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Curvature Filters Efficiently Reduce Certain Variational Energies.
- Source :
-
IEEE Transactions on Image Processing . Apr2017, Vol. 26 Issue 4, p1786-1798. 13p. - Publication Year :
- 2017
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10577149
- Volume :
- 26
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Image Processing
- Publication Type :
- Academic Journal
- Accession number :
- 121551281
- Full Text :
- https://doi.org/10.1109/TIP.2017.2658954