Fast Domain Decomposition for Global Image Smoothing

Edge-preserving smoothing (EPS) can be formulated as minimizing an objective function that consists of data and regularization terms. At the price of high-computational cost, this global EPS approach is more robust and versatile than a local one that typically has a form of weighted averaging. In th...

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Bibliographic Details
Published in:IEEE transactions on image processing Vol. 26; no. 8; pp. 4079 - 4091
Main Authors: Kim, Youngjung, Min, Dongbo, Ham, Bumsub, Sohn, Kwanghoon
Format: Journal Article
Language:English
Published: IEEE 01.08.2017
Subjects:
Acceleration
alternating minimization
Edge-preserving image smoothing
Histograms
joint image filtering
Linear programming
Linear systems
majorization-minimization algorithm
Optimization
Photography
Smoothing methods
weighted-least squares
ISSN:1057-7149, 1941-0042
Online Access:Get full text
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Summary:Edge-preserving smoothing (EPS) can be formulated as minimizing an objective function that consists of data and regularization terms. At the price of high-computational cost, this global EPS approach is more robust and versatile than a local one that typically has a form of weighted averaging. In this paper, we introduce an efficient decomposition-based method for global EPS that minimizes the objective function of L2 data and (possibly non-smooth and non-convex) regularization terms in linear time. Different from previous decompositionbased methods, which require solving a large linear system, our approach solves an equivalent constrained optimization problem, resulting in a sequence of 1-D sub-problems. This enables applying fast linear time solver for weighted-least squares and -L1 smoothing problems. An alternating direction method of multipliers algorithm is adopted to guarantee fast convergence. Our method is fully parallelizable, and its runtime is even comparable to the state-of-the-art local EPS approaches. We also propose a family of fast majorization-minimization algorithms that minimize an objective with non-convex regularization terms. Experimental results demonstrate the effectiveness and flexibility of our approach in a range of image processing and computational photography applications.
ISSN:1057-7149
1941-0042
DOI:10.1109/TIP.2017.2710621