Magnetic resonance imaging and the signal-image processing techniques developed under the umbrella of the unifying theory -- The intuition -- The conception of the intensity-curvature functional -- The conception of the sub-pixel efficacy region -- Assessment of the truth foreseen in the intuition -- The notion -- The theoretical approach to the improvement of the interpolation error: bivariate linear interpolation function -- The results of the sub-pixel efficacy region based bivariate linear interpolation function -- Interpolation procedures -- The extension of the theory to the trivariate linear interpolation function -- The results of the sub-pixel efficacy region based trivariate linear interpolation function -- Equating the two intensity-curature terms, before and after interpoliation, attempting to obtain resilient interpoliaiton: trivariate linear interpolation function -- On the literature of B-spline interpolation functions -- The extension of theory and methodology to B-splines -- The results of the sub-pixel efficacy region based B-spline interpolation functions -- On the properties of the unifying theory and the derived sub-pixel efficacy region -- The main innovation determined by the sub-pixel efficacy region -- The unifying theory embraces lagrange and sinc interpolation functions -- The results of the sub-pixel efficacy region based lagrange and sinc interpolation functions -- On the implications of the sub-pixel efficacy region and the bridging concept of the unifying theory.