Directional Global Three-part Image Decomposition

TL;DR

The paper introduces DG3PD, a novel image decomposition model that separates images into cartoon, texture, and residual components using new multi-directional norms, improving reconstruction and applications like compression and feature extraction.

Contribution

The paper proposes a new DG3PD model with multi-directional norms that generalizes existing methods and enhances image decomposition quality.

Findings

DG3PD effectively decomposes images into smooth cartoon, oscillating texture, and residual components.

The model achieves better perfect reconstruction than previous methods.

Applications include improved image compression and feature extraction.

Abstract

We consider the task of image decomposition and we introduce a new model coined directional global three-part decomposition (DG3PD) for solving it. As key ingredients of the DG3PD model, we introduce a discrete multi-directional total variation norm and a discrete multi-directional G-norm. Using these novel norms, the proposed discrete DG3PD model can decompose an image into two parts or into three parts. Existing models for image decomposition by Vese and Osher, by Aujol and Chambolle, by Starck et al., and by Thai and Gottschlich are included as special cases in the new model. Decomposition of an image by DG3PD results in a cartoon image, a texture image and a residual image. Advantages of the DG3PD model over existing ones lie in the properties enforced on the cartoon and texture images. The geometric objects in the cartoon image have a very smooth surface and sharp edges. The texture image yields oscillating patterns on a defined scale which is both smooth and sparse. Moreover, the DG3PD method achieves the goal of perfect reconstruction by summation of all components better than the other considered methods. Relevant applications of DG3PD are a novel way of image compression as well as feature extraction for applications such as latent fingerprint processing and optical character recognition.