Abstract. An O(N2) algorithm for the convolution of compactly supported Legendre series is described. The algorithm is derived from the convolution theorem for Legendre polynomials and the recurrence relation satisfied by spherical Bessel functions. Combining with previous work yields an O(N2) algorithm for the convolution of Chebyshev series. Numerical results are presented to demonstrate the ...

In this correspondence, we present a fast thresholded linear convolution representation of morphological operations. The thresholded linear convolution representation of dilation and erosion is first proposed. A comparison of the efficiency of the direct implementation of morphological operations and the thresholded linear convolution representation of morphological operations is subsequently c...

Hajek's [17] convolution theorem was a major advance in understanding the classical information inequality. This re-examination of the convolution theorem discusses historical background to asymptotic estimation theory; the role of superefficiency in current estimation practice; the link between convergence of bootstrap distributions and convolution structure; and a dimensional asymptotics view...

We present new methods that approximate the ooset and convolution of planar curves. They can be used as fundamental tools in various interesting geometric applications such as NC machining and collision detection of planar curved objects. Using quadratic curve approximation and tangent eld matching, the oo-set and convolution curves can be approximated by polynomial or rational curves within th...

Detecting edges in images which are distorted by unreliable or missing data samples can be done using normalized (differential) convolution. This work presents a comparison between gradient estimation using normalized convolution and gradient estimation using normalized differential convolution with regard to speed, accuracy, and noisesensitivity.

The key step in classical convolution and correlation algorithms, the componentwise multiplication of vectors after initial Fourier Transforms, is shown to be physically impossible to do on quantum states. Then this is used to show that computing the convolution or correlation of quantum state coefficients violates quantum mechanics, making convolution and correlation of quantum coefficients ph...

This paper explores the relation between discrete convolution/correlation and string matching for different specific classes of input signals. We examine the time complexity of computation for both convolution/correlation and string matching, and explore the possibility of a deterministic algorithm for discrete convolution/correlation.

background: various variance reduction techniques such as forced detection (fd) have been implemented in monte carlo (mc) simulation of nuclear medicine in an effort to decrease the simulation time while keeping accuracy. however most of these techniques still result in very long mc simulation times for being implemented into routine use. materials and methods: convolution-based forced detectio...

introduction: it is a common protocol to use 201tl for the rest and 99mtc for the stress cardiac spect imaging. theoretically, both types of imaging may be performed simultaneously using different energy windows for each radionuclide. however, a potential limitation is the cross-contamination of scattered photons from 99mtc and collimator x-rays into the 201tl energy window. we used a middle en...

‎For a homogeneous spaces ‎$‎G/H‎$‎, we show that the convolution on $L^1(G/H)$ is the same as convolution on $L^1(K)$, where $G$ is semidirect product of a closed subgroup $H$ and a normal subgroup $K $ of ‎$‎G‎$‎. ‎Also we prove that there exists a one to one correspondence between nondegenerat $ast$-representations of $L^1(G/H)$ and representations of ...