Abstract: On the basis of the continuous equation of image fusion based on Partial Differentiation Equations（PDE） proposed by Pop.S et al, a new numerical scheme of the equation is presented. The former discrete scheme of divergence by the calculation of gradient is changed to the scheme of the calculation of Laplace, and the regularization term of equation is also adjusted accordingly. The comparison experiments are designed for two schemes on some 1D and 2D signals. The results show that the new scheme can perform the fusion effectively for all the tested signals; and the new scheme can accelerate the convergence process and make the quality of fused image improved by means of a quality factor for some of the tested 1D and 2D signals. However for the other tested signals, the convergence and the quality of output signals obtained by both the new scheme and the former scheme are also very much closed.

Key words: image fusion, partial differential equation, discrete scheme, Laplace, gradient

摘要： 基于Pop.S等提出的基于偏微分方程（PDE）的连续图像融合方程，提出了一种新的离散化方案，将原来的先计算梯度再求散度的离散化方案变化为直接计算拉普拉斯的离散化方案，对方程的正则化项进行相应的调整。将这两种离散化方案分别对一些一维信号和二维信号进行融合对比实验，实验结果显示：对所有的测试信号，新方案都能进行有效的融合；对某些测试的一维和二维信号，新方案能够加速信号的收敛过程并且使得到的融合图像在质量指标上比原方案有提高；而对某些测试信号，新方案与原方案在输出信号的收敛速度上和输出图像的质量指标上也是十分接近的。

关键词: 图像融合, 偏微分方程, 离散化方案, 拉普拉斯, 梯度