Fast actualization of moments in sliding window applications

This paper describes a fast actualization rule for accumulation moments. Geometric and accumulation moments are related through a one-to-one linear transformation: any set of geometric moments up to a given order is uniquely related to a set of accumulation moments up to the same order. When accumulation moments are used instead of geometric moments as description parameters in sliding window applications, it is shown how the actualization cost drops from O(m³) to O(m²), where m refers to the amount of moments. Therefore, any application of this kind that traditionally required geometric moments can benefit from the use of accumulation moments.