Mapping-Based Image Diffusion

Abstract

In this work, we introduce a novel tensorbased functional for targeted image enhancement and denoising. Via explicit regularization, our formulation incorporates application dependent and contextual information using first principles. Few works in literature treat variational models that describe both application dependent information and contextual knowledge of the denoising problem. We prove the existence of a minimizer and present results on tensor symmetry constraints, convexity, and geometric interpretation of the proposed functional. We show that our framework excels in applications where nonlinear functions are present such as in gamma correction and targeted value range filtering. We also study general denoising performance where we show comparable results to dedicated PDE-based state of the art methods.

Mapping Forests: A Comprehensive Approach for Nonlinear Mapping Problems

“…Most of the approaches use the more discriminant space for classification or segmentation purposes. Moreover, there are attempts that provide robustness by means of mapping approaches [1] or supervised mappings between noisy data and ground truth data [13]. A recent approach proposed by [21] introduced pairwise linear transformation by means of linear ridge regression to map data from source space to destination space.…”