A compilation on the contribution of the classic-curvature and the intensity-curvature functional to the study of healthy and pathological MRI of the human brain

Int J Appl Sci Biotechnol

Shikoska

Veljanovski³

et al. 2017

Self Cite

The intensity-curvature term is the concept at the root foundation of this paper. The concept entails the multiplication between the value of the image pixel intensity and the value of the classic-curvature (CC(x, y)). The CC(x, y) is the sum of all of the second order partial derivatives of the model polynomial function fitted to the image pixel. The intensity-curvature term (ICT) before interpolation E0(x, y) is defined as the antiderivative of the product between the pixel intensity and the classic-curvature calculated at the origin of the pixel coordinate system (CC(0, 0)). The intensity-curvature term (ICT) after interpolation EIN(x, y) is defined as the antiderivative of the product between the signal re-sampled by the model polynomial function at the intra-pixel location (x, y) and the classic-curvature. The intensity-curvature functional (ICF) is defined as the ratio between E0(x, y) and EIN(x, y). When the ICF is almost equal to the numerical value of one (‘1’), E0(x, y) and EIN(x, y) are two additional domains (images) where to study the image from which they are calculated. The ICTs presented in this paper are able to highlight the human brain vessels detected with Magnetic Resonance Imaging (MRI), through a signal processing technique called inverse Fourier transformation procedure. The real and imaginary parts of the k-space of the ICT are subtracted from the real and imaginary parts of the k-space of the MRI signal. The resulting k-space is inverse Fourier transformed, and the human brain vessels are highlighted.Int. J. Appl. Sci. Biotechnol. Vol 5(3): 326-335

Section: The Motivation Of the Studymentioning

confidence: 99%

The Intensity-Curvature of Human Brain Vessels Detected with Magnetic Resonance Imaging

Int J Appl Sci Biotechnol

Shikoska

Veljanovski³

et al. 2017

Self Cite

“…The property of second-order differentiability in its domain of definition (the pixel) and 2. The non-null classic-curvature of the model function calculated at the origin (0, 0) of the pixel coordinate system [10]. It uses the pixel intensity value f(0, 0) and eight neighboring pixel intensity values: f (1/2, 1/2), f (− 1/2, − 1/2), f (2/3, 2/3), f (− 2/3, − 2/3), f (− 1, − 1), f (1, 1), f (3/2, 3/2) and f (− 3/2, − 3/2).…”

Section: Icf Of Bivariate Cubic B-spline Model Functionmentioning

confidence: 99%

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

Vis. Comput. Ind. Biomed. Art

Agyapong

2019

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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.

“…The denominator (which is labeled E IN ( x , y )) is defined as the antiderivative of the product between the model function and the classic‐curvature. The classic‐curvature is also a function of the independent variables: the tuple ( x , y ) in two dimensions and the triplet ( x , y , z ) in three dimensions (Ciulla et al., ). This paper presents the following: (a) A class of functions attuned to the calculation of the ICF in 2D; (b) Novel results obtained through the extension of the intensity‐curvature concept to 3D; (c) Novel results obtained when the ICF is used as filter to reconstruct human brain vessels imaged through T2 MRI.…”

Section: Introductionmentioning

confidence: 99%

Intensity‐curvature functional‐based filtering in image space and k‐space: Applications in magnetic resonance imaging of the human brain

2019

High Frequency

Self Cite

This research examines the use of the intensity‐curvature functional (ICF) as filter in image space and in k‐space. The novelty of this study is three‐folded: (a) The evidence that the ICF calculated from three additional (International Journal of Imaging Systems and Technology, 28, 2018, 54) two‐dimensional model polynomial functions is an image space filter; (b) An additional (The use of the intensity‐curvature functional as k‐space filter: Applications in magnetic resonance imaging of the human brain, 2018) ICF‐based k‐space filtering technique applicable to two‐dimensional magnetic resonance images; (c) Results obtained through the calculation of the ICF of the trivariate cubic Lagrange model polynomial function (LGR3D). Although ICF‐based k‐space filtering delivers clear and well‐defined images, ICF‐based image space filtering remains superior when reconstructing vessel images in T2 MRI. The ICF of the LGR3D function provides sharp images too.