A Color Elastica Model for Vector-Valued Image Regularization

Models related to the Euler's elastica energy have proven be useful for many applications including image processing. Extending models color images and multichannel data is a challenging task, as stable consistent numerical solvers these geometric often involve high order derivatives. Like single channel model total variation models, measures that derivatives could help when considering formation minimize elastic properties. In past, Polyakov action from physics has been successfully applied Here, we introduce an addition minimizes manifold curvature. The curvature computed by applying Laplace--Beltrami operator channels. When reduced gray-scale images, while selecting appropriate scaling between space color, proposed operating on level sets. Finding minimizer nonlinear challenge address in this paper. Specifically, present operator-splitting method functional. nonlinearity decoupled introducing three vector-valued matrix-valued variables. problem then converted into solving steady state of associated initial-value problem. time split fractional steps, such each subproblem closed form solution, or can solved fast algorithms. efficiency robustness are demonstrated systematic experiments.