Cartoon-texture evolution for two-region image segmentation

Abstract

Two-region image segmentation is the process of dividing an image into two regions of interest, i.e., the foreground and the background. To this aim, Chan et al. (SIAM J Appl Math 66(5):1632–1648, 2006) designed a model well suited for smooth images. One drawback of this model is that it may produce a bad segmentation when the image contains oscillatory components. Based on a cartoon-texture decomposition of the image to be segmented, we propose a new model that is able to produce an accurate segmentation of images also containing noise or oscillatory information like texture. The novel model leads to a non-smooth constrained optimization problem which we solve by means of the ADMM method. The convergence of the numerical scheme is also proved. Several experiments on smooth, noisy, and textural images show the effectiveness of the proposed model.

A view of computational models for image segmentation

“…Note that we focus on basic models, with the aim of providing a general idea of these approaches while avoiding technical details that are outside the scope of this work. It is also worth observing that these models are the basis of modern ones, developed either to improve the effectiveness of the original models in some applications [9] or to complement and refine Machine Learning techniques for segmentation [10].…”

Special issue for SIMAI 2020–2021: large-scale optimization and applications

“…In [1], the authors presents a strategy to segment images in two parts, by considering an image as the sum of a geometric component, the cartoon one, and of a oscillatory component, this latter containing texture and/or noise. Since the oscillatory content of these regions may badly affect the segmentation result, a joint cartoon-texture decomposition model is merged with the binary segmentation approach to improve the quality of a rough given initialization.…”