This methodology benefits from the intensity-curvature concept and is based on the calculation of the intensity-curvature functional (ICF). Recently, we reported a methodology to design digital HPFs from three model polynomial functions. This research provides confirmation on the math procedure to use in order to design 2D HPF from a model bivariate polynomial function. The contribution of this research can be summarized as follows: (1) Math description of the constraints that ICF need to obey to in order to function as HPF (2) Math of ICF-based HPF of bivariate cubic B-spline (3) Image space comparisons between HPFs (4) K-space magnitude comparisons between HPFs. Images filtered with traditional HPF are sharper than images filtered with ICF-based filter. Traditional HPF filtering and ICF-based filtering are superior to PSO-based filtering. Through comparison of image space and k-space magnitude, results indicate that HPFs behave differently. Empirical evidence then validates the assumption and also extends the comparison between ICF-based HPF and ten different HPFs among which is traditional HPF and particle swarm optimization (PSO) based HPF. Theoretical treatise is presented to demonstrate the hypothesis that ICF is HPF signal. Extrapolation of the concept in two-dimensions (2D) makes it possible to calculate the ICF of an image. The concept envisions to replace signal intensity with the product between signal intensity and sum of second order partial derivatives of the model function. The theoretical basis of this research is called intensity-curvature concept.
In order to calculate ICF, the model function needs to be second order differentiable and to have non-null classic-curvature calculated at the origin (0, 0) of the pixel coordinate system. ICF is calculated from bivariate cubic B-spline model polynomial function and is called ICF-based HPF. This research addresses the design of intensity-curvature functional (ICF) based digital high pass filter (HPF).
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