No abstract

No abstract

This paper presents a new efficient approach for the solution of the ℓp-ℓq minimization problem based on the application of successive orthogonal projections onto generalized Krylov subspaces of increasing dimension. The subspaces are generated according to the iteratively reweighted least-squares strategy for the approximation of ℓp/ℓq-norms by weighted ℓ 2-norms. Computed image restoration examples illustrate that it suffices to carry out only a few iterations to achieve highquality restorations. The combination of a low iteration count and a modest storage requirement makes the proposed method attractive.

We introduce linear semi-implicit complementary volume numerical scheme for solving level set like nonlinear degenerate diffusion equations arising in image processing and curve evolution problems. We study discretization of image selective smoothing equation of mean curvature flow type given by Alvarez, Lions and Morel ([3]). Solution of the level set equation of Osher and Sethian ([26], [30]) is also included in the study. We prove L ∞ and W 1,1 estimates for the proposed scheme and give existence of its (generalized) solution in every discrete time-scale step. Efficiency of the scheme is given by its linearity and stability. Preconditioned iterative solvers are used for computing arising linear systems. We present computational results related to image processing and plane curve evolution.

The performance of three methods for evaluation of motion on synthesized 2-D echo image sequences with features similar to real ones are examined. The selected techniques based on the computation of optical flow are of the differential type and assume that the image brightness pattern is constant over time. They differ in the choice of the smoothing term and in the local or global treatment of the domain. The images were synthesized by simulating the process of echo formation, considering the interaction between ultrasonic fields and human tissues. Moreover, two different approaches were followed to generate the sequences: 1) a known motion field was applied to the intensity distribution of the synthesized images; 2) a known motion field was applied directly to the point scatterer distribution of the tissue. Favorable results were obtained by applying Lucas-Kanade and Horn-Schunck techniques to the sequences of the first type, while all the techniques produced large errors when applied to the other type of sequences. A discussion about the suitability of the above-mentioned techniques for evaluation of motion on real echocardiographic images is also presented together with some results.

We introduce a Convex Non-Convex (CNC) denoising variational model for restoring images corrupted by Additive White Gaussian Noise (AWGN). We propose the use of parameterized non-convex regularizers to effectively induce sparsity of the gradient magnitudes in the solution, while maintaining strict convexity of the total cost functional. Some widely used non-convex regularization functions are evaluated and a new one is analyzed which allows for better restorations. An efficient minimization algorithm based on the Alternating Directions Methods of Multipliers (ADMM) strategy is proposed for simultaneously restoring the image and automatically selecting the regularization parameter by exploiting the discrepancy principle. Theoretical convexity conditions for both the proposed CNC variational model and the optimization sub-problems arising in the ADMM-based procedure are provided which guarantee convergence to a unique global minimizer. Numerical examples are presented which indicate how the proposed approach is particularly effective and well suited for images characterized by moderately sparse gradients.

Abstract. We introduce a three-dimensional (3D) semi-implicit complementary volume numerical scheme for solving the level set formulation of (Riemannian) mean curvature flow problem. We apply the scheme to segmentation of objects (with interrupted edges) in 3D images. The method is unconditionally stable and efficient regarding computational times. The study of its experimental order of convergence on 3D examples shows its second order accuracy for smooth solutions and first order accuracy for highly singular solutions with vanishing gradients as arising in image segmentation. 1. Introduction. In this paper we introduce a fast and stable computational method for a three-dimensional (3D) image segmentation based on a solution of the following Riemannian mean curvature flow equation:

No abstract