The Intensity-Curvature Functional of The Trivariate Cubic Lagrange Interpolation Formula
Carlo Ciulla · International Journal of Image Graphics and Signal Processing · 2013
A Signal-Image fitted with a model function, embeds the property of the intensity-curvature content, which is defined through the math formu lae merging together the signal intensity with the second order derivatives of the model function.This work presents one of the measures of the intensity-curvature content, which is called the Intensity-Curvature Functional along with qualitative results obtained with Magnetic Resonance Imaging (MRI) of the hu man brain and also with a samp le contextual image.The Intensity-Curvature Functional is calculated in three dimensions while re-sampling the signal-image with the trivariate cubic Lagrange interpolation formu la and also in two dimensions while re-samp ling using the b ivariate cubic Lagrange interpolation formu la.The Intensity-Curvature Functional is defined as the ratio between the numerator called intensity-curvature term before interpolation and the denominator called intensity-curvature term after interpolation.The intensity-curvature term before interpolation is calculated through the multiplication between: (i) the signal intensity and (ii) the su m of the second order partial derivatives of the model function, both of them calculated at the grid point.The intensitycurvature term after interpolation is calculated through the mu ltiplication between: (i) the signal intensity and (ii) the sum of second order partial derivatives of the model function, both of them calculated at the intrapixel location chosen to re-sample the signal.Two most relevant properties are discernible through the Intensity-Curvature Functional.One property is the intensitycurvature content, and the other property is that the signal-image is re-imaged so to create a novel mapping of the original signal-image fro m which the Intensity-Curvature Functional is calculated.The novel mapping highlights and portraits the original image features under a different perspective.