Abstract: In the decomposition of natural image containing texture, the edge information of structure image is easy to be regarded as the texture, which results in blurred edge of the structural image and inaccurate detected edge. An image decomposition and edge detection method was proposed based on wavelet transform of Partial Differential Equation (PDE). At first, wavelet transform threshold was used to extract texture information. Then the improved PDE image decomposition model was used to further decompose the image and extract the edge. The numerical experimental results show that this method improves the quality of image decomposition, makes the texture extraction through and the structure image piecewise smooth, and better protects the edge of the structure.

Key words: wavelet transform, Partial Differential Equation (PDE), image decomposition, edge detection, structure, texture

摘要： 针对含纹理的自然图像在图像分解时，结构图像的边缘信息容易被当作纹理分解到纹理图像中，致使结构图像的边缘不清晰，检测到的边缘不准确，提出了基于小波分解的偏微分方程(PDE)图像分解及边缘检测模型。首先利用小波变换阈值提取部分纹理信息，再利用改进的保边缘的偏微分方程图像分解模型进一步分解图像并提取边缘。实验结果表明，新方法提高了图像分解的质量，纹理信息提取充分，结构图像有较好的分片光滑性和较清晰的边缘，检测到的结构边缘更准确。

关键词: 小波变换, 偏微分方程, 图像分解, 边缘检测, 结构, 纹理