A study on Rényi entropy and Shannon entropy of image segmentation based on finite multivariate skew t distribution mixture model

Image segmentation technology has been widely used in various business and social fields. In recent years, more and more scholars have studied the theories in this field. Many models and methods have good effects in image segmentation. However, as people's demand for image is getting higher and higher, people often face images with complex structure and multimode, which makes us need to study and analyze the theory of image segmentation more deeply. In this paper, we study the Rényi entropy and Shannon entropy of finite multivariate skew t mixture distribution (this distribution was proposed based on Sahu and Branco (2003; https://doi.org/10.2307/3316064), and it has better properties and wider application range than the traditional skew t distribution). In addition to the specific calculation results of the two kinds of entropy, we use Hölder inequality and polynomial theorem to obtain the upper bound and lower bound of the two kinds of entropy of finite multivariate skew t mixture distribution.