal shapes," inProc. Seventh ACM Symp. Comput. Geometry, 1991.
[3] E. Arkin, L. P. Chew, D. P. Huttenlocher, K. Kedem, and J. S. B. Mitchell, "An efficiently computable metric for comparing polygonal shapes,"IEEE Trans. Patt. Anal. Machine Intell., vol. 13, no. 3, pp. 209-216, 1991.
[4] P. J. Besl and R. C. Jain, "Three-dimensional object recognition,"ACM Comput. Surveys, vol. 17, no. 1, pp. 75-145, Mar. 1985.
[5] G. Borgefors, "Distance transformations in digital images,"Comput. Vision, Graphics, Image Processing, vol. 34, pp. 334-371, 1986.
[6] J. F. Canny, "A computational approach to edge detection,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 679-697, 1986.
[7] L. P. Chew and K. Kedem, "Improvements on geometric pattern matching problems," to be published inProc. Scand. Workshop Automata Theory.
[8] R.T. Chin and C. R. Dyer, "Model-based recognition in robot vision,"ACM Comput. Surveys, vol. 18, no. 1, pp. 67-108, Mar. 1986.
[9] A. Csaszar,General Topology. Bristol: Adam Hilger, 1978.
[10] P. E. Danielsson, "Euclidean distance mapping,"Comput. Graphics Image Processing, vol. 14, pp. 227-248, 1980.
[11] W.E.L. Grimson,Object Recognition by Computer: The Role of Geometric Constraints, MIT Press, Cambridge, Mass., 1990.
[12] D. P. Huttenlocher and K. Kedem, "Computing the minimum Hausdorff distance for point sets under translation," inProc. ACM Symp. Computational Geometry, 1990, pp. 340-349.
[13] D. P. Huttenlocher, K. Kedem, and J. M. Kleinberg, "On dynamic Voronoi diagrams and the minimum Hausdorff distance for point sets under Euclidean motion in the plane," to be published inProc. Eighth ACM Symp. Computat. Geometry.
[14] D. P. Huttenlocher, K. Kedem, and M. Sharir, "The upper envelope of Voronoi surfaces and its applications," inProc. Seventh ACM Symp. Computat. Geometry, 1991, pp. 194-293.
[15] D. W. Paglieroni, "Distance transforms: Properties and machine vision applications,"Comput. Vision Graphics Image Processing: Graphical Models Image Processing, vol. 54, no. 1, pp. 56-74, 1992.
[16] F. P. Preparata and M. I. Shamos,Computational Geometry, an Introduction. New York: Springer-Verlag, 1985.
[17] A. Rosenfeld and A. Kak,Digital Picture Processing, New York: Academic, 1976.

Index Terms:
image comparison; translation; position error tolerance; Hausdorff distance; binary image; rigid motion; shape comparison methods; image processing
Citation:
D.P. Huttenlocher, G.A. Klanderman, W.A. Rucklidge, "Comparing Images Using the Hausdorff Distance," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 15, no. 9, pp. 850-863, Sept. 1993, doi:10.1109/34.232073
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