Efficient Mean/Sigma Estimation at Arbitrary Spatial Positions with Arbitrary Scales within A 2D Image

Abstract

This paper contributes a novel two-step method for estimating local statistical image features: the mean and the standard deviation (σ) of pixel intensities, within random-access ROIs. In the first step, three summation maps will be created with O(n) computational complexity for the entire image; based on such maps the area, the mean intensity as well as the σ of an arbitrarily defined rectangular ROI could be calculated by fixed and limited arithmetic operations on scalar values. Without any repeated calculation on individual pixels, this method provides a promising efficiency and flexibility for further image analysis based on local statistical features. For instance, by performing the "zero-mean-σ-normalization" as fast post-processing on arbitrary image overlaps rather than performing it as slower pre-processing on individual pixels, this paper further contributes a non-classical normalized cross-correlation method for general image registration beyond the scope of (single) template matching.