This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
The Robust Sequential Estimator: A General Approach and its Application to Surface Organization in Range Data
October 1994 (vol. 16 no. 10)
pp. 987-1001

Presents an autonomous, statistically robust, sequential function approximation approach to simultaneous parameterization and organization of (possibly partially occluded) surfaces in noisy, outlier-ridden (not Gaussian), functional range data. At the core of this approach is the Robust Sequential Estimator, a robust extension to the method of sequential least squares. Unlike most existing surface characterization techniques, the authors' method generates complete surface hypotheses in parameter space. Given a noisy depth map of an unknown 3-D scene, the algorithm first selects appropriate seed points representing possible surfaces. For each nonredundant seed it chooses the best approximating model from a given set of competing models using a modified Akaike Information Criterion. With this best model, each surface is expanded from its seed over the entire image, and this step is repeated for all seeds. Those points which appear to be outliers with respect to the model in growth are not included in the (possibly disconnected) surface. Point regions are deleted from each newly grown surface in the prune stage. Noise, outliers, or coincidental surface alignment may cause some points to appear to belong to more than one surface. These ambiguities are resolved by a weighted voting scheme within a 5/spl times/5 decision window centered around the ambiguous point. The isolated point regions left after the resolve stage are removed and any missing points in the data are filled by the surface having a majority consensus in an 8-neighborhood.

[1] P. J. Huber,Robust Statistics. New York: John Wiley, 1981.
[2] P. J. Rousseeuw and A. M. Leroy,Robust Regression&Outlier Detection. New York: Wiley, 1987.
[3] R. M. Haralick, "Computer vision theory: The lack thereof,"Comput. Vision Graphics Image Processing, vol. 36, pp. 372-386, 1986.
[4] W. Förstner, "Reliability analysis of parameter estimation in linear models with applications to mensuration problems in computer vision,"Comput. vision, Graphics, Image Processing, vol. 40, pp. 273-310, 1987.
[5] P. J. Besl, J. B. Birch, and L. T. Watson, "Robust window operations," inProc. IEEE 2nd Int. Conf. Comp. vision, Dec. 1988, pp. 591-600.
[6] O. Faugeras and M. Berthod, "Improving consistency and reducing ambiguity in stochastic labeling: An optimization approach,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-3, pp. 412-424, July 1981.
[7] P. Meer, D. Mintz, A. Rosenfeld, and D. Kim, "Robust regression methods for computer vision: A review,"Int. J. Comput. Vision, vol. 6, pp. 59-70, Apr. 1991.
[8] H. Akaike, "Information theory and an extention of the maximum likelihood principle," inSecond Int. Symp. Inform. Theory, 1973, pp. 267-281.
[9] M. J. Mirza and K. L. Boyer, "Performance evaluation of a class of M-estimators for surface parameter estimation in noisy range data,"IEEE Trans. Robotics Automat., vol. 9, pp. 75-85, Feb. 1993.
[10] M. J. Mirza and K. L. Boyer, "An information theoretic robust sequential procedure for surface order selection in noisy range data," inProc. 1992 IEEE Conf. Comput. Vision Pattern Recognit., June 1992, pp. 366-371.
[11] P. Besl and R. Jain, "Invariant surface characteristics for 3-D object recognition in range images,"Comput. Vision Graphics Image Processing, 1986, pp. 33-80, vol. 33.
[12] M. Brady, J. Ponce, A. Yuille, and H. Asada, "Describing surfaces,"Comput. Vision, Graphics, and Image Processing, vol. 32, pp. 1-28, 1985.
[13] T. Fan, G. Medioni, and R. Nevatia, "Description of surfaces from range data using curvature properties," inProc. 1986 IEEE Conf. on Comput. Vision and Pattern Recognition, May 1986, pp. 86-91.
[14] R. Hoffman and A. K. Jain, "Segmentation and classification of range images,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-9, pp. 608-619, 1987.
[15] A. K. Jain and S. G. Nadabar, "Range image segmentation using MRF models," inMarkov Random Field Models, R. Chellappa and A. K. Jain, Eds. San Diego, CA: Academic Press, 1993, pp. 543-572.
[16] T. Fan, G. Medioni, and R. Nevatia, "Surface segmentation and description from curvature features," inProc 1987 DARPA Image Understanding Workshop, 1987, pp. 351-359.
[17] T. E. Boult and M. Lerner, "Energy-based segmentation of very sparse range surfaces," inProc. IEEE Int. Conf. Robotics Automat., 1990, pp. 232-237.
[18] P. J. Besl and R. C. Jain, "Segmentation through variable-order surface fitting,"IEEE Trans. Pattern. Anal. Machine Intell., vol. 9, no. 2, pp. 167-192, 1988.
[19] M. W. Koch and R. L. Kashyap, "Using polygons to recognize and locate partially occluded objects,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-9, no. 4, pp. 483-494, July 1987.
[20] R. C. Boles and R. A. Cain, "Recognizing and locating partially visible object: The local-feature-focus method,"Int. J. Robotics Res., vol. 1, pp. 57-81, Fall 1982.
[21] R. B. Fisher,From Surfaces to Objects: Computer Vision and Three Dimensional Science Analysis. New York: John Wiley, 1989.
[22] G. E. P. Box and N. R. Draper,Empirical Model-Buiding and Response Surfaces. New York: John Wiley, 1987.
[23] A. E. Beaton and J. W. Tukey, "The Fitting of Power Series, Meaning Polynomials, Illustrated on Band-Spectroscopic Data,"Technometrics, Vol.16, pp. 147-185, May 1974.
[24] C. Goodall, "M-Estimator of Location: An Outline of the Theory," inUnderstanding, Robust and Exploratory Data Analysis, D. C. Hoaglin, F. Mosteller, and J. W. Tukey, Eds. New York: John Wiley, 1983, pp. 339-403.
[25] D. Andrews, P. Bickel, F. Hampel, P. Huber, W. Rogers, and J. Tukey,Robust Estimates of Location: Survey and Advances, Princeton, NJ: Princeton Univ. Press, 1972.
[26] T. C. Hsia,System Identification: Least-Squares Methods. Lexington, MA: Lexington Books, 1976.
[27] H. Bozdogan, "Model selection and Akaike's information criterion (AIC): The general theory and its analytical extensions,"Psychometrika, vol. 52, no. 3, pp. 345-370, 1987.
[28] Y. Shirai,Three-Dimensional Computer Vision. New York: Springer-Verlag, 1987.

Index Terms:
function approximation; estimation theory; image segmentation; information theory; decision theory; robust sequential estimator; surface organization; range data; autonomous statistically robust sequential function approximation; parameterization; partially occluded surfaces; noisy outlier-ridden functional range data; sequential least squares; surface characterization techniques; surface hypotheses; parameter space; noisy depth map; unknown 3-D scene; seed points; modified Akaike Information Criterion; prune stage; coincidental surface alignment; weighted voting scheme; 5/spl times/5 decision window; ambiguous point; majority consensus
Citation:
K.L. Boyer, M.J. Mirza, G. Ganguly, "The Robust Sequential Estimator: A General Approach and its Application to Surface Organization in Range Data," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 16, no. 10, pp. 987-1001, Oct. 1994, doi:10.1109/34.329010
Usage of this product signifies your acceptance of the Terms of Use.