Generic 2D/3D smoothing via regional variation

In this paper, we propose a method to measure the relationship between data samples, which is dependent on the possibility whether they are within a homogeneous region or not. By considering the regional variation, this possibility is formulated in terms of the maximum local variation along the shortest path connecting the samples. The metric is concretized in both 2D images and 3D meshes, and then integrated into smoothing filters. Benefited from our method, the improved filters tend to effectively preserve the structural component of data. Moreover, our method is implemented in various applications such as image denoising, image decomposition and mesh smoothing, which demonstrates better performance in comparison to the previous work.