Abstract: The Tsallis entropy is a recent development in statistical mechanics and it is a new formalism in which a real quantity q was introduced as parameter for physical systems that present long range interactions,long time memories and fractal-type structures.In this paper,we present a thresholding technique based on two-dimensional Tsallis entropy,which was obtained form the two-dimensional histogram which was determined by using the gray value of the pixels and the local average gray value of the pixels.However,its time-consuming computation is often an obstacle in real time application systems.In our method the threshold vector （s,t）,where s is a threshold for pixel intensity and t is another threshold for the local average intensity of pixels,is obtained through a new optimization algorithm,namely,the Particle Swarm Optimization（PSO） algorithm.The effectiveness of the proposed method is demonstrated by using examples from the real-world and synthetic images.

Key words: Tsallis entropy, two-dimensional histogram, image segmentation, thresholding, Particle Swarm Optimization（PSO）

摘要： Tsallis熵首先出现在统计力学中。对于呈现远距离交互,长时间记忆以及具有不规则结构的物理系统来说,它的表达式中引入了一个实数q作为参数。在利用图像像素的灰度值和像素的邻域平均灰度值建立的二维直方图的基础上,提出了基于二维Tsallis熵的阈值方法;同时为解决计算复杂度高、运算时间长这一缺点,利用群体智能中的粒子群优化（PSO）算法来优化搜索分割阈值（t,s）的过程,其中t和s分别是图像的像素灰度阈值以及邻域平均灰度阈值。通过对真实图像的处理实验证明,该方法不仅能够对目标图像进行准确的分割,而且大大减少了运算时间。

关键词: Tsallis, 二维直方图, 图像分割, 阈值, 粒子群优化（PSO）