对图像处理中二维经验模式分解(EMD)算法提出改进。在二维EMD中涉及到像素极值的选取和对极值点进行插值, 在插值过程中会出现边界点变异现象。利用Delaunay三角剖分方法对选取的极值点进行分划, 对不包含在Delaunay多边形内的边界像素采用对称处理, 抑制了3次样条插值过程中边界点变异现象。用改进算法对一幅图像进行EMD处理, 计算得到重构图像与原始图像之间标准差为6.667×10-6, 可见重构图像与原始图像之间的灰度值波动很小。实验结果表明重构图像与原始图像吻合非常好, 论证了这种改进算法的准确性和可行性。EMD方法在图像压缩以及去噪过程中运用越来越广泛, 因此本文的改进算法也将在基于EMD的图像处理中起到提高运算速度的作用。

An improved algorithm of 2-D empirical mode decomposition (EMD) in image processing has been presented. It contains selecting extrema of the pixels and interpolation of them in the course of EMD, in which a variance phenomenon of boundary pixels has been discovered. Delaunay triangulation has been used to partition the selected extrema, then replaces the pixels that not contained in the Delaunay polygon through symmetry principle, which can restrain the variance phenomenon that appeared in the cubic spline interpolation. An image has been processed with the improved algorithm, and the result indicates that the standard deviation between the original image and the reconstructed image is 6.667×10-6 . The reconstructed image is in good agreement with the original image. It demonstrates that the improved algorithm presented is accurate and feasible. The application of method of EMD is more and more popular in image compression and de-noising, therefore, the improved algorithm will increase the calculation speed of image processing based on EMD.