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Single Photon Emission Computed Tomography (SPECT) and SPECT/CT Hybrid Imaging
Published in Michael Ljungberg, Handbook of Nuclear Medicine and Molecular Imaging for Physicists, 2022
Michael Ljungberg, Kjell Erlandsson
The consequence of this theorem is that it is theoretically possible to reconstruct an image from its Radon transform. One way to do this could be to first construct the 2D-FT of the image and then apply Eq. 16.3. However, this would require interpolation of the data from polar to Cartesian coordinates in the frequency domain, which is doable but not straightforward.
Preliminary notions
Published in Daniele Panetta, Niccoló Camarlinghi, 3D Image Reconstruction for CT and PET, 2020
Daniele Panetta, Niccoló Camarlinghi
In two dimensions, the Radon Transform (RT) of a function f is another function representing a complete set of line integrals of f, for all possible lines intersecting the object. Given a line of equation the RT of a function f in the xy plane can be written as where δ1 is the 1-dimensional Dirac delta function. In the n-dimensional case, with n > 2, the RT is no longer the set of line integrals of f but instead a set of plane integrals, through hyperplanes with dimension n − 1. Among its various properties, the RT is linear and it represents in a idealized fashion the process of projection data acquisition in real imaging systems.
Radiographic Imaging
Published in Eric Ford, Primer on Radiation Oncology Physics, 2020
The mathematics behind computed tomography (CT) dates back to the early 20th century (c.f. Radon transform and its uses). The modern incarnation of this for medical imaging was pioneered by Sir Godfrey Hounsfield at EMI research in the UK and, separately, Allan Cormack at Tufts. CT was first used in 1971 by Hounsfield to image a patient, and the first scanner was installed shortly after in the United States at the Mayo Clinic. Hounsfield and Cormack shared the 1979 Nobel Prize in medicine for this work.
Quantifying the similarity of 2D images using edge pixels: an application to the forensic comparison of footwear impressions
Published in Journal of Applied Statistics, 2021
Soyoung Park, Alicia Carriquiry
The problem that consists of comparing two images is not new and has arisen in many different disciplines, including footwear examination. Bouridane et al. [4] proposed a fully automatic system for matching and retrieval of 2D images that uses a fractal decomposition based on pattern comparison. AlGarni and Hamiane [1] extract features of the outsole using Hu moments [14] in their algorithm and Wei and Gwo [34] and Gwo and Wei [12] summarize outsole patterns using Zernike moments. Patil and Kulkarni [23] propose a matching method that relies on a Gabor transform for feature extraction and a Radon transform for estimating the rotation angle between the images. Other authors, including [7] rely on a Fourier transformation (FT) of the image and on power spectral densities (PSD) to automatically retrieve shoe outsole images from a database.
Optical flow and image segmentation analysis for noninvasive precise mapping of microwave thermal ablation in X-ray CT scans - ex vivo study
Published in International Journal of Hyperthermia, 2018
Omri Ziv, S. Nahum Goldberg, Yitzhak Nissenbaum, Jacob Sosna, Noam Weiss, Haim Azhari
The second analysis was performed by generating a sinogram (Radon transform) for each acquired frame. The sinogram was then down sampled by factors of 2, 4 and 8, by choosing subsets from the Radon sinogram. Using the inverse Radon transform new sets of images (with lower quality) were generated and analysed (Figure 7). The corresponding obtained contours were compared to the gold standard so the performances of both algorithms can be compared with each other.