Gaussian convolutions are perhaps the most often used image operators in low-level computer vision tasks. Surprisingly though, there are precious few articles that describe efficient and accurate implementations of these operators. In this paper we describe numerical approximations of Gaussian convolutions based on interpolation. We start with the continuous convolution integral and use an inte...

In the present paper we study convolution properties for subclasses of univalent harmonic functions in the open unit disc and obtain some basic properties such as coefficient characterization and extreme points.  

This interactive teaching gem shows the convolution concept for continuous signals and discrete samples. Signals occurring frequently in computer graphics education are predefined; others can be drawn or integrated easily. We explain how the material can be used for in-class demonstration and for homework, and describe the experiences we made with two courses on image processing and introductio...

The polynomials that arise as coefficients when a power series is raised to the power x include many important special cases, which have surprising properties that are not widely known. This paper explains how to recognize and use such properties, and it closes with a general result about approximating such polynomials asymptotically.

can be calculated with the FFT and bring the order of arithmetic operations down to Nlog (N) which can be signi cant for large N . This approach, which is called fast convolutions", is a form of block processing since a whole block or segment of x (n) must be available to calculate even one output value, y (n). So, a time delay of one block length is always required. Another problem is the lter...

In NLP, convolution neural networks (CNNs) have benefited less than recurrent neural networks (RNNs) from attention mechanisms. We hypothesize that this is because attention in CNNs has been mainly implemented as attentive pooling (i.e., it is applied to pooling) rather than as attentive convolution (i.e., it is integrated into convolution). Convolution is the differentiator of CNNs in that it ...

In this paper, we study $L^p$-conjecture on locally compact hypergroups and by some technical proofs we give some sufficient and necessary conditions  for a weighted Lebesgue space  $L^p(K,w)$ to be a convolution Banach algebra, where $1<p<infty$, $K$ is a locally compact hypergroup and $w$ is a weight function on $K$.  Among the other things, we also show that if $K$ is a locally compact hyper...

We define a Fourier transform and a convolution product for functions and distributions on Heisenberg–Clifford Lie supergroups. The Fourier transform exchanges the convolution and a pointwise product, and is an intertwining operator for the left regular representation. We generalize various classical theorems, including the Paley–Wiener–Schwartz theorem, and define a convolution Banach algebra.

This paper presents a new algorithm for the implementation of an N-point prime-length discrete sine transform (DST) through cyclic convolution. The proposed algorithm is based on the idea of reformulating prime N-length DST into two 1 /2 point cyclic convolutions. Thus, the hardware complexity can be reduced. This cyclic convolution –based algorithm is used to obtain a simple systolic array for...