#### The Intensity-Curvature Functional of The Trivariate Cubic Lagrange Interpolation Formula

Full Text (PDF, 1926KB), PP.36-44

##### Author(s)

Carlo Ciulla 1,*

1. University for Information Science and Technology "St. Paul the Apostle" Partizanska bb., 6000 Ohrid, Republic of Macedonia

* Corresponding author.

Received: 11 Apr. 2013 / Revised: 15 May 2013 / Accepted: 13 Jun. 2013 / Published: 8 Aug. 2013

##### Index Terms

Model Function, Second Order Partial Derivative, Intensity-Curvature Functional, Signal-Image Content, Trivariate Cubic Lagrange Interpolation Formula

##### Abstract

A Signal-Image fitted with a model function, embeds the property of the intensity-curvature content, which is defined through the math formulae 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 human brain and also with a sample contextual image. The Intensity-Curvature Functional is calculated in three dimensions while re-sampling the signal-image with the trivariate cubic Lagrange interpolation formula and also in two dimensions while re-sampling using the bivariate cubic Lagrange interpolation formula. 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 sum of the second order partial derivatives of the model function, both of them calculated at the grid point. The intensity-curvature term after interpolation is calculated through the multiplication between: (i) the signal intensity and (ii) the sum of second order partial derivatives of the model function, both of them calculated at the intra-pixel location chosen to re-sample the signal. Two most relevant properties are discernible through the Intensity-Curvature Functional. One property is the intensity-curvature content, and the other property is that the signal-image is re-imaged so to create a novel mapping of the original signal-image from which the Intensity-Curvature Functional is calculated. The novel mapping highlights and portraits the original image features under a different perspective.

##### Cite This Paper

Carlo Ciulla,"The Intensity-Curvature Functional of The Trivariate Cubic Lagrange Interpolation Formula", IJIGSP, vol.5, no.10, pp.36-44, 2013. DOI: 10.5815/ijigsp.2013.10.05

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