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Model Function, Second Order Derivative, Total Curvature, Intensity-Curvature Functional, Intensity-Curvature Measure, Signal-Image Content
The biomedical engineering problem addressed in this work is the one of finding a novel signal-image content measure called intensity-curvature functional making use of all of the second order derivatives of the model function fitted to the data. Given a signal-image made of a sequel of discrete samples and given a model function which embeds the property of second order differentiability, it is possible to quantify the content of the signal-image through a novel approach based on both of the intensity and of the total curvature of the signal-image. The signal-image is fitted with the model function. The total curvature can be calculated through the sum of all of the second order derivatives of the Hessian of the model function fitted to the data. The intensity-curvature functional is defined as the ratio between: (i) the integral of the multiplication between the value of the signal modeled through an interpolation function and the total curvature of the signal-image; both of them at the temporal-spatial location of its sampling (the grid nodes) and, (ii) the integral of the value of the multiplication between the signal modeled through an interpolation function and the total curvature of the signal-image; both of them at any given temporal-spatial location of its re-sampling (intra-pixel location). This manuscript shows both of the formulae and the qualitative results of: the intensity-curvature functional and the intensity-curvature measures which are conceptually linked to the intensity-curvature functional. The formulations here presented make the engineering innovation. The intensity-curvature functional depends on both of the model function fitting the signal-image and the magnitude of re-sampling employed to calculate the second order derivatives of the Hessian of the model function.
Carlo Ciulla,"On the Signal-Image Intensity-Curvature Content", IJIGSP, vol.5, no.5, pp.15-21, 2013. DOI: 10.5815/ijigsp.2013.05.02
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