Adaptive diffusion constrained total variation scheme with application to `cartoon + texture + edge' image decomposition
This work addresses image processing tasks like decomposition and denoising for applications in computer vision, though it appears incremental as it builds on existing variational and PDE-based methods.
The authors tackled the problem of decomposing images into cartoon, texture, and edge components by developing an adaptive diffusion-constrained total variation scheme, achieving effective decomposition and denoising as demonstrated through extensive experimental comparisons.
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.