Accurate object localization in gray level images using the center of gravity measure: accuracy versus precision

A widely used subpixel precision estimate of an object center is the weighted center of gravity (COG). We derive three maximum-likelihood estimators for the variance of the two-dimensional (2-D) COG as a function of the noise in the image. We assume that the noise is additive, Gaussian distributed and independent between neighboring pixels. Repeated experiments using 2500 generated 2-D bell-shaped markers superimposed with an increasing amount of Gaussian noise were performed, to compare the three approximations. The error of the most exact approximative variance estimate with respect to true variance was always less than 5% of the latter. This deviation decreases with increasing signal-to-noise ratio. Our second approximation to the variance estimate performed better than the third approximation, which was originally presented by Oron et al. by up to a factor ≈10. The difference in performance between these two approximations increased with an increasing misplacement of the window in which the COG was calculated with respect to the real COG.