Fast Global Image Smoothing Based on Weighted Least Squares

作者：Min, Dongbo; Choi, Sunghwan; Lu, Jiangbo^*; Ham, Bumsub; Sohn, Kwanghoon; Do, Minh N.

来源：IEEE Transactions on Image Processing, 2014, 23(12): 5638-5653.

DOI：10.1109/TIP.2014.2366600

• Edge-preserving smoothing (EPS)
• weighted least squares (WLS)
• fast global smoother (FGS)
• iterative re-weighted least squares (IRLS)
• aggregated data constraint
• imprecise input

This paper presents an efficient technique for performing a spatially inhomogeneous edge-preserving image smoothing, called fast global smoother. Focusing on sparse Laplacian matrices consisting of a data term and a prior term (typically defined using four or eight neighbors for 2D image), our approach efficiently solves such global objective functions. In particular, we approximate the solution of the memoryand computation-intensive large linear system, defined over a d-dimensional spatial domain, by solving a sequence of 1D subsystems. Our separable implementation enables applying a linear-time tridiagonal matrix algorithm to solve d three-point Laplacian matrices iteratively. Our approach combines the best of two paradigms, i.e., efficient edge-preserving filters and optimization-based smoothing. Our method has a comparable runtime to the fast edge-preserving filters, but its global optimization formulation overcomes many limitations of the local filtering approaches. Our method also achieves high-quality results as the state-of-the-art optimization-based techniques, but runs similar to 10-30 times faster. Besides, considering the flexibility in defining an objective function, we further propose generalized fast algorithms that perform L-gamma norm smoothing (0 < gamma < 2) and support an aggregated (robust) data term for handling imprecise data constraints. We demonstrate the effectiveness and efficiency of our techniques in a range of image processing and computer graphics applications.

• 出版日期2014-12