Intensity-curvature functional based digital high pass filter of the bivariate cubic B-spline model polynomial function

Abstract

This research addresses the design of intensity-curvature functional (ICF) based digital high pass filter (HPF). ICF is calculated from bivariate cubic B-spline model polynomial function and is called ICF-based HPF. 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. The theoretical basis of this research is called intensitycurvature concept. The concept envisions to replace signal intensity with the product between signal intensity and sum of second order partial derivatives of the model function. Extrapolation of the concept in two-dimensions (2D) makes it possible to calculate the ICF of an image. Theoretical treatise is presented to demonstrate the hypothesis that ICF is HPF signal. 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. Through comparison of image space and k-space magnitude, results indicate that HPFs behave differently. Traditional HPF filtering and ICF-based filtering are superior to PSO-based filtering. Images filtered with traditional HPF are sharper than images filtered with ICF-based filter. 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. This research provides confirmation on the math procedure to use in order to design 2D HPF from a model bivariate polynomial function.

Combined inverse Fourier transformation of magnetic resonance andintensity‐curvaturefunctional images

“…T2‐weighted MRI is not indicated for vessel imaging, and in this context, the paper proposes a technique able to improve vessels detection in T2‐MRI. This aspect is not reported elsewhere and is thus the main novelty of this research vs recent developments 27‐30 . Moreover, this research makes a neat progress vs the inverse Fourier transformation procedure reported earlier 28 .…”

“…Improvement of vessel detection in T2‐MRI and change of contrast of T2‐MRI and MRA are caused by sharpening effect of ICF and reconstructed ICF images. Present state of knowledge in intensity‐curvature image processing is based on evidence provided in support to the use of ICF as image space and k‐space filter 27‐30 . The main contribution of this research is the signal processing technique illustrated in Figure 1.…”

“…The present research relates to vessel imaging, it looks at the computational aspect and is motivated by recent developments, 27‐30 which indicate ICF of MR images as filtering technique able to achieve vessel detection and to change the contrast. Hence, this paper proposes a novel fully computational technique which explores the combination of MR images with ICF images.…”

“…Bivariate linear. The mathematics of the model polynomial functions were reported elsewhere while describing the ICF calculated from MRI 27‐29 . Table 1 shows the abbreviations used in this manuscript when referring to model polynomial functions 27‐29 …”

“…An immediate application of ICF is re‐sampling which yields to the ICF image. The ICF image has been proposed as image space and k‐space filter in MRI 27‐29 . To calculate the ICF of the model function requires the model polynomial function to be second‐order differentiable and to have non‐null sum of second‐order partial derivatives calculated at the origin of the pixel coordinate system.…”