Optimal approximation for functions prescribed at equally spaced points

A Linear Approximation Scheme for Planar Closed Contours with 2 Number of Equally Spaced Points

Planar closed contours are used in number of applications such as optical character recognition (OCR), content based image retrieval (CBIR), medical image processing, etc., for object representation, feature vector extraction and object recognition. Some feature generation techniques, for example Fourier descriptors (FDs), require contours to be represented with 2 number of equally spaced point...

Two Results on Polynomial Interpolation in Equally Spaced Points

We present two results that quantify the poor behavior of polynomial interpolation in n equally spaced points. First, in band-limited interpolation of complex exponential functions e‘li (c( E Iw), the error decreases to 0 as n + a, if and only if d( is small enough to provide at least six points per wavelength. Second, the Lebesgue constant ,4. (supremum norm of the nth interpolation operator) ...

Polarization Optimality of Equally Spaced Points on the Circle for Discrete Potentials

We prove a conjecture of Ambrus, Ball and Erdélyi that equally spaced points maximize the minimum of discrete potentials on the unit circle whenever the potential is of the form n X

Optimal Approximation of Functions

Identifying Nearly Equally Spaced Isosurfaces for Volumetric Data Sets

Isosurfaces are an important visual representation of volumetric data sets and isosurface extraction and rendering remains one of the most popular methods for volume visualization. Previous works identify a small set of representative isosurfaces from a set of sample ones, providing a concise description of the underlying volume. However, these methods do not lend themselves to equally spaced i...