近年来,考虑到基于偏微分方程的图像处理具有更强的局部自适应特性和高度的灵活性,因此该方法成为继小波图像处理之后新的研究热点。在对热扩散模型和TV(total variation)模型分析的基础上,针对这两个模型在图像平滑区域及边缘或纹理区域扩散所表现出的不同特性和优势,提出一种基于图像局部特性的自适应混合图像放大模型。该模型以双线性插值后的放大图像为初始值,根据像素点梯度特性在平滑区域和边缘或纹理区域自适应地调整扩散模型。使得在平滑区域进行热传导的同性扩散,而在边缘和纹理区域处则进行沿着与梯度方向相垂直的方向扩散。该模型很好地抑制了图像插值放大后所带来的块状效应,以及放大后边缘或纹理区域的假边缘现象。理论上证明了该模型解的存在性,同时大量的仿真实验结果验证了该模型的有效性。

In recent years, image processing based on the partial differential equation has stronger local adaptive characteristics and a high degree of flexibility. This method becomes a new research hotspot after image processing based on wavelet. Based on the different characteristic and superiority represented by the thermal diffusion model and the TV(total variation)model in the image smooth area and edge or texture area,we propose the adaptive hybrid-image magnification model based on image local characteristics. Initialized by the amplification image after the double linear interpolation, this model adaptively adjusts the diffusion model according to the pixel gradient characteristic in the smooth area and edge or texture area. The proposed model makes the isotropic diffusion in the smooth area, and the direction diffusion along the vertical gradient direction in the edge or texture region. This model inhibits the massive effect and the false edge phenomenon brought by the image interpolation amplification. The proposed model is proved theoretically, and at the same time, a lot of simulation results verify the effectiveness of the proposed model.