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Local moments have attracted attention as local features in applications such as edge detection and texture segmentation. The main reason for this is that they are inherently integral-based features, so that their use reduces the effect of uncorrelated noise. The computation of local moments, when viewed as a neighborhood operation, can be interpreted as a convolution of the image with a set of masks. Nevertheless, moments computed inside overlapping windows are not independent and convolution does not take this fact into account. By introducing a matrix formulation and the concept of accumulation moments, this paper presents an algorithm which is computationally much more efficient than convolving and yet as simple.