Painters of panoramic landscape maps use specific manual techniques to solve problems of occlusion, foreshortening and unfavourable orientation of landscape elements to the map viewer. Using digital means, the painters’ techniques may be translated into geometry deformation algorithms for digital panorama creation. This article explores the advantages and the suitability of applying local geome...

Preoperative planning is an essential step before performing any surgical procedure. Computer Aided Orthopedic Surgery (CAOS) systems are extensively used for the planning of surgeries for fractures of lower extremities. These systems are input an X-Ray image and the planning can be digitally overlaid onto the image. The planning includes reassembling the fractured bone and possibly adding impl...

This report surveys recent techniques for reconstructing surfaces from points. We describe four main ideas in the graphics literature: signed distance estimation, Voronoi-based reconstruction, implicit surface fitting, and moving least squares surfaces. The main challenges include reconstruction without surface normals, robustness to noise, accuracy to sharp features, and provable reconstructio...

In this paper a new technique aimed to obtain accurate estimates of the error in energy norm using a moving least squares (MLS) recovery-based procedure is presented. We explore the capabilities of a recovery technique based on an enhanced MLS fitting, which directly provides continuous interpolated fields, to obtain estimates of the error in energy norm as an alternative to the superconvergent...

The Meshless Local Petrov–Galerkin method (MLPG) is one of the popular meshless methods that has been used very successfully to solve several types of boundary value problems since the late nineties. In this paper, using a generalized moving least squares (GMLS) approximation, a new direct MLPG technique, called DMLPG, is presented. Following the principle of meshless methods to express everyth...

For multivariate problems with many scattered data locations the use of radial functions has proven to be advantageous. However, using the usual radial basis function approach one needs to solve a large (possibly dense) linear system. In the moving least squares (MLS) method one obtains a best approximation of the given data in a (moving) weighted least-squares sense. The computational burden i...

Introduction Moving least squares approximation is one kind of meshless methods in which the approximation is built from nodes only. Comparing to mesh-based methods, meshless methods have advantages on (1) refining is simpler to incorporate, (2) moving discontinuities can be treated easily, (3) large deformation can be handled robustly, (4) higher-order continuous shape functions, (5) non-local...

As an extension of the chronobiological serial section, gliding spectra illustrate the changing time structure (chronome) of physiological, physical and/or other variables in a given frequency range. For this purpose, least squares spectra are computed over a specified interval (much shorter than the observation span) that is progressively displaced by a given increment throughout the entire re...

In order to avoid the curse of dimensionality, frequently encountered in Big Data analysis, there was a vast development in the field of linear and non-linear dimension reduction techniques in recent years. These techniques (sometimes referred to as manifold learning) assume that the scattered input data is lying on a lower dimensional manifold, thus the high dimensionality problem can be overc...

We present an algorithm for approximating a function defined over a d-dimensional manifold utilizing only noisy function values at locations sampled from the manifold with noise. To produce the approximation we do not require any knowledge regarding the manifold other than its dimension d. The approximation scheme is based upon the Manifold Moving Least-Squares (MMLS) presented in [25]. The pro...