Robustizing robust M-estimation using deterministic annealing

Abstract This paper presents a modified robust M-estimator referred to as the annealing M-estimator (AM-estimator) to avoid problems with the M-estimator. The AM-estimator combines the annealing technique into the M-estimator. It has the following advantages: it approximates the global solution regardless of the initialization. It involves no scale estimator nor free parameters, avoiding the unreliability therein, nor does it need order statistics such as the median and hence no sorting. Experimental results show that the AM-estimator is very stable and has an elegant behavior with respect to percentage of outliers and noise variance.

[1]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[2]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[3]  Kim L. Boyer,et al.  The Robust Sequential Estimator: A General Approach and its Application to Surface Organization in Range Data , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[4]  A. R. Hanson,et al.  Robust estimation of camera location and orientation from noisy data having outliers , 1989, [1989] Proceedings. Workshop on Interpretation of 3D Scenes.

[5]  D. Shulman,et al.  Regularization of discontinuous flow fields , 1989, [1989] Proceedings. Workshop on Visual Motion.

[6]  R. H. Myers.  Classical and modern regression with applications , 1986 .

[7]  Andrew Stein,et al.  Robust statistics in shape fitting , 1992, Proceedings 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[8]  C Koch,et al.  Analog "neuronal" networks in early vision. , 1986, Proceedings of the National Academy of Sciences of the United States of America.

[9]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[10]  Xinhua Zhuang,et al.  Pose estimation from corresponding point data , 1989, IEEE Trans. Syst. Man Cybern..

[11]  Stan Z. Li,et al.  Markov Random Field Modeling in Computer Vision , 1995, Computer Science Workbench.

[12]  Geoffrey E. Hinton,et al.  A Learning Algorithm for Boltzmann Machines , 1985, Cogn. Sci..

[13]  Layne T. Watson,et al.  Robust window operators , 1988, [1988 Proceedings] Second International Conference on Computer Vision.

[14]  Rangasami L. Kashyap,et al.  Robust image modeling techniques with an image restoration application , 1988, IEEE Trans. Acoust. Speech Signal Process..

[15]  Stan Z. Li,et al.  Discontinuous MRF prior and robust statistics: a comparative study , 1995, Image Vis. Comput..

[16]  Stan Z. Li,et al.  On Discontinuity-Adaptive Smoothness Priors in Computer Vision , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[17]  Andrew Blake,et al.  Visual Reconstruction , 1987, Deep Learning for EEG-Based Brain–Computer Interfaces.

[18]  Jean-Michel Jolion,et al.  Robust Clustering with Applications in Computer Vision , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[19]  Peng Zhang,et al.  A Highly Robust Estimator Through Partially Likelihood Function Modeling and Its Application in Computer Vision , 1992, IEEE Trans. Pattern Anal. Mach. Intell..