A new formulation of geometric moments from lower output values of digital filters

An important aspect of the real-time image processing applications using orthogonal moments is the speed of their computation. They can be computed directly or via geometric moments (GMs). One of the fast methods to generate GMs is the usage of the cascaded digital filter outputs. However, a concern of this design is that the outputs of the digital filters, which operate as accumulators, increase exponentially as the orders of moment increase. It is shown in previous works, for an N × N image, the digital filter outputs are sampled at N or later instances. In this paper, we propose a new formulation to solve this problem by using a set of lower digital filter output values as the order of moments increases. This is achieved by sampling the digital filter outputs at earlier instances, N, N - 1, N - 2,...,N - p, where p is the maximum moment order. This method enables the usage of the lower digital filter output values for higher-order moments. As the moment order approaches N, the number of additions is approximately 45% less for the proposed method when compared with the existing methods, resulting in a corresponding reduction in computation time.