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Fast global image smoothing based on weighted least squares.

Authors
  • Min, Dongbo
  • Choi, Sunghwan
  • Lu, Jiangbo
  • Ham, Bumsub
  • Sohn, Kwanghoon
  • Do, Minh N
Type
Published Article
Journal
IEEE Transactions on Image Processing
Publisher
Institute of Electrical and Electronics Engineers
Publication Date
Dec 01, 2014
Volume
23
Issue
12
Pages
5638–5653
Identifiers
PMID: 25373085
Source
Medline
License
Unknown

Abstract

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 memory-and 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 ∼10-30 times faster. Besides, considering the flexibility in defining an objective function, we further propose generalized fast algorithms that perform Lγ norm smoothing (0 < γ < 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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