Multiscale Image Representation and Texture Extraction Using Hierarchical Variational Decomposition

Abstract

In order to achieve a mutiscale representation and texture extraction for textured image, a hierarchical $(BV,G_p,L^2)$ decomposition model is proposed in this paper. We firstly introduce the proposed model which is obtained by replacing the fixed scale parameter of the original $(BV,G_p,L^2)$ decomposition with a varying sequence. And then, the existence and convergence of the hierarchical decomposition are proved. Furthermore, we show the nontrivial property of this hierarchical decomposition. Finally, we introduce a simple numerical method for the hierarchical decomposition, which utilizes gradient decent for energy minimization and finite difference for the associated gradient flow equations. Numerical results show that the proposed hierarchical $(BV,G_p,L^2)$ decomposition is very appropriate for multiscale representation and texture extraction of textured image.