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

Abstract

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.

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 .…”

“…The Z‐Test in Figure 5D shows that the one‐tailed P ‐value is true for all of the bins of the histogram in (B). The ICF calculated from the bivariate linear model function (SRE2D) is the optimal ICF of the six reported, is a k‐space filter 27 and an image space high pass filter 28,30 …”

“…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.…”