Cross-based local multipoint filtering

This paper presents a cross-based framework of performing local multipoint filtering efficiently. We formulate the filtering process as a local multipoint regression problem, consisting of two main steps: 1) multipoint estimation, calculating the estimates for a set of points within a shape-adaptive local support, and 2) aggregation, fusing a number of multipoint estimates available for each point. Compared with the guided filter that applies the linear regression to all pixels covered by a fixed-sized square window non-adaptively, the proposed filtering framework is a more generalized form. Two specific filtering methods are instantiated from this framework, based on piecewise constant and piecewise linear modeling, respectively. Leveraging a cross-based local support representation and integration technique, the proposed filtering methods achieve theoretically strong results in an efficient manner, with the two main steps´ complexity independent of the filtering kernel size. We demonstrate the strength of the proposed filters in various applications including stereo matching, depth map enhancement, edge-preserving smoothing, color image denoising, detail enhancement, and flash/no-flash denoising.