The sub-pixel efficacy region of the bivariate linear interpolation function

This paper reports on a methodology to improve the approximation properties of the bivariate linear interpolation function when faced with the problem of sampling the signal at the intra-pixel misplacement (x0, y0). The energy measure, called intensity-curvature functional, is purposely designed yielding a polynomial system which zeros are the spatial set of points called sub-pixel efficacy region (SRE) of the interpolation function. The SRE uses empirically validated mathematical processes to determine the novel re-sampling locations (xr0, yr0) where the signal is sampled (calculated with the bivariate linear interpolation function) showing the optimisation of the interpolation error, which becomes smaller than the interpolation error obtained when sampling at the misplacement (x0, y0). The novel re-sampling locations have been sized to be a fraction of the pixel size whereas earlier they were sized to be a fraction of the misplacement (Ciulla and Deek, 2005). This research reflects the results previously published.