Curvature Filters Efficiently Reduce Certain Variational Energies

被引:124
作者
Gong, Yuanhao [1 ,2 ]
Sbalzarini, Ivo F. [1 ,2 ]
机构
[1] Tech Univ Dresden, Fac Comp Sci, Chair Sci Comp Syst Biol, D-01187 Dresden, Germany
[2] Max Planck Inst Mol Cell Biol & Genet, MOSAIC Grp, Ctr Syst Biol Dresden, D-01307 Dresden, Germany
关键词
Approximation; filter; gaussian curvature; half-window regression; mean curvature; regularization; total variation; variational model; AUGMENTED LAGRANGIAN METHOD; MEAN-CURVATURE; IMAGE-RECONSTRUCTION; GAUSSIAN CURVATURE; BREGMAN ITERATION; NOISE REMOVAL; REGULARIZATION; SPACE;
D O I
10.1109/TIP.2017.2658954
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
In image processing, the rapid approximate solution of variational problems involving generic data-fitting terms is often of practical relevance, for example in real-time applications. Variational solvers based on diffusion schemes or the Euler-Lagrange equations are too slow and restricted in the types of data-fitting terms. Here, we present a filter-based approach to reduce variational energies that contain generic data-fitting terms, but are restricted to specific regularizations. Our approach is based on reducing the regularization part of the variational energy, while guaranteeing non-increasing total energy. This is applicable to regularization-dominated models, where the data-fitting energy initially increases, while the regularization energy initially decreases. We present fast discrete filters for regularizers based on Gaussian curvature, mean curvature, and total variation. These pixel-local filters can be used to rapidly reduce the energy of the full model. We prove the convergence of the resulting iterative scheme in a greedy sense, and we show several experiments to demonstrate applications in image-processing problems involving regularization-dominated variational models.
引用
收藏
页码:1786 / 1798
页数:13
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