Convolution and correlation are very basic image processing operations with numerous applications ranging from image restoration to target detection to image resampling and geometrical transformation. In real time applications, the crucial issue is the processing speed, which implies mandatory use of algorithms with the lowest possible computational complexity. Fast image convolution and correl...

We prove a uniform generalized Gaussian bound for the powers of discrete convolution operator in one space dimension. Our is derived under assumption that Fourier transform coefficients trigonometric rational function, which generalizes previous results were restricted to polynomials. also allow modulus attain its maximum at finitely many points over period.

We propose a method that we call auto-adaptive convolution which extends the classical notion of convolution in pictures analysis to function analysis on a discrete set. We define an averaging kernel which takes into account the local geometry of a discrete shape and adapts itself to the curvature. Its defining property is to be local and to follow a normal law on discrete lines of any slope. W...

In 1944 Favard [5, pp. 229, 239] introduced a discretely defined operator which is a discrete analogue of the familiar GaussWeierstrass singular convolution integral. In the present paper we consider a slight generalization Fn,σn of the Favard operator and its Durrmeyer variant F̃n,σn and study the local rate of convergence when applied to locally smooth functions. The main result consists of th...