Fast and robust parameter estimation in the polynomial regression model of images

Roman M. Palenichka; Iryna B. Ivasenko

doi:10.1117/12.341096

5 March 1999 Fast and robust parameter estimation in the polynomial regression model of images

Roman M. Palenichka, Iryna B. Ivasenko

Proceedings Volume 3646, Nonlinear Image Processing X; (1999) https://doi.org/10.1117/12.341096
Event: Electronic Imaging '99, 1999, San Jose, CA, United States

Abstract

In the proposed paper, the problem of robust estimation of the polynomial regression parameters is considered with application to image processing. The polynomial regression model states that the intensity function of an image can be represented as a polynomial function of defined order within a sample window plus independent noise which is assumed to be Gaussian distributed with a small fracture of outliers. The developed procedure for robust estimation of the polynomial regression parameters is based on computation of partial optimal estimates using the least squares method which exploits the fact that the majority of the regression residuals have Gaussian distribution. The final estimate is selected by the principle of maximum a posteriori probability. In direct form, the proposed technique is computationally expensive. Since the regression parameters can be represented as a linear combination of local moments, it allows to decrease the computational complexity of the proposed technique by an order (i.e. by O(N), where N is the size of the used subsamples) because local moments can be calculated recursively. The estimated regression parameters can be used for robust estimation of image and background intensity, noise variance, as well as for adaptive image filtering and segmentation.

Citation Download Citation

Roman M. Palenichka and Iryna B. Ivasenko "Fast and robust parameter estimation in the polynomial regression model of images", Proc. SPIE 3646, Nonlinear Image Processing X, (5 March 1999); https://doi.org/10.1117/12.341096

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