We present the first subquadratic algorithms for computing similarity between a pair of point sequences in R, for any fixed d > 1, using dynamic time warping (DTW) and edit distance, assuming that the point sequences are drawn from certain natural families of curves. In particular, our algorithms compute (1 + ε)-approximations of DTW and ED in near-linear time for point sequences drawn from κ-p...

1. Introduction The data collected during an MRI experiment is the spatial frequency information of the proton density of the object being imaged. The data space is referred to as k-space and is related to the image of the object through a Fourier transform relationship. When a Cartesian trajectory is used to traverse k-space, data are acquired on equally spaced grid points in k-space and a fas...

To describe small scotomas in visual field examinations several statistical models are proposed and applied to the evaluation of angioscotoma in 13 ophthalmologically normal subjects. A special perimetric grid is used where thresholds can be estimated along a line of narrow-spaced test points which crosses the predicted location of the retinal vessel. A two-stage analysis employs single estimat...

Given the periodicity of our model problem, it suffices to consider a single period cell (the dotted square in Figure 1), which has side length d. The front of the evolving step in this cell can be described by a simple 1D curve in the plane. We first discretize this 1D curve in space with N grid points, (xi, yi), i = 1, 2, . . . , N , which are uniformly spaced with respect to the arc length, ...

A Chebyshev or Fourier series may be evaluated on the standard collocation grid by the Fast Fourier Transform (FFT). Unfortunately, the FFT does not apply when one needs to sum a spectral series at N points which are spaced irregularly. The cost becomes O(N2) operations instead of the FFT's O(N log N). This sort of "off-grid" interpolation is needed by codes which dynamically readjust the grid ...

We consider the problem of resampling for the data obtained by laser scanning on an irregular grid. The data obtained by airborne laser scanning are scattered, and the resampling on a regular grid is needed for the generation of digital surface models (DSM). Some well-known methods are considered in this article: triangle-based linear interpolation, trianglebased nearest neighbor interpolation ...

Two distinct redistribution grids - adaptation techniques, spring analogy and elliptic grid generator are applied to two-dimensional steady, inviscid, shocked flows, and the ability of each technique is examined and compared. Euler equations are solved base on Roe's Reimann solver approach to simulate supersonic flow around a sphere, transonic flow about an airfoil and supersonic flow in a symm...

An adaptive unstructured grid generation scheme is introduced to use finite volume (FV) and finite element (FE) formulation to solve the heat equation with singular boundary conditions. Regular grids could not acheive accurate solution to this problem. The grid generation scheme uses an optimal time complexity frontal method for the automatic generation and delaunay triangulation of the grid po...

The pseudo-polar Fourier transform is a specialized non-equally spaced Fourier transform, which evaluates the Fourier transform on a near-polar grid, known as the pseudo-polar grid. The advantage of the pseudo-polar grid over other non-uniform sampling geometries is that the transformation, which samples the Fourier transform on the pseudo-polar grid, can be inverted using a fast and stable alg...

The pseudo-polar Fourier transform is a specialized nonequally spaced Fourier transform, which evaluates the Fourier transform on a near-polar grid known as the pseudo-polar grid. The advantage of the pseudo-polar grid over other nonuniform sampling geometries is that the transformation, which samples the Fourier transform on the pseudo-polar grid, can be inverted using a fast and stable algori...