Robust orthogonal linear regression on histogram in small-dimensional spaces

© 2017 E. N. Asvatov, E. I. Ershov, D. P. Nikolaev

Institute for Information Transmission Problems RAS 127051 Moscow, Bolshoi Karetny lane, 19

Received 14 Jul 2017

The article deals with the problem of orthogonal robust linear regression on histograms. It is proved that the evaluation of the M-estimate is equivalent in the given problem with the search for the maximum of a certain convolution and Radon transform of the original histogram. Next, we consider the discretization of the Radon space and its effect on the accuracy of calculating the M-estimate using the Hough transform (HT). Computational experiments have been carried out to analyze the change in the calculation accuracy of the M-estimate in the transition from HT to the fast Hough transform. The question’s essence is how strongly the type of the pattern approximating the line affects the accuracy of calculating the M-estimate. An experimental comparison of the proposed and classical methods realizing the solution of the orthogonal linear regression problem is carried out for the case of two-dimensional and three-dimensional histograms.

Key words: M-estimation, Radon transform, fast Hough transform, linear regression, orthogonal regression, robustness

Cite: Asvatov E. N., Ershov E. I., Nikolaev D. P.. Robastnaya ortogonalnaya lineinaya regressiya dlya malomernykh gistogramm [Robust orthogonal linear regression on histogram in small-dimensional spaces]. Sensornye sistemy [Sensory systems]. 2017. V. 31(4). P. 331-342 (in Russian).

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