Intensity‐curvature functional‐based digital high‐pass filters

Abstract

The intensity-curvature functional (ICF) of a model polynomial function is defined on a pixel-by-pixel basis by the ratio between the intensity-curvature term before interpolation and the intensity-curvature term after interpolation. Through the comparison with the traditional high-pass filter (HPF), this work presents evidence that the ICFs of three model polynomial functions can be tuned as HPFs. The evidence consists of the mathematical characterization of the ICF-based HPFs, qualitative comparisons in magnetic resonance imaging (MRI) of the human brain, and the determination of the finite impulse response (FIR) of the filters. The ICF-based HPFs can remove periodic noise in the low-frequency band. K E Y W O R D S finite impulse response, high-pass filter, intensity-curvature functional, model polynomial function, magnetic resonance imaging wileyonlinelibrary.com/journal/ima Int J Imaging Syst Technol.

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

“…The mathematical formulae for the calculation of the ICFs of the B32D, G42D, and SRE2D polynomial model functions were reported in Ciulla et al. ().…”

“…The model function is given in equation 1 in Ciulla et al. (). This formula is characterized by three gradients.…”

“…The ICTs are reported in equations 2 and 3 in Ciulla et al. ()), and the ICF is reported in equation 8 in Ciulla et al. ().…”

“…()), and the ICF is reported in equation 8 in Ciulla et al. (). Figure shows in (d) another example of ICF which displays information complementary to the T2 MRI (a) in relationship to the visibility of the vessel structures.…”

“…While Frangi et al. () use the Hessian of the Gaussian (Frangi et al., ), the intensity‐curvature concept uses the second‐order partial derivatives of the model polynomial function fitted pixel‐by‐pixel to the image data (Ciulla, Rechkoska, Risteski et al., ; Ciulla et al., ).…”