Abstract: Recently, fast neural networks for object/face
detection were presented in [1-3]. The speed up factor of these
networks relies on performing cross correlation in the frequency
domain between the input image and the weights of the hidden
layer. But, these equations given in [1-3] for conventional and fast
neural networks are not valid for many reasons presented here. In
this paper, correct equations for cross correlation in the spatial and
frequency domains are presented. Furthermore, correct formulas for
the number of computation steps required by conventional and fast
neural networks given in [1-3] are introduced. A new formula for
the speed up ratio is established. Also, corrections for the equations
of fast multi scale object/face detection are given. Moreover,
commutative cross correlation is achieved. Simulation results show
that sub-image detection based on cross correlation in the frequency
domain is faster than classical neural networks.