Robust Computer Vision through Kernel Density Estimation

Two new techniques based on nonparametric estimation of probability densities are introduced which improve on the performance of equivalent robust methods currently employed in computer vision. The first technique draws from the projection pursuit paradigm in statistics, and carries out regression M-estimation with a weak dependence on the accuracy of the scale estimate. The second technique exploits the properties of the multivariate adaptive mean shift, and accomplishes the fusion of uncertain measurements arising from an unknown number of sources. As an example, the two techniques are extensively used in an algorithm for the recovery of multiple structures from heavily corrupted data.

[1]  Dorin Comaniciu,et al.  Mean Shift: A Robust Approach Toward Feature Space Analysis , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[2]  R. Zamar.  Robust estimation in the errors-in-variables model , 1989 .

[3]  Michal Irani,et al.  Video indexing based on mosaic representations , 1998, Proc. IEEE.

[4]  Dorin Comaniciu,et al.  The Variable Bandwidth Mean Shift and Data-Driven Scale Selection , 2001, ICCV.

[5]  Harpreet S. Sawhney,et al.  Independent motion detection in 3D scenes , 1999, Proceedings of the Seventh IEEE International Conference on Computer Vision.

[6]  David G. Stork,et al.  Pattern Classification , 1973 .

[7]  David G. Stork,et al.  Pattern classification, 2nd Edition , 2000 .

[8]  C. D. Kemp,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[9]  Matthew P. Wand,et al.  Kernel Smoothing , 1995 .

[10]  Kenichi Kanatani,et al.  Motion segmentation by subspace separation and model selection , 2001, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001.

[11]  Peter J. Rousseeuw,et al.  Robust Regression and Outlier Detection , 2005, Wiley Series in Probability and Statistics.

[12]  Peter Meer,et al.  Robust regression for data with multiple structures , 2001, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001.

[13]  Leo Breiman,et al.  Bagging Predictors , 1996, Machine Learning.

[14]  Larry D. Hostetler,et al.  The estimation of the gradient of a density function, with applications in pattern recognition , 1975, IEEE Trans. Inf. Theory.

[15]  Josef Kittler,et al.  Combining multiple classifiers by averaging or by multiplying? , 2000, Pattern Recognit..

[16]  Takeo Kanade,et al.  A Multibody Factorization Method for Independently Moving Objects , 1998, International Journal of Computer Vision.

[17]  Robin Sibson,et al.  What is projection pursuit , 1987 .

[18]  Werner A. Stahel,et al.  Discussion: Projection Pursuit , 1985 .