Combined inverse Fourier transformation of magnetic resonance andintensity‐curvaturefunctional images

Abstract

This research reports an image processing technique used to merge Magnetic Resonance Imaging (MRI) or Magnetic Resonance Angiography (MRA) with their intensity‐curvature functional (ICF). Given a two‐dimensional MR image, six 2D model polynomial functions were fitted to the image, and six ICF images were calculated. The MR image and its ICF were direct Fourier transformed. The phase of MR image is estimated pixel‐by‐pixel as arctangent of ratio between imaginary and real components of k‐space and is called phase ratio. The phase of ICF is the phase of inverse Fourier transformation and is called base phase. The two values of phase were summed up and used to reconstruct ICF images through inverse Fourier transformation. The reconstructed ICF image is the combination of MR and ICF. Data obtained with T2‐MRI and MRA indicate that the image processing technique elucidates two findings: improvement of vessel detection in T2‐MRI; and change of the contrast of T2‐MRI and MRA. ICF and reconstructed ICF images are sharper than T2‐MRI and MRA are. The degree of sharpness of such images causes improvement of vessel detection and also changes the contrast. The practical implication and potential clinical benefit that the technique offers is to allow expansion of T2‐MRI functionality because reconstructed ICF images allow detection and highlight of either hypo‐intense tissue or hyper‐intense tissue.

Edge detection in two-dimensional images through model polynomial fitting and first order derivative

“…The calculation of the FOD is carried out through calculus on a continuous function fitted to the image pixels. The calculation of first and second order partial derivatives of an image fitted with polynomials is also of recent inception, it yields to re-sampling techniques capable to extract information from images, and it has found a number of applications in MRI processing of the human brain (Ciulla, 2019a(Ciulla, , 2019b(Ciulla, , 2020Ciulla and Agyapong, 2019). The key to edge detection property of the model function is the mathematical expression of gradients in the formula of the function.…”