Fast Global Image Smoothing Based on Weighted Least Squares
This paper presents an efficient technique for performing 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. Specifically, we approximate the solution of the memory- and computation-intensive large linear system, defined over a d-dimensional spatial domain, by solving a sequence of 1D sub-systems. 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 about 10 to 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.
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