Adaptive diffusion constrained total variation scheme with application to `cartoon + texture + edge' image decomposition

TL;DR

This paper introduces an adaptive diffusion constrained total variation scheme for image decomposition into cartoon, texture, and edges, demonstrating its effectiveness through extensive experiments and comparisons.

Contribution

It presents a novel adaptive diffusion constrained TV scheme for image decomposition, combining variational and PDE approaches with an efficient numerical method.

Findings

Effective separation of cartoon, texture, and edges in images.

Outperforms related variational and PDE-based methods in experiments.

Provides a well-posed coupled variational-PDE framework.

Abstract

We consider an image decomposition model involving a variational (minimization) problem and an evolutionary partial differential equation (PDE). We utilize a linear inhomogenuous diffusion constrained and weighted total variation (TV) scheme for image adaptive decomposition. An adaptive weight along with TV regularization splits a given image into three components representing the geometrical (cartoon), textural (small scale - microtextures), and edges (big scale - macrotextures). We study the wellposedness of the coupled variational-PDE scheme along with an efficient numerical scheme based on Chambolle's dual minimization method. We provide extensive experimental results in cartoon-texture-edges decomposition, and denoising as well compare with other related variational, coupled anisotropic diffusion PDE based methods.