Fast Global Image Smoothing Based on Weighted Least Squares

Dongbo Min1, Sunghwan Choi2, Jiangbo Lu1, Bumsub Ham3, Kwanghoon Sohn2, and Minh N. Do4

1ADSC 2Yonsei Univ. 3INRIA 4UIUC

IEEE Trans. on Image Processing, Dec. 2014

This work was officially integrated into OpenCV 3.1. (Dec. 2015)

(included in 'Filters' class of OpenCV 3.1).


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.


Paper: high-res version (24MB) [pdf], low-res version (6.7MB) [pdf]

Code: [zip]

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