Piecewise H−1+H0+H1 images and the Mumford-Shah-Sobolevmodel for segmented image decomposition

Pattern analysis of naturally synthesized images is crucial for a number of important fields includingimage processing, computer vision, artificial intelligence, andcomputer graphics. Benefited from several important works inexistence, the current research paper proposes a novelfree-boundary variational model for segmented imagedecomposition. As an inverse problem solver, the new modeloutputs not only the boundaries of individual objects as achievedby the Mumford-Shah model, but also a structure decompositioncomprising a smooth (or cartoonish) component, an oscillatorycomponent (or texture), and a square-integrable residue (ornoise). Motivations and justifications from vision research areemphasized, and some preliminary mathematical analysis is given.