Calculation of the Classic-Curvature and the Intensity-Curvature Term Before Interpolation of a Bivariate Polynomial

Abstract

Abstract-This paper presents the calculation of the classic-curvature and the intensity-curvature term before interpolation of a bivariate polynomial model function. The classic-curvature is termed as y c (x, y) and the intensity-curvature term before interpolation is termed as E 0 . The classic-curvature is defined as the sum of the four second order partial derivatives of the bivariate polynomial. The intensity-curvature term before interpolation is defined as the integral of the product between the pixel intensity value termed as f(0, 0) and the classic-curvature calculated at the origin of the coordinate system of the pixel. This paper presents an application of the calculation of classic-curvature and the intensitycurvature term before interpolation using twodimensional Magnetic Resonance Imaging (MRI) data and reports for the first time in the literature on the behavior of the intensity-curvature term before interpolation.Index Terms-Magnetic Resonance Imaging (MRI), classic-curvature, intensity-curvature term before interpolation, intensity-curvature measurement approaches, first order partial derivative, second order partial derivative, bivariate polynomial, model function, image.