On the Intensity-Curvature Functional of the Bivariate Linear Function: The Third Dimension of Magnetic Resonance 2D Images in a Tumor Case Study
Carlo Ciulla, Ustijana Rechkoska Shikoska, Dijana Capeska Bogatinoska, Filip A. Risteski, Dimitar Veljanovski · American Journal of Signal Processing · 2014
The Intensity-Curvature Functional is a mathematical engineering instrument which is calculated using the following procedure. The ratio between: (i) the product between the signal-image pixel intensity and the Classic-Curvature, both of them calculated at the grid node of the sequel of digital samples; and (ii) the product between the signal-image and the Classic-Curvature, both of them calculated at the intra-pixel location chosen for re-sampling the sequel of digital samples. This manuscript reports on the following phenomenon observed when using the bivariate linear function to model the signal-image data and to calculate the Intensity-Curvature Functional of 2D Magnetic Resonance Imaging (MRI) of a human brain affected by a tumor. A third dimension perpendicular to the image plane appears from the two-dimensional MRI images. The third dimension highlights the features of the 2D image and allows the identification of the tumor contour line.