We advocate the use of point sets to represent shapes. We provide a definition of a smooth manifold surface from a set of points close to the original surface. The definition is based on local maps from differential geometry, which are approximated by the method of moving least squares (MLS). The computation of points on the surface is local, which results in an out-of-core technique that can h...

In this work we review the opportunities given by the use of local maximumentropy approximants (LME) for the simulation of forming processes. This approximation can be considered as a meshless approximation scheme, and thus presents some appealing features for the numerical simulation of forming processes in a Galerkin framework. Especially the behavior of these shape functions at the boundary ...

In this paper, we target enhanced 3D reconstruction of non-rigidly deforming objects based on a view-independent surface representation with an automated recursive filtering scheme. This work improves upon the KinectDeform algorithm which we recently proposed. KinectDeform uses an implicit viewdependent volumetric truncated signed distance function (TSDF) based surface representation. The view-...

Pasting onto a deformable surfaces requires either a non-parametric warp or a high d.o.f global warp approximation. Previous works utilized techniques such as moving least squares or hierarchical big data to define a non-parametric mapping from an image to a known template. In this paper, I use Dense SIFT Flow to generate a dense pixel mapping which is used to warp regions from a mesh template ...

This paper presents a novel robust processing methodology for computing 2.5D thickness maps from dense 3D collocated surfaces. The proposed pipeline is suitable to faithfully adjust data representation detailing as required, from preserving fine surface features to coarse interpretations. The foundations of the proposed technique exploit spatial point-based filtering, ray tracing techniques and...

New depth camera technology has potential to make a significant impact on computer systems interaction with 3D objects; yet, it is currently limited due to its poor noise and resolution characteristics. In this thesis we propose to use depth camera’s strongest characteristic, its video rate capture speeds, to overcome these limitations. Previous work to utilize sequences of depth images used 2D...

Owing to the meshless and local characteristics, moving least squares (MLS) methods have been used extensively to approximate the unknown function of partial differential equation initial boundary value problem. In this paper, based on matrix analysis, a sufficient and necessary condition for the existence of inverse of coefficient matrix used in MLS methods is developed firstly. Then in the li...

Two meshless local Petrov-Galerkin (MLPG) methods based on two different trial functions but that use a simple linear test function were developed for beam and column problems. These methods used generalized moving least squares (GMLS) and radial basis (RB) interpolation functions as trial functions. These two methods were tested on various patch test problems. Both methods passed the patch tes...

A particular meshless method, named meshless local Petrov–Galerkin is investigated. To treat the essential boundary condition problem, an alternative approach is proposed. The basic idea is to merge the best features of two different methods of shape function generation: the moving least squares (MLS) and the radial basis functions with polynomial terms (RBFp). Whereas the MLS has lower computa...

Moving least squares (MLS) and radial basis function (RBF) methods play a central role in multivariate approximation theory. In this paper we provide a unified framework for both RBF and MLS approximation. This framework turns out to be a linearly constrained quadratic minimization problem. We show that RBF approximation can be considered as a special case of MLS approximation. This sheds new l...