Gradient flows in the Sobolev space H1 have been shown to enjoy favorable regularity properties. We propose a generalization of prior approaches for Sobolev active contour segmentation by changing the notion of distance in the Sobolev space, which is achieved through treatment of the function and its derivative in Riemannian manifolds. The resulting generalized Riemannian Sobolev space provides...

Tomographic reconstruction from cone-beam X-ray data is only solved for static objects, e. g. the abdomen. In cardiac imaging, a rotational angiography sequence takes approx. 5 s and therefore spans several heart beats. Since such an acquisition scheme forces a trade-off between consistency of the scene and reasonable angular spacings between camera positions, standard reconstruction techniques...

We introduce a framework and construct algorithms based on it to handle optimization problems that deal with the maximization of visibility information for observers when obstacles to vision are present in the environment. This framework uses at its core the approach developed in [14] which adopts the level set framework of [10] to construct a function that encodes visibility information in a c...

This paper aims at studying the level set segmentation technique using Variational Level Set Formulation techniques without reintialisation with various filtering methods applied on biomedical images and analyzing the results obtained after applying various filters to the segmented images. The various steps taken in the development of the program and then the testing of the simulation program w...

As already indicated in (2), the recipe described above implicitly assumes that V = L2. Therefore it is mathematically correct to refer to ∇E as the L2-gradient and not simply the gradient. Unfortunately, the L2-gradient is, to put it simply, too local and therefore prone to lead into an undesired local minimum as pointed out by Charpiat et al. [2] as well as Sundaramoorthi et al. [3]. Thus reg...

At fertility clinics, living human embryos are evaluated by visual inspection of light microscopy images. The criteria to assess the quality are number of blastomeres (cells) of the embryo, regularity of size and degree of fragmentation. Today, this evaluation process is based on interpretation of 3D information projected to 2D images. It is believed that an overall improvement in the process c...

We focus on the robust principal component analysis (RPCA) problem, and review a range of old and new convex formulations for the problem and its variants. We then review dual smoothing and level set techniques in convex optimization, present several novel theoretical results, and apply the techniques on the RPCA problem. In the final sections, we show a range of numerical experiments for simul...

Title of thesis: A HYBRID VARIATIONAL-LEVEL SET APPROACH TO HANDLE TOPOLOGICAL CHANGES Shawn W. Walker, Master of Science, 2007 Thesis directed by: Professor Ricardo H. Nochetto Program of Applied Mathematics and Scientific Computation We present a method for allowing explicit, Lagrangian meshes to undergo topological changes in an automatic way. We employ a method for detecting when topologica...

Level set methods are the numerical techniques for tracking interfaces and shapes. They have been successfully used in image segmentation. A new variational level set evolving algorithm without re-initialization is presented in this paper. It consists of an internal energy term that penalizes deviations of the level set function from a signed distance function, and an external energy term that ...

The point at which they meet (the triple junction) has prescribed angles which can be shown [12] to be defined by A coupled level set method for the motion of multiple junctions (of, e.g., solid, liquid, and grain boundaries), which follows the gradient flow for an energy functional consisting of surface tension (proportional to length) and bulk energies (proportional to area), is sin u1 f23 5 ...