$t$ -Tests, $F$ -Tests and Otsu\´s Methods for Image Thresholding

Otsu´s binarization method is one of the most popular image-thresholding methods; Student´s t -test is one of the most widely-used statistical tests to compare two groups. This paper aims to stress the equivalence between Otsu´s binarization method and the search for an optimal threshold that provides the largest absolute Student´s t-statistic. It is then naturally demonstrated that the extension of Otsu´s binarization method to multi-level thresholding is equivalent to the search for optimal thresholds that provide the largest F -statistic through one-way analysis of variance (ANOVA). Furthermore, general equivalences between some parametric image-thresholding methods and the search for optimal thresholds with the largest likelihood-ratio test statistics are briefly discussed.