| Abstract: | This paper describes a novel theoretical approach for the improvement of the bivariate linear interpolation function. The basic premise of this theory consists of quantifying the effect of the interpolation function on an image’s pixel by the product of the value of the pixel intensity times the sum of non-null second order derivatives of the function. The product is called intensity-curvature term and it is calculated at the grid node (x, y) = (0, 0) and termed Eo(x, y), and at the generic intra-pixel location (x, y) ? (0, 0) and termed EIN(x, y). The ratio between the two terms Eo(x, y) and EIN(x, y) consists of the Intensity-Curvature Functional (?E). First order derivatives of ?E are computed to derive a polynomial system, with zeros at the extreme points of ?E within the pixel and that are called Sub-pixel Efficacy Region (SRE). Given a re-sampling location (x0, y0), the SRE is used to project it onto a novel location (xr0, yr0) where the approximation properties of the interpolation function lead to error minimization. Two conceptions are thus derived from ?E: (i) error improvement is set dependent on pixel intensity and curvature of the interpolation function and (ii) the novel re-sampling location varies locally between pixels depending on local properties of the interpolation function as expressed by the intensity-curvature distribution at the neighbourhood. Accordingly, a novel scheme of bivariate linear interpolation is determined with improved approximation properties.
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