Computation of the normalized cross-correlation by fast Fourier transform

Fast Normalized Cross-Correlation

Although it is well known that cross correlation can be efficiently implemented in the transform domain, the normalized form of cross correlation preferred for feature matching applications does not have a simple frequency domain expression. Normalized cross correlation has been computed in the spatial domain for this reason. This short paper shows that unnormalized cross correlation can be eff...

Fast normalized cross correlation for defect detection

Normalized cross correlation has been used extensively for many machine vision applications, but the traditional normalized correlation operation does not meet speed requirements for time-critical applications. In this paper, we propose a fast normalized cross correlation computation for defect detection application. A sum-table scheme is utilized, which allows the calculations of image mean, i...

Template Matching using Fast Normalized Cross Correlation

In this paper we present an algorithm for fast calculation of the normalized cross correlation NCC and its applica tion to the problem of template matching Given a template t whose position is to be determined in an image f the basic idea of the algorithm is to represent the template for which the normalized cross correlation is calculated as a sum of rectangular basis functions Then the correl...

Nonequispaced Hyperbolic Cross Fast Fourier Transform

A straightforward discretisation of problems in d spatial dimensions often leads to an exponential growth in the number of degrees of freedom. Thus, even efficient algorithms like the fast Fourier transform (FFT) have high computational costs. Hyperbolic cross approximations allow for a severe decrease in the number of used Fourier coefficients to represent functions with bounded mixed derivati...

Computation of Configuration-Space Obstacles Using the Fast Fourier Transform