A Fast Hough Transform for the Parametrisation of Straight Lines using Fourier Methods |
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| Affiliation: | 1. Department of Interventional Radiology, Gustave Roussy, Villejuif, France;2. Biostatistics and Epidemiology Unit, Gustave Roussy, Université Paris-Saclay University, CESP, INSERM, Villejuif, F-94805, France;3. Drug Development Department (DITEP), Gustave Roussy, Villejuif, France;4. Department of Pathology and Laboratory Medicine, Gustave Roussy, Villejuif, France;5. Faculté de Médecine, Kremlin-Bicêtre, Université Paris Sud, France;6. Laboratory of Translational Research and Biological Resource Center – AMMICA, INSERM US23/CNRS UMS3655, France;7. Laboratory of Translational Research in Immunology – LRTI, INSERM U1015, Gustave Roussy, France;1. Department of Physics, Gustaf Hällströmin katu 2a, FI-00014 University of Helsinki, Finland;2. Finnish Geospatial Research Institute (FGI), Geodeetinrinne 2, FI-02430 Masala, Finland;3. Institute Astronomical Observatory, Faculty of Physics, Adam Mickiewicz University, ul. Sloneczna 36, PL-60-286 Poznan, Poland;4. Observatoire de la Côte d׳Azur, route de l׳Observatoire, BP4229, F-06304 Nice Cedex 4, France;5. Observatoire de Paris, IMCCE, Institut de mécanique céleste et de calcul des éphémérides, Unité Mixte de Recherche UMR-CNRS 8028, 77 avenue Denfert-Rochereau, F-75014 Paris, France;6. INAF, Osservatorio Astrofisico di Arcetri, Largo Enrico Fermi 5, I-50125 Firenze, Italy;1. Urologic Oncology Branch, National Cancer Institute, National Institutes of Health, Bethesda, Maryland;2. Molecular Imaging Program, National Cancer Institute, National Institutes of Health, Bethesda, Maryland;3. Center for Interventional Oncology, National Cancer Institute, National Institutes of Health, Bethesda, Maryland;4. Department of Urology, George Washington University, Washington, D. C.;5. Department of Urology and Pediatric Urology, University Medical Center Mainz, Johannes Gutenberg University Mainz, Germany;1. Department of Earth and Planetary Sciences and Institute of Earth, Ocean, and Atmospheric Sciences, Rutgers University, Piscataway, NJ, 08854, USA;2. Department of Earth and Planetary Sciences, Harvard University, 20 Oxford Street, Cambridge, MA, 02138, USA;3. Rutgers Energy Institute, Rutgers University, New Brunswick, NJ, 08901, USA;4. Department of Geosciences and Earth and Environmental Systems Institute, Pennsylvania State University, University Park, PA, 16802, USA |
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| Abstract: | The Hough transform is a useful technique in the detection of straight lines and curves in an image. Due to the mathematical similarity of the Hough transform and the forward Radon transform, the Hough transform can be computed using the Radon transform which, in turn, can be evaluated using the central slice theorem. This involves a two-dimensional Fourier transform, an x-y to r-θ mapping and a 1D Fourier transform. This can be implemented in specialized hardware to take advantage of the computational savings of the fast Fourier transform. In this paper, we outline a fast and efficient method for the computation of the Hough transform using Fourier methods. The maxima points generated in the Radon space, corresponding to the parametrisation of straight lines, can be enhanced with a post transform convolutional filter. This can be applied as a 1D filtering operation on the resampled data whilst in the Fourier space, so further speeding the computation. Additionally, any edge enhancement or smoothing operations on the input function can be combined into the filter and applied as a net filter function. |
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