一种极值约束的边缘保持图像平滑算法

Smoothing Algorithm with Edge-preserving by Extrema Constraints

边缘保持的图像平滑在图像预处理以及许多图像编辑应用中都具有重要的意义。图像的边缘保持与细节平滑是一对矛盾。提出一种以极值为约束的边缘保持的图像平滑算法。该方法的基本思想是对处理后图像的极值进行约束,即要求其在给定位置处取得相应的极大(小)值来保持原图像的主边缘,同时平滑消除副边缘和信号小起伏。首先对原图像进行初步平滑,然后从中提取出极值点,再把这些极值点作为处理后图像的约束。在所有满足这些约束的函数中,取与原图像最接近的作为最终平滑结果。利用半二次技术和交替最小化得到了有效的数值求解方法。实验结果表明,提出的方法在一些基于边缘保持平滑的图像处理(如细节增强)中取得了更好的效果。

Edge-aware smoothing is important for many image editing applications as well as image preprocessing. Edge preservation and detail suppression form a contradictory pair. An edge-preserving smoothing algorithm was proposed, in which a signal is asked to attain its extrema at some given points. By manipulations on extrema of the resulting image, significant edges are retained, and at the same time, side edges and small fluctuations are subdued. Our method first obtains a preliminary smoothing version, whose extrema are used as constraints on the resulting image. Among all functions that meet these constraints, we pursued the one that is most similar to the original signal as the smoothing result. This optimization problem is solved by the half-quadratic technique and alternating minimization. Experimental results show that applications such as detail enhancement can benefit from the better performance of our method for preserving edges.