Ultrasound images present major challanges to just about any segmentation algorithm, including active contour techniques, due to increased specularity, non-uniform edges along the boundaries of interest, incomplete and misleading visual support. Active contours that depend on a vector of parameters (e.g. B-splines), have been proposed in the literature, and have the advantage over traditional s...

Boundary integral techniques provide a convenient way to study the evolution of an interface between inviscid liquids. Several studies have revealed that standard numerical approximations tend to lead to unstable methods, and various remedies have been introduced and tested. In this paper, we conduct a stability analysis of the linearized equations with a particular objective in mind | the dete...

Moving mesh methods provide an efficient way of solving partial differential equations for which large, localised variations in the solution necessitate locally dense spatial meshes. In one-dimension, meshes are typically specified using the arclength mesh density function. This choice is well-justified for piecewise polynomial interpolants, but it is only justified for spectral methods when mo...

In this paper, we investigate the evolution of curves of the projective plane according to a family of projective invariant intrinsic equations. This is motivated by previous work for the Euclidean 9, 10, 13] and the aane cases 19, 20, 3, 2] as well as by applications in the perception of two-dimensional shapes. We establish the evolution laws for the projective arclength and curvature. Among t...

Abstract. Modeling and control of grasping an object with arbitrary shape by a pair of robot fingers with hemispherical ends in a horizontal plane are proposed in a mathematical and computational standpoint. The curvature of an object contour is variable due to the change of the contact point between the finger tip and object surface. Therefore, not only the time parameter “t” but also the arcl...

relative to a hereditary torsion theory $tau$ we introduce a dimension for a module $m$, called {em $tau$-rank of} $m$, which coincides with the reduced rank of $m$ whenever $tau$ is the goldie torsion theory. it is shown that the $tau$-rank of $m$ is measured by the length of certain decompositions of the $tau$-injective hull of $m$. moreover, some relations between the $tau$-rank of $m$ and c...

Abstract In this paper we consider a spatial discretization scheme with an adaptive grid for the Nagumo PDE and establish existence of travelling waves. particular, time dependent mesh adaptation method that aims to equidistribute arclength solution under consideration. We assume equidistribution is strictly enforced, which leads non-local problem infinite range interactions derived in Hupkes V...