A Color Elastica Model for Vector-Valued Image Regularization
Hao Liu, Xue-Cheng Tai, Ron Kimmel, Roland Glowinski

TL;DR
This paper introduces a novel color elastica model for vector-valued image regularization, extending elastica concepts to color images by minimizing color manifold curvature and proposing an efficient operator-splitting numerical method.
Contribution
The paper develops a new color elastica model based on the Polyakov action, incorporating color manifold curvature, and introduces a fast, robust operator-splitting algorithm for its minimization.
Findings
The proposed model effectively minimizes elastica on color images.
The operator-splitting method converges efficiently and is robust.
Numerical experiments demonstrate superior performance in image regularization.
Abstract
Models related to the Euler's elastica energy have proven to be useful for many applications including image processing. Extending elastica models to color images and multi-channel data is a challenging task, as stable and consistent numerical solvers for these geometric models often involve high order derivatives. Like the single channel Euler's elastica model and the total variation (TV) models, geometric measures that involve high order derivatives could help when considering image formation models that minimize elastic properties. In the past, the Polyakov action from high energy physics has been successfully applied to color image processing. Here, we introduce an addition to the Polyakov action for color images that minimizes the color manifold curvature. The color image curvature is computed by applying of the Laplace-Beltrami operator to the color image channels. When reduced to…
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Taxonomy
TopicsMedical Image Segmentation Techniques · Image and Signal Denoising Methods · Advanced Image Processing Techniques
