Abstract
This article proposes a new approach to segment a discrete 3-D object into a structure of characteristic topological primitives with attached qualitative features. This structure can be seen itself as a qualitative description of the object, because
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—it is intrinsic to the 3-D object, which means it is stable to rigid transformations (rotations and translations);
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—it is locally defined, and therefore stable to partial occlusions and local modifications of the object structure;
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—it is robust to noise and small deformations, as confirmed by our experimental results.
Our approach concentrates on topological properties of discrete surfaces. These surfaces may correspond to theexternal surface of the objects extracted by a 3-D edge detector, or to theskeleton surface obtained by a new thinning algorithm. Our labeling algorithm is based on very local computations, allowing massively parallel computations and real-time computations.
An indirect result of these topological properties is a new characterization of simple points.
We present a realistic experiment to characterize and locate spatially a complex 3-D medical object using the proposed segmentation of its skeleton.
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References
Ayache, N.; Boissonnat, J.D., Brunet, E., Cohen, L., Chièze, J.P., Geiger, B., Monga, O., Rocchisani, J.M., and Sander, P., 1989. Building highly structured volume representations in 3D medical images,Computer Aided Radiology, Berlin.
Ayache, N., Boissonnat, J.D., Cohen, L., Geiger, B., Lévy-Véhel, J., Monga, O. and Sander, P., 1990. Steps toward the automatic interpretation of 3d images,Workshop on 3D Imaging in Medecine, Travemunde, R.F.A., June, NATO. Edited by Springer.
Bertrand, G., and Malandain, G., 1992a. A new characterization of three-dimensional simple points, Internal report, ESIEE, submitted for publication.
Bertrand, G., and Malandain, G., 1992b. A new topological segmentation of discrete surfaces,Proc. 2nd Europ. Conf. Comput. Vis. pp. 710–714, May 18–23, Santa Margherita, Ligure, Italy.
Borgefors, G., 1984. Distance transformations in arbitrary dimensions,Comput. Vis. Graph. Image Process. 27:321–345.
Gong, W.X., and Bertrand, G., 1990. A simple paralled 3D thinning algorithm,10th Intern. Conf. Patt. Recog. June 17–21, Atlantic City.
Hafford, K.J., and Preston, K., Jr., 1984. Three dimensional skeletonization of elongated solids,Comput. Vis. Graph. Image Process. 27:78–91.
Keskes, N., and Faugeras, O., 1981. Surface simple dansz 3,3éme Congrès Reconnaissance des Formes et d'Intelligence Artificielle, pp. 718–729, AFCET, September.
Kim, C.E., 1984. Three-dimensional digital planes,IEEE Trans. Patt. Anal. Mach. Intell. 6(5):639–645.
Kovalevsky, V.A. 1989. Finite topology as applied to image analysis,Comput. Vis. Graph. Image Process. 46:141–161.
Kong, T.Y., and Rosenfeld, A., 1989. Digital topology: introduction and survey.Comput. Vis. Graph. Image Process. 48:357–393.
Lobregt, S., Verbeck, P.W., and Groen, F.C., 1980. Three-dimensional skeletonization: principle and algorithm,IEEE Trans. Patt. Anal. Mach. Intell. 2(1):75–77.
Malandain, G., and Bertrand, G., 1992. Fast characterization of 3d simple points,11th Intern. Conf. Patt. Recog. August 30–September 3, The Hague.
Malandain, G., Bertrand, G., and Ayache, N., 1991a. Topological classification in digital space. In12th Intern. Conf. lnformat. Process. Med. Imaging, Wye, Kent, England, July. Lecture notes in Computer Science 511, Springer-Verlag: Heidelberg.
Malandain, G., Bertrand, G., and Ayache, N., 1991b. Topological segmentation of discrete surfaces,Proc. IEEE Conf. Comput. Vis. Patt. Recog., June 3–6, Hawaii.
Monga, O., Deriche, R., Malandain, G., and Cocquerez, J.P., 1990. Recursive filtering and edge closing: two primary tools for 3D edge detection.Proc. 1st. Europ. Conf. Comput. Vis., Nice, France, April. Lecture notes in computer science 427, Springer Verlag: New York.
Morgenthaler, D.G., 1980. Three-dimensional digital topology: the genus. Tech. Rpt. 980, Computer Science Center, University of Maryland, College Park, MD 20742, November.
Morgenthaler, D.G., 1981. Three-dimensional simple points: serial erosion, parallel thinning, and skeletonization. Tech. Rpt. 1005, Computer Science Center, University of Maryland, College Park, MD 20742, February.
Morgenthaler, D.G., and Rosenfeld, A., 1980. Surfaces in three-dimensional digital images. Tech. Rpt. 940, Computer Science Center, University of Maryland, College Park, MD 20742, September.
Nakamura, A., and Aizawa, K., 1985. On the recognition of properties of three-dimensional pictures,IEEE Trans. Patt. Anal. Mach. Intell. 7(6):708–713.
Park, C.M., and Rosenfeld, A., 1971. Connectivity and genus in three dimensions. Tech. Rpt. 156, Computer Science Center, University of Maryland, College Park, MD 20742, May.
Rosenfeld, A., 1980. Three-dimensional digital topology. Tech. Rpt. 936, Computer Science Center, University of Maryland, College Park, MD 20742, September.
Sander, P., 1989. Generic curvature features from 3D images.IEEE Trans. Syst. Man. Cybern., special issue on computer vision, November.
Serra, J., 1982.Image Analysis and Mathematical Morphology, vol. 1. Academic Press: San Diego, CA.
Serra, J., 1988.Image Analysis and Mathematical Morphology: Theoretical Advances, vol. 2. Academic Press: San Diego, CA.
Toriwaki, J.I., Yokoi, S., Yonekura, T., and Fukumura, T., 1982. Topological properties and topology-preserving transformation of a three-dimensional binary picture.Proc. 6th Intern. Conf. Patt. Recog. pp. 414–419, October, Munich.
Tsao, Y.F., and Fu, K.S., 1981. A parallel thinning algorithm for 3D pictures,Comput. Graph. Image Process. 17:315–331.
Tsao, Y.F. and Fu, K.S., 1982. A 3D parallel skeletonization thinning algorithm,Proc. IEEE Conf. Patt. Recog. Image Process. pp. 678–683.
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Malandain, G., Bertrand, G. & Ayache, N. Topological segmentation of discrete surfaces. Int J Comput Vision 10, 183–197 (1993). https://doi.org/10.1007/BF01420736
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DOI: https://doi.org/10.1007/BF01420736