DocumentCode :
46160
Title :
Variational Mesh Denoising Using Total Variation and Piecewise Constant Function Space
Author :
Huayan Zhang ; Chunlin Wu ; Juyong Zhang ; Jiansong Deng
Author_Institution :
Sch. of Math. Sci., Univ. of Sci. & Technol. of China, Hefei, China
Volume :
21
Issue :
7
fYear :
2015
fDate :
July 1 2015
Firstpage :
873
Lastpage :
886
Abstract :
Mesh surface denoising is a fundamental problem in geometry processing. The main challenge is to remove noise while preserving sharp features (such as edges and corners) and preventing generating false edges. We propose in this paper to combine total variation (TV) and piecewise constant function space for variational mesh denoising. We first give definitions of piecewise constant function spaces and associated operators. A variational mesh denoising method will then be presented by combining TV and piecewise constant function space. It is proved that, the solution of the variational problem (the key part of the method) is in some sense continuously dependent on its parameter, indicating that the solution is robust to small perturbations of this parameter. To solve the variational problem, we propose an efficient iterative algorithm (with an additional algorithmic parameter) based on variable splitting and augmented Lagrangian method, each step of which has closed form solution. Our denoising method is discussed and compared to several typical existing methods in various aspects. Experimental results show that our method outperforms all the compared methods for both CAD and non-CAD meshes at reasonable costs. It can preserve different levels of features well, and prevent generating false edges in most cases, even with the parameters evaluated by our estimation formulae.
Keywords :
computational geometry; edge detection; feature extraction; image denoising; iterative methods; mesh generation; algorithmic parameter; augmented Lagrangian method; computer graphics; false edge generation prevention; geometry processing; iterative algorithm; noise removal; piecewise constant function space; sharp feature preservation; total variation; triangulated surfaces; variable splitting method; variational mesh denoising method; Face; Image edge detection; Iterative methods; Noise; Noise measurement; Noise reduction; TV; Mesh denoising; piecewise constant function space; sharp feature; total variation;
fLanguage :
English
Journal_Title :
Visualization and Computer Graphics, IEEE Transactions on
Publisher :
ieee
ISSN :
1077-2626
Type :
jour
DOI :
10.1109/TVCG.2015.2398432
Filename :
7029103
Link To Document :
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