In this paper we present the application of two level set methods (active contour without edges and fast marching) to the problem of segmenting arteries from medical images. The two methods fit in the same Hamilton-Jacobi type equation but their underlying mechanisms are quite different. The first method finds the objects of interest using an energy minimization equation without the information...

ÐVector field visualization is an important topic in scientific visualization. Its aim is to graphically represent field data on twoand three-dimensional domains and on surfaces in an intuitively understandable way. Here, a new approach based on anisotropicnonlinear diffusion is introduced. It enables an easy perception of vector field data and serves as an appropriate scale space metho...

Image segmentation and object extraction are among the most well addressed topics in computational vision. In this chapter we present a comprehensive tutorial of level sets towards a flexible frame partition paradigm that could integrate edge-drive, regional-based and prior knowledge to object extraction. The central idea behind such an approach is to perform image partition through the propaga...

The aim of this paper is to investigate the use of topological derivatives in combination with the level set method for shape reconstruction and optimization problems. We propose a new approach generalizing the standard speed method, which is obtained by using a source term in the level set equation that depends on the topological derivative of the objective functional. The resulting approach c...

We approach the problem of unfolding the surface of the cerebral cortex by modeling the problem as a front propagation governed by a Partial Differential Equation (PDE) which is solved using level set techniques. As a first step in this direction, we present multi-scale representations of closed surfaces that preserve their total area or enclosed volume. This is the three-dimensional extension ...