为了在进行病变组织检查时，能检测出微小的病变硬化组织，在介绍α稳定分布和与之对应的分数低阶统计量（FLOS）（即分数低阶矩，FLOM）的基础上，给出了非高斯条件下基于分数低阶统计量的阈值检测方法、图像颗粒度分布函数和自相关矩，并首先以超声医学图像为例，分别用高斯分布的方法和α稳定分布方法对超声医学图像进行阈值检测；然后对经过阈值检测后的图像，利用数学形态学方法计算水平方向和垂直方向的颗粒度分布函数；最后求出两个方向的相关系数。实验结果表明，基于分数低阶统计量的阈值检测和颗粒度分析方法优于传统的高斯分析与处理方法。

To detect the tiny sclerotic tissues in pathological examination, the α stable distribution and the fractional lower order statistics (FLOS) (i.e. fractional lower order moment, FLOM) are introduced. The threshold detection method based on FLOS under the non Gaussian condition, the definition of the granularity distribution function and the autocorrelation moment are proposed as well. Firstly, taking the supersonic medical image as an example, the method based on Gaussian distribution and the α stable distribution method respectively to carry on the threshold detection for the supersonic medical image are discussed. After the detection, mathematics morphology is applied to calculate granularity distribution function of the horizontal direction and the vertical direction respectively. At last, the correlation coefficients of two directions are obtained. The experimental results show the threshold detection and granularity analysis method based on the fractional lower order statistics has its superiority.