Fast computation of Krawtchouk moments
The paper describes the calculation of the Krawtchouk Moments (KMs) from an image, which is a computationally demanding task. We present two original methods that use the outputs of cascaded digital filters in deriving KMs. The first approach uses the digital filter outputs to form geometric moments (GMs) and the KMs are obtained via GMs. The second method uses a direct relationship to obtain KMs from the digital filter outputs. This is possible thanks to the formulation of Krawtchouk polynomials in terms of binomial functions, which are equivalent to the digital filter outputs. In this study, the performance of the proposed techniques is compared with other existing methods of KMs calculation. The experimental study shows that the first and the second proposed techniques perform 57% and 87% faster than the recurrence method for a real image of a size 128128 128  128 pixels, which performs a significant improvement.
fast computation krawtchouk moment digital filter geometric moment krawtchouk polynomial impulse response