Cartoon and Texture Image Decomposition Driven by Weighted Curvature

In this paper, we propose a curvature-guided model with divergence-free constraints to facilitate image decomposition. Since basic TV regularization has difficulty in processing edge geometry information of cartoon image, in order to preserve the edge features, we introduce a level set curvature term to smooth the uniform area, and use the edge indicator function as the weighted regularization to preserve the edge. In addition, to control the smoothness, a gradient function is proposed to balance the edge indicator function and the curvature term. On the other hand, we find that the existing partial decomposition models measure the oscillation function with the
$H^{-1}$
functional, but this functional ignores the divergence-free vector field during the Hodge decomposition process, then the texture will lose some vector direction information, and then affects the decomposition results. By analyzing the theory of divergence-free vector field, a new decomposition model with the constraint of divergence-free vector field is proposed in this paper. Numerical experiments show that the proposed model can well preserves the edges of cartoon and protects the texture of repetitive patterns.