Abstract
A Robust Approach to Estimation of Parametric Models. This article presents a robust method for estimation of parametric models. The method consists of two procedures: model-recovery and model-selection. The model-recovery procedure systematically recovers a redundant set of parametric models in a local-to-global fashion, iteratively combining data classification and parameter estimation. The model-selection procedure, defined as a quadratic Boolean problem, then searches for the subset of the recovered models which produce the simplest global description. To achieve a computationally efficient method the model-recovery and the model-selection are combined in an iterative way. The main features of the method are a high degree of resistance to outliers and the insensitivity to incorrect initial estimates. The method has been successfully applied to linear as well as nonlinear parameter estimation problems, e.g. for recovering variable-order bivariate polynomials and superquadric models in range images, and parametric curve models in edge images.
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This work was supported in part by The Ministry for Science and Technology of The Republic of Slovenia (Projects P2-1122 and J2-6187).
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References
Besl, P. J.: Surfaces in range image understanding. New York: Springer 1988.
Besl, P. J., Birch, J. B., Watson, L. T.: Robust window operators. In: Proceedings of the 2nd International Conference on Computer Vision, pp. 591–600. Tampa, FL, December 1988. Washington: IEEE Computer Society Press 1988.
Chen, D. S.: A data-driven intermediate level feature extraction algorithm. IEEE Trans. Pattern Anal. Machine Intell. PAMI-11, 749–758 (1989).
Fischler, M. A., Bolles, R. C.: Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography. Commun. ACM 24, 381–395 (1981).
Fua, P., Hanson, A. J.: Objective functions for feature discrimination. In: Proceedings of the 11th International Joint Conference on Artificial Intelligence, pp. 1596–1602. Detroit, MI, August 1989. San Mateo: Morgan Kaufmann.
Huber, P. J.: Robust statistics. New York: Wiley 1981.
Kim, D. Y., Kim, J. J., Meer, P., Mintz, D., Rosenfeld, A.: Robust computer vision: A least-median of squares based approach. In: Proceedings of the Image Understanding Workshop, pp. 1117–1134. Palo Alto, CA, May 1989. San Mateo: Morgan Kaufmann.
Leclerc, Y. G.: Constructing simple stable descriptions for image partitioning. Int. J. Comput. Vision 3, 73–102 (1989).
Leonardis, A.: Image analysis using parametric models: Model-recovery and model-selection paradigm. PhD thesis, Faculty of Electrical Engineering and Computer Science, University of Ljubljana, Slovenia, May 1993. Technical Report LRV-93-3.
Leonardis, A., Bajcsy, R.: Finding parametric curves in an image. In: Proceedings of The Second European Conference on Computer Vision—ECCV-92, Santa Margherita Ligure, Italy (Sandini, G., ed.), pp. 653–657. Berlin, Heidelberg, New York, Tokyo: Springer 1992 (Lecture Notes in Computer Science, Vol. 588).
Leonardis, A., Gupta, A., Bajcsy, R.: Segmentation of range images as the search for geometric parametric models. Int. J. Comput. Vision 14, 253–277 (1995).
Leonardis, A., Solina, F., Macerl, A.: A direct recovery of superquadric models in range images using recover-and-select paradigm. In: Proceedings of The Third European Conference on Computer Vision-ECCV-94, Stockholm, Sweden (Eklundh, J.-O., ed.), pp. 309–318. Berlin, Heidelberg, New York, Tokyo: Springer 1994 (Lecture Notes in Computer Science, Vol. 800).
Li, G.: Robust regression. In: Exploring data tables, trends and shapes (Hoaglin, D. C., Mosteller, F., Tukey, J. W., eds.), pp. 281–343. New York: J. Wiley 1985.
Meer, P., Mintz, D., Rosenfeld, A., Kim, D. Y.: Robust regression methods for computer vision: A review. Int. J. Comput. Vision 6, 59–70 (1991).
Mirza, M. J., Boyer, K. L.: Performance evaluation of a class of M-estimators for surface parameter estimation in noisy range data. IEEE Trans. Robotics Automation 9, 75–85 (1993).
Pentland, A. P.: Part segmentation for object recognition. Neural Comput. 1, 82–91 (1989).
Rousseuw, P. J., Leroy, A. M.: Robust regression and outlier detection. New York: Wiley 1987.
Schunck, B. G.: Robust computational vision. In: Proceedings of the International Workshop on Robust Computer Vision, Seattle, WA, October 1990.
Sinha, S. S., Schunck, B. G.: A two-stage algorithm for discontinuity-preserving surface reconstruction. IEEE Trans. Pattern Anal. Machine Intell. PAMI-14, 36–55 (1992).
Solina, F., Bajcsy, R.: Recovery of parametric models from range images: The case for superquadrics with global deformations. IEEE Trans. Pattern Anal. Machine Intell. PAMI-12, 131–147 (1990).
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© 1996 Springer-Verlag Wien
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Leonardis, A. (1996). A Robust Approach to Estimation of Parametric Models. In: Kropatsch, W., Klette, R., Solina, F., Albrecht, R. (eds) Theoretical Foundations of Computer Vision. Computing Supplement, vol 11. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6586-7_7
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DOI: https://doi.org/10.1007/978-3-7091-6586-7_7
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