The Secrets of Penalty Functions on Edge-preserving Image Smoothing

Recently, penalty functions are applied to the optimization-based edge-preserving image smoothing problem. But, to select appropriate parameter(s) for a penalty function to achieve desired smoothing effect is nontrivial. In this paper, we study the influence of penalty function on the performance of the edge-preserving image smoothing from the shrinkage rule perspective. We find some interesting secrets about penalty function on the edge-preserving image smoothing. Firstly, the shrinkage rule of a penalty function can help to determine its appropriate parameter(s). Secondly, it is more important is to select appropriate parameters for a penalty function than to select a specific penalty function, because different penalties may have very similar shrinkage rules by changing their parameter(s). Thirdly, a simple optimization framework with an appropriate parameter(s) setting of a penalty function can achieve comparable smoothing effects to those produced by much complex algorithms. To cope with the difficulties brought by nonconvex penalties, we propose an iterative algorithm by virtue of local quadratic approximation.