Decorrelating the Structure and Texture Components of a Variational Decomposition Model

• Published in: IEEE transactions on image processing 2009-02, Vol.18 (2), p.299-309
• Main Authors: Shahidi, R., Moloney, C.
• Format: Article
• Language: English
• Subjects: Algorithms; Applied sciences; Artificial Intelligence; Calculus; Computer Simulation; Correlation coefficient; Councils; Decomposition; Decorrelation; Derivation; Discrimination; Exact sciences and technology; Image coding; Image decomposition; Image denoising; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Image processing; Image registration; Information, signal and communications theory; Laplace equations; Mathematical models; Models, Statistical; Optimization; Parameter estimation; Pattern Recognition, Automated - methods; Reproducibility of Results; Sensitivity and Specificity; Signal processing; Statistics as Topic; Surface layer; Telecommunications and information theory; Texture; texture discrimination; variational methods
• ISSN: 1057-7149; 1941-0042
• DOI: 10.1109/TIP.2008.2008046

The observation has been made by Aujol and Gilboa that the cartoon and texture components of the decomposition of an image should not be correlated, as they are generated from independent processes. They use this observation in order to choose an optimal fidelity parameter lambda for the decomposition process. However, this determination can be quite inefficient since a wide range of parameters lambda must be searched through before an estimated optimal parameter can be found. In the present paper, we take a different approach, in which the cartoon and texture components are explicitly decorrelated by adding a decorrelation term to the energy functional of the decomposition model of Osher, Sole, and Vese (the OSV model). Decomposition results of improved quality over those from the OSV model are obtained, as quantified by a series of new decomposition quality measures, with cartoon and texture information better separated into their respective components. A new derivation of the OSV model is developed which maintains the texture subcomponents g 1 and g 2 so that discrimination results similar to those from other decomposition models (e.g., from the model of Vese and Osher and Improved Edge Segregation) may be obtained. This derivation is extended to the proposed model, for which discrimination results are obtained in a substantially smaller number of iterations.