中文摘要：

梯度是图像处理中常用的重要信息，但目前还缺乏较准确的数学模型来描述图像梯度与图像组成之间的联系。为此，在分析图像梯度直方图的特点的基础上，提出了一种基于Gamma混合分布的梯度数学模型，随后推导了基于EM算法的模型求解方法，最后通过应用实例和结果分析验证了该模型的准确性和有效性。

英文摘要：

The Gradient is important information which is frequently used in image processing, while there is hardly any accurate mathematics model to describe the relationship between image gradient and image module at present. Therefore, after analyzing the character of image gradient histogram, a mathematics model based on Gamma distribution is proposed, and then a solution to the model found on EM algorithm is presented. At last, accuracy and validity of the model are verified by an application example and result analysis.