Intensity-Curvature Measurement Approaches for the Diagnosis of Magnetic Resonance Imaging Brain Tumors

Ciulla, Carlo; Veljanovski, Dimitar; Shikoska, Ustijana Rechkoska; Risteski, Filip A.

doi:10.1016/j.jare.2015.01.001

Cited by 15 publications

(47 citation statements)

References 49 publications

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“…The intensity-curvature term before interpolation is defined as the integral of the multiplication between the pixel intensity f(0, 0) and the classic-curvature calculated at the origin of the pixel coordinate system ((x, y) = (0, 0)). Both of the classiccurvature and the intensity-curvature term before interpolation fall into the category of intensity-curvature measurement approaches [7].…”

Section: Theory and Methodsmentioning

confidence: 99%

“…The intensity-curvature functional before interpolation image can be calculated on the basis of the classic-curvature image. Both of the aforementioned intensity-curvature measurement approaches [7] descend from the model function used to create the continuum in the MRI data. The second order partial order derivatives, the classic-curvature, and the intensity-curvature term before interpolation were implemented in software and were successfully calculated and visualized with the use of the following computer technology applications: (i) Visual Studio IDE, (ii) jdk-6u-45windows-x64 (Java), (iii) jre-7u71windows-x64 (Java), (iv) the computer Operating System (OS) command prompt and (iv) ImageJ (http://imagej.nih.gov/ij/).…”

Section: B the Technological Effortmentioning

confidence: 99%

“…The classic-curvature images have been object of considerable study [7,12,14,17] and allow to distinguish clearly the brain tumor. Moreover, similarly to the original MRI image, the classic-curvature image shows a clear layout of the tumor and the surrounding brain structures.…”

Section: The Scope Of the Researchmentioning

confidence: 99%

“…In order to frame into the literature the works of this research, which recalls works reported earlier [7,[12][13][14][15][16][17], it is necessary to consider the rationale of the study presented in this paper. So far, no studies have been reported attempting to achieve the characterization of the intensity-curvature term before interpolation.…”

Section: The Scope Of the Researchmentioning

confidence: 99%

“…The work presented in this paper may frame the two intensity-curvature measurement approaches named: (i) classic-curvature image and (ii) intensity-curvature term before interpolation image [7]; within the context of ICT technologies which aim is to post-process MRI data in order to extract information about the human brain tumor mass, and to help physicians to study and analyze the tumor.…”

Section: Introduction Magnetic Resonance Imaging (Mri) Computerizedmentioning

confidence: 99%

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Calculation of the Classic-Curvature and the Intensity-Curvature Term Before Interpolation of a Bivariate Polynomial

Agyapong

2015

IJIEEB

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Abstract-This paper presents the calculation of the classic-curvature and the intensity-curvature term before interpolation of a bivariate polynomial model function. The classic-curvature is termed as y c (x, y) and the intensity-curvature term before interpolation is termed as E 0 . The classic-curvature is defined as the sum of the four second order partial derivatives of the bivariate polynomial. The intensity-curvature term before interpolation is defined as the integral of the product between the pixel intensity value termed as f(0, 0) and the classic-curvature calculated at the origin of the coordinate system of the pixel. This paper presents an application of the calculation of classic-curvature and the intensitycurvature term before interpolation using twodimensional Magnetic Resonance Imaging (MRI) data and reports for the first time in the literature on the behavior of the intensity-curvature term before interpolation.Index Terms-Magnetic Resonance Imaging (MRI), classic-curvature, intensity-curvature term before interpolation, intensity-curvature measurement approaches, first order partial derivative, second order partial derivative, bivariate polynomial, model function, image.

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Section: Theory and Methodsmentioning

confidence: 99%

Section: B the Technological Effortmentioning

confidence: 99%

Section: The Scope Of the Researchmentioning

confidence: 99%

Section: The Scope Of the Researchmentioning

confidence: 99%

Section: Introduction Magnetic Resonance Imaging (Mri) Computerizedmentioning

confidence: 99%

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Calculation of the Classic-Curvature and the Intensity-Curvature Term Before Interpolation of a Bivariate Polynomial

Agyapong

2015

IJIEEB

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Sampling technique for Fourier convolution theorem based k‐space filtering

et al. 2023

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This research presents a sampling technique for Fourier convolution theorem (FCT) based k-space filtering. One polynomial function and three transfer functions were selected: (1) Gaussian, (2) Bessel, (3) Butterworth, and (4) Chebyshev. The functions were sampled on the image grid, and they are called filtering functions. Each filtering function was multiplied by the Sinc function to obtain the "Sinc-shaped convolving function." The k-space of the Sinc-shaped convolving function is calculated by direct Fourier transform (FT) and it is featured by a central region. This central region of the k-space is rectangular in its shape because it is consequential to the direct FT of the product between the filtering function and the Sinc function. Low-pass and highpass filtering is obtained by inverse FT of the pointwise multiplication between the k-space of the departing image and the k-space of the Sinc-shaped convolving function. A variety of cut-off frequencies, bandwidth, sampling rates, and numbers of poles of the filters were verified as effective to filter the images. Filtering strength can be modified by fine-tuning the size of the central rectangular k-space region of the Sinc-shaped convolving functions. K-space analysis of departing images and filtered images provide additional evidence of effective filtering. Moreover, k-space filtering was compared to Z-space filtering using the extension of the FCT to Zspace. The novelty of this research is the sampling technique used to determine the Sinc-shaped convolving function. The sampling technique uses fine-tuning of bandwidth and sampling rate to determine the strength of the k-space filter.

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The use of the intensity‐curvature measurement approaches: Applications in magnetic resonance imaging of the human brain

Ciulla

2019

Engineering Reports

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This research describes signal processing techniques useful to highlight and contrast enhance human brain vessels detected with magnetic resonance imaging (MRI). The signal is here represented as multiplication between image intensity and the sum of second‐order partial derivatives of the model function fitted to MRI data. The implication of this novel and different concept is the introduction of the new variable called intensity‐curvature. The following six intensity‐curvature measurement approaches (ICMAs) can hence be calculated: classic‐curvature, intensity‐curvature functional (ICF), signal resilient to interpolation, resilient curvature, and intensity‐curvature terms (ICTs) before and after interpolation. This paper explores the use of ICMAs with applications in human brain MRI. Studying vasculature of the human brain is possible through two techniques apt to measure human brain MRI intensity‐curvature. The first technique is the inverse Fourier transformation procedure, which uses as k‐space filters the ICTs before and after interpolation. The other technique is called intensity‐curvature masking procedure, and it raises each ICMA to a power determining a nonlinear combination of ICMAs to sum up to MRI image intensity on a pixel‐by‐pixel basis. This paper reports that ICTs are k‐space filters, ICF is a high‐pass filter, and ICMAs are mask images. The major implication of these methodologies is effective k‐space filtering. The techniques here presented support visualization of human brain vessels. The advantage of these methods relies in speed of computation.

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Intensity-Curvature Measurement Approaches for the Diagnosis of Magnetic Resonance Imaging Brain Tumors

Cited by 15 publications

References 49 publications

Calculation of the Classic-Curvature and the Intensity-Curvature Term Before Interpolation of a Bivariate Polynomial

Calculation of the Classic-Curvature and the Intensity-Curvature Term Before Interpolation of a Bivariate Polynomial

Sampling technique for Fourier convolution theorem based k‐space filtering

The use of the intensity‐curvature measurement approaches: Applications in magnetic resonance imaging of the human brain

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