一个基于各向异性的热传导方程导出的图像锐化算子

AN IMAGE ENHANCEMENT METHOD DESIGNED BY A NEW ANISOTROPY DIFFUSION EQUATION

Witkin等人的尺度空间滤波办法是对原图像一个逐渐平滑的过程，这个过程可以用传统的热传导方程来描述．假设“热量”由低温向高温处流动，导出一个各向异性的反向热传导方程．将它用于图像处理，通过选择合适的各向异性函数，使得在感兴趣的边缘处“热量”由低温向高温处流动，即“灰度”从“低灰度”向“高灰度”流动，以此得到一个适合一类图像的图像锐化算子．实验证明，这种锐化算子的导出方法能够有效利用已有的尺度空间研究成果，基于目的设计合适的图像锐化算子，得到理想的结果．

The scale space technique introduced by Witkin proposed an edge detection method by smoothing the image step by step. The smoothing process can be described as a traditional heat diffusion equation. In this paper it is assumed that heat diffuses from low temperature position to high temperature position and a new anisotropy reverse heat diffusion equation is obtained. This equation is used to design an image enhancement method (IEM ), and through a suitable anisotropy function the gray value transfers from low gray value to high gray value mainly in the edges to be enhanced. The experiment results show that designing IEM through the new heat diffusion equation can make an efficient use of the conclusion of the scale-space technique, and a good enhancement result is obtained.