On the accuracy of classifiers and the corresponding digital discretely colored images. (Russian) Zbl 1059.62100

Belyaev, Yu. K.

Teor. Jmovirn. Mat. Stat. 66, 15-25 (2002); translation in Theory Probab. Math. Stat. 66, 15-25 (2003).

The author deals with the problem of estimation of the accuracy of discretely colored maps created with the help of classifiers. The digital discretely colored maps consist of sets of pixels. Every pixel is defined by \(\{\{i_1,i_2\},c(i_1,i_2)\}\), where \(\{i_1+\delta_1,i_2+\delta_2\}\), \(\delta_1,\delta_2=0,1\), defines the position of a pixel and \(c(i_1,i_2)\) defines its color. The number of colors is finite. The correct image consists of the set of pixels \(\{\{i_1,i_2\},c(i_1,i_2)\},\{i_1,i_2\}\in \mathcal A_1\), where \(c(i_1,i_2)\) is a correct color.
The author proposes a procedure for estimation of the number of correct colored pixels of the observed image. The classifiers with known probabilities of wrong choice of color are used. In the last part of the article, a method is proposed for estimation of the unknown probabilities of cross-classifications which improves the one proposed by B. Efron and R. Tibshirani [J. Am. Stat. Assoc. 92, No. 438, 548–560 (1997; Zbl 0887.62044)].

Reviewer: Mikhail Moklyachuk (Kyïv)

MSC:

62M40	Random fields; image analysis
62H30	Classification and discrimination; cluster analysis (statistical aspects)
62H35	Image analysis in multivariate analysis
62G09	Nonparametric statistical resampling methods

Keywords:

unbiased estimation; accuracy; digital discretely colored images; pixel; classifier; asymptotic distribution

Citations:

Zbl 0887.62044