Multiscale Texture Extraction with Hierarchical (BV,G(p),L-2) Decomposition

作者：Tang Liming; He Chuanjiang^*

来源：Journal of Mathematical Imaging and Vision, 2013, 45(2): 148-163.

DOI：10.1007/s10851-012-0351-1

• Multiscale texture extraction
• Variational decomposition
• Hierarchical decomposition
• Duality
• Projection algorithm
• Fixed point iteration scheme

In this paper, we first present a hierarchical (BV,G (p) ,L (2)) variational decomposition model and then use it to achieve multiscale texture extraction which offers a hierarchical, separated representation of image texture in different scales. The starting point is the use of the variational (BV,G (p) ,L (2)) decomposition; a given image faL (2)(Omega) is decomposed into a sum of u (0)+v (0)+r (0), where (u (0),v (0))a(BV(Omega),G (p) (Omega)) is the minimizer of an energy functional E(f,lambda (0);u,v) and r (0) is the residual (i.e. r (0)=f-u (0)-v (0)). In this decomposition, v (0) represents the fixed scale texture of f, which is measured by the parameter lambda (0). To achieve a multiscale representation, we proceed to capture essential textures of f which have been absorbed by the residuals. Such a goal can be achieved by iterating a refinement decomposition to the residual of the previous step, i.e. r (i) =u (i+1)+v (i+1)+r (i+1), where (u (i+1),v (i+1)) is the minimizer of E(r (i) ,lambda (0)/2 (i+1);u,v). In this manner, we can obtain a hierarchical representation of f. In addition, we discuss some theoretical properties of the hierarchical (BV,G (p) ,L (2)) decomposition and give its numerical implementation. Finally, we apply this hierarchical decomposition to the multiscale texture extraction. The performance of this method is demonstrated with both synthetic and real images.

• 出版日期2013-2
• 单位重庆大学