We consider local minimizers of the Ginzburg-Landau energy functional

This paper presents a new approach to the tracking of regions in an image sequence. Unlike most other methods, the proposed approach can handle topology changes, i.e., regions may split or merge. This flexibility is naturally embedded into a partial differential equation that solves a minimum description length (MDL) estimation problem. The basic estimation criterion consists of only two terms:...

Consider the problem of selecting the member of a parametrized family of curves that best matches a given curve. This is a key step in determining proper values for adjustable parameters in low-order plasma etching and deposition models. Level set methods o er several attractive features for treating such problems. This paper presents a parameter estimation scheme that exploits the level set fo...

It has been understood for sometime that the classical smoothness spaces, such as the Sobolev and Besov classes, are not satisfactory for certain problems in image processing and nonlinear PDEs. Their deficiency lies in their isotropy. Functions in these smoothness spaces must be simultaneously smooth in all directions. The anisotropic generalizations of these spaces also have the deficiency th...

We consider a class of sparsity-inducing regularization terms based on submodular functions. While previous work has focused on non-decreasing functions, we explore symmetric submodular functions and their Lovász extensions. We show that the Lovász extension may be seen as the convex envelope of a function that depends on level sets (i.e., the set of indices whose corresponding components of th...

Multifractal analysis studies level sets of asymptotically defined quantities in a topological dynamical system. We consider the topological pressure function on such level sets, relating it both to the pressure on the entire phase space and to a conditional variational principle. We use this to recover information on the topological entropy and Hausdorff dimension of the level sets. Our approa...

In this paper, we use a level set based segmentation algorithm to extract the vascular tree from Magnetic Resonance Angiography, “MRA”. Classification model finds an optimal partition of homogeneous classes with regular interfaces. Regions and their interfaces are represented by level set functions. The algorithm initializes level sets in each image slice using automatic seed initialization and...

This paper is concerned with the simulation of the Partial Diierential Equation (PDE) driven evolution of a closed surface by means of an implicit representation. In most applications, the natural choice for the implicit representation is the signed distance function to the closed surface. Osher and Sethian propose to evolve the distance function with a Hamilton-Jacobi equation. Unfortunately t...

his article describes how to use level sets to represent and compute deformable surfaces. A deformable surface is a sequence of surface models obtained by taking an initial model and incrementally modifying its shape. Typically, we can parameterize the deformation over time, and thus we can imagine that a surface moves or flows under the influence of a vector field. The surface flow, v, can be ...