Simplified expression and recursive algorithm of multi-threshold Tsallis entropy

Shaoxun Wang

doi:10.1016/j.eswa.2023.121690

Simplified expression and recursive algorithm of multi-threshold Tsallis entropy

2024-03-01

6

PRE

AI

DOI：10.1016/j.eswa.2023.121690

Original

Original request for help

Save

Abstract

En 中文

Image segmentation is an important step in obtaining image information, and it has always been an extremely critical link in the fields of computer vision and pattern recognition. Because of its simplicity and effectiveness, threshold-based image segmentation technology has received significant attention and research by researchers. Tsallis entropy and Renyi entropy are two important global threshold selection methods in image thresholding. They not only have a special correspondence in mathematical expression, but also have a certain relationship in the field of image segmentation. Considering the number of thresholds increases, the complexity of the expression of Tsallis entropy criterion function also increases sharply, which is difficult to apply in multiple thresholds. Given this, this paper proposes a simplified expression of Tsallis entropy with multiple thresholds, which is proved by mathematical induction. Simultaneously, it is concluded that the multiple-threshold seg-mentation of Tsallis entropy and Renyi entropy with the same parameters is equivalent. To overcome the inconvenience of high calculation cost under multi-threshold and to improve calculation efficiency, recursive algorithms based on simplified Tsallis entropy and Renyi entropy under multi-threshold are given. The calcu-lation costs of the traditional Tsallis entropy and Renyi entropy threshold, simplified Tsallis entropy and Renyi entropy threshold, and the recursive simplified Tsallis entropy and Renyi entropy are compared through ex-periments. The results have revealed that the calculation time of simplified Tsallis entropy and Renyi entropy is shorter than the traditional methods, and the calculation time of the recursive simplified Tsallis entropy and Renyi entropy is much lower than that of the simplified expression. Finally, we use the three optimization al-gorithms including particle swarm, differential evolution and Harris hawks algorithm to solve the optimal so-lutions of the six expressions in the case of multilevel thresholds. Experiments also show that recursive simplified Tsallis entropy and Renyi entropy have the lowest calculation time cost under the same parameters.

Keywords:

Multi -threshold segmentation

Tsallis entropy

Renyi entropy

Recursive formula

Particle swarm algorithm

Differential evolution algorithm

Harris hawks algorithm

Simplified expression and recursive algorithm of multi-threshold Tsallis entropy

Abstract

Journal

Organization