$t$-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.