Pixel-driven computation of parallel and fan-beam projections of a digital image based on pixel-representation using a new formula

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Abstract

Background: The computation of the projections of a digital image – modelled as a superposition of square pixels – is essential in several algorithms in computed tomography, and also in many machine vision applications. Projections of digital images are computed through the ray-driven approach. Current pixel-driven methods, though simpler, involve interpolation kernels in the projection-domain – not based on the exact Radon transform (RT) of a square. Methods: A new analytical formula – for the line-integral of the unit pixel – simpler than that published previously, is derived. The formula allows easy, pixel-driven computation of the RT of a digital image based on the pixel model i.e., Riemann-sum approximation to the line integral. The method naturally allows pixel-driven backprojection, based on the same (pixel) model. The approach is extended to computing projections over divergent (fan-) beams, and its application as a generalized version of the traditional Hough transform, is discussed. Results: The Radon transform of the unit-pixel match that of a digital square image. The RT, of a mathematical phantom consisting of a superposition of elliptical disks, compares well with that based on analytical formula. A comparative study with the pixel driven approach with interpolation in the projection-domain, and its important variant, is included. The fan-beam projections of the square image and the phantom are presented. The applicability of the RT in estimating the Hough transform over precise lines, is shown. Conclusion: The new formula, a simplified version of that of Deans, is useful in pixel-driven computation of parallel and fan-beam projections based on Riemann-sum approximation, which is exact in the case of the common pixel-based image model. Pixel-driven approach is amenable to parallel, and also region-of-interest computation. The method is useful in CT as well as machine vision applications.

Original languageEnglish
Article number106672
JournalComputer Methods and Programs in Biomedicine
Volume216
DOIs
Publication statusPublished - 04-2022

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Science Applications
  • Health Informatics

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