Curvature Filters Efficiently Reduce Certain Variational Energies

Research output: Contribution to journalResearch articleContributedpeer-review



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.


Original languageEnglish
Pages (from-to)1786-1798
Number of pages13
JournalIEEE transactions on image processing
Issue number4
Publication statusPublished - Apr 2017

External IDs

PubMed 28141519
ORCID /0000-0003-4414-4340/work/142252148



  • Approximation, filter, Gaussian curvature, half-window regression, mean curvature, regularization, total variation, variational model

Library keywords