This paper intends to reinforce on the mathematical formalism of the calculation of the Intensity-Curvature Functional (ICF) of the signal-image and to present applications of the ICF to Magnetic Resonance Imaging (MRI) of human brain tumors. The ICF of the signal-image in one dimension or multiple dimensions is calculated as the ratio between two terms. The two terms are: (i) the integral of the product between the model function fitted to the MRI data and the classic-curvature, which are both calculated at the grid node of the sampled signal, and (ii) the integral of the product between the model function fit-ted to the MRI data and the classic-curvature, which are both calculated at the intra-node location used to re-sample the signal-image. The Intensity-Curvature Functional is therefore employed to re-map the MRI data into a new domain. This paper also emphasizes on three major findings provided with the Intensity-Curvature Functional when applied to two-dimensional Magnetic Resonance Imaging (MRI) data of human brain tumors. The three findings are: (i) the visu-ally perceptible third dimension perpendicular to the imaging plane of the MRI, (ii) the medical intensity-curvature measure map related to the accumulation of fluids in the tumor area of the brain and more generally of the human brain cortex, and (iii) the fact that the ICF is a filter mask which can be convolved to the MRI data so to filter the MRI, which benefits of an enhanced gray level scale. Indeed the novelty of this research is that, in four subjects out of eight, the ICF based filtering of the Fluid Attenuated Inversion Recovery (FLAIR) imaging modality benefits of an enhanced gray scale which allows the observation of details not visible in the FLAIR.
intensity-curvature functional, magnetic resonance imaging, visually perceptible third dimension, medical intensity-curvature measure map, filter mask.