We present a new type of Voronoi diagram in R that respects the anisotropy exerted on the plane by a given distance graph. It is based on a metric obtained by smoothly and injectively embedding R into R, and a scalar-valued function for re-scaling the distances. A spline representation of the embedding surface is constructed with the Gauß-Newton algorithm, which approximates the given distance ...

We discuss the reproducing kernel structure in shift-invariant spaces and the weighted shift-invariant spaces, and obtain the reconstruction formula in time-warped weighted shift-invariant spaces, then apply them to a spline subspace. In the spline subspace, we give a reconstruction formula in a time-warped spline subspace. 1. Introduction. The problem of reconstruction of a function f has been...

This paper introduces a new class of quasi-Newton algorithms for unconstrained minimization in which no line search is necessary and the inverse Hessian approximations are positive definite. These algorithms are based on a two-parameter family of rank two, updating formulae used earlier with line search in self-scaling variable metric algorithms. It is proved that, in a quadratic case, the new ...

We present multiresolution B-spline surfaces of arbitrary order defined over triangular domains. Unlike existing methods, the basic idea of our approach is to construct the triangular basis functions from their tensor product relatives in the spirit of box splines by projecting them onto the barycentric plane. The scheme works for splines of any order where the fundamental building blocks of th...

This paper describes a fast algorithm for scattered data interpolation and approximation. Multilevel B-splines are introduced to compute a C 2 -continuous surface through a set of irregularly spaced points. The algorithm makes use of a coarse-tofine hierarchy of control lattices to generate a sequence of bicubic B-spline functions whose sum approaches the desired interpolation function. Large p...

We present a system of interpolating splines with first and approximate second order geometric continuity. The curves are easily computed in linear time by solving a system of linear equations without the need to resort to any kind of successive approximation scheme. Emphasis is placed on the need to find aesthetically pleasing curves in a wide range of circumstances; favorable results are obta...

Our concern is with the construction of a frame in L 2 (S) consisting of smooth functions based on kernels of spherical harmonics. The corresponding decomposition and reconstruction algorithms utilize discrete spherical Fourier transforms. Numerical examples connrm the theoretical expectations. x1. Introduction Traditionally, wavelets were tailored to problems on the Euclidean space IR d. Howev...

Wind field analysis from synthetic aperture radar images allows the estimation of wind direction and speed based on image descriptors. In this paper, we propose a framework to automate wind direction retrieval based on wavelet decomposition associated with spectral processing. We extend existing undecimated wavelet transform approaches, by including à trous with B(3) spline scaling function, in...

This paper presents a novel minutiae matching method that describes elastic distortions by means of a thin-plate spline model and uses that model to normalize the shape of the test fingerprint with respect to the template. The method first determines possible matching minutiae pairs by means of comparing local neighborhoods of the minutiae. Next, a thin-plate spline model is used to describe th...

Seismological images represent maps of the earth’s structure. Apparent bandwidth limitation of seismic data prevents successful estimation of transition sharpness by the multiscale wavelet transform. We discuss the application of two recently developed techniques for (non-linear) singularity analysis designed for bandwidth limited data, such as imaged seismic reflectivity. The first method is a...