We present a novel method of segmentation of lymph valve leaflets from confocal microscopy studies. By using a user informed, layer based segmentation framework, we segment the outer boundary of the lymph valve in 3D from a series of confocal images. This boundary is then used to compute the surface structure of the vessel by providing a boundary constraint to a dual graph based on minimum surf...

This paper first provides a common framework for partial differential equation problems in both strong and weak form by rewriting them as generalized interpolation problems. Then it is proven that any well–posed linear problem in strong or weak form can be solved by certain meshless kernel methods to any prescribed accuracy. AMS Subject Classification: 35A25, 65N35

Some of the meshless radial basis function methods used for the numerical solution of partial diierential equations are reviewed. In particular, the diierences between globally and locally supported methods are discussed, and for locally supported methods the important role of smoothing within a multilevel framework is demonstrated. A possible connection between multigrid nite elements and mult...

A meshless local Petrov-Galerkin (MLPG) method is applied to solve problems of Reissner-Mindlin shells under thermal loading. Both stationary and thermal shock loads are analyzed here. Functionally graded materials with a continuous variation of properties in the shell thickness direction are considered here. A weak formulation for the set of governing equations in the Reissner-Mindlin theory i...

in the present work, a meshless method called finite point method (fpm) is developed to simulate the solidification process of a continuously cast steel bloom in both primary and secondary cooling regions. the method is based on the use of a weighted least-square interpolation procedure. a transverse slice of the bloom moving at casting speed is considered as the computational domain and two di...

In the context of radial basis function interpolation, the construction of native spaces and the techniques for proving error bounds deserve some further clari cation and improvement. This can be described by applying the general theory to the special case of cubic splines. It shows the prevailing gaps in the general theory and yields a simple approach to local error bounds for cubic spline int...

This invited contribution first reviews basic features of multivariate interpolation by radial basis functions, before selected of its advanced topics are addressed, including recent results concerning local polyharmonic spline interpolation. The latter is one main ingredient of a novel class of adaptive meshfree semi-Lagrangian methods for transport problems. The construction of these particle...

The need for the processing of surface geometry represents an ubiquitous problem in computer graphics and related disciplines. It arises in numerous important applications such as computer-aided design, reverse engineering, rapid prototyping, medical imaging , cultural heritage acquisition and preservation, video gaming and the movie industry. Existing surface processing techniques predominantl...

We study meshless collocation methods using radial basis functions to approximate regular solutions of systems of equations with linear diier-ential or integral operators. Our method can be interpreted as one of the emerging meshless methods, cf. 1]. Its range of application is not conned to elliptic problems. However, the application to the boundary value problem for an elliptic operator, conn...