This paper solves the biomedical engineering problem of the extraction of complementary and/or additional information related to the depths of the anatomical structures of the human brain tumor imaged with Magnetic Resonance Imaging (MRI). The combined calculation of the signal resilient to interpolation and the Intensity-Curvature Functional provides with the complementary and/or additional information. The steps to undertake for the calculation of the signal resilient to interpolation are: (i) fitting a polynomial function to the signal, (ii) the calculation of the classic-curvature of the signal, (iii) the calculation of the Intensity-Curvature term before interpolation of the signal, (iv) the calculation of the Intensity-Curvature term after interpolation of the signal, (v) the solution of the equation of the two aforementioned Intensity-Curvature terms of the signal provides with the signal resilient to interpolation. The Intensity-Curvature Functional is the result of the ratio between the two Intensity-Curvature terms before and after interpolation. Because of the fact that the signal resilient to interpolation and the Intensity-Curvature Functional are derived through the process of re-sampling the original signal, it is possible to obtain an immense number of images from the original MRI signal. This paper shows the combined use of the signal resilient to interpolation and the Intensity-Curvature Functional in diagnostic settings when evaluating a tumor imaged with MRI. Additionally, the Intensity-Curvature Functional can identify the tumor contour line.

This research solves the computational intelligence problem of devising two mathematical engineering tools called Classic-Curvature and Intensity-Curvature Functional. It is possible to calculate the two mathematical engineering tools from any model polynomial function which embeds the property of second-order differentiability. This work presents results obtained with bivariate and trivariate cubic Lagrange polynomials. The use of the Classic-Curvature and the Intensity-Curvature Functional can add complementary information in medical imaging, specifically in Magnetic Resonance Imaging (MRI) of the human brain.