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Curvature Filters Efficiently Reduce Certain Variational Energies.

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Gong, Y., & Sbalzarini, I. F. (2017). Curvature Filters Efficiently Reduce Certain Variational Energies. IEEE transactions on image processing: a publication of the IEEE Signal Processing Society, 26(4), 1786-1798. doi:10.1109/TIP.2017.2658954.

Cite as: https://hdl.handle.net/21.11116/0000-0002-8BC4-4
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.