Use of discrete gradient operators for the automatic determination of vanishing points: Comparative analysis |
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| Authors: | José Ignacio Rojas-Sola Antonio Romero-Manchado |
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| Affiliation: | 1. University of Jaen, Department of Engineering Graphics, Design and Projects, Campus de las Lagunillas, Jaen 23071, Spain;2. University of Jaen, Department of Cartographic Engineering, Geodesy and Photogrammetry, Campus de las Lagunillas, Jaen 23071, Spain;1. KERMIT, Department of Data Analysis and Mathematical Modelling, Ghent University, Coupure links 653, B-9000 Gent, Belgium;2. Departamento de Estadistica, Informatica y Matematicas, Universidad Publica de Navarra, 31006 Pamplona, Spain;1. Department of Informatics, King’s College London, London WC2R 2LS, UK;2. School of Computing, University of Leeds, Leeds LS2 9JT, UK;3. School of Mathematics and Statistics, UNSW Australia, Sydney, NSW 2052, Australia;1. Japan Atomic Energy Agency, Tokai-mura Naka-gun Ibaraki 319-1195, Japan;2. University of California, Berkeley, 7 Gauss Way Berkeley, CA 94720-7450, USA;3. Faculty of Eng. Hokkaido Univ, Kita-13 Nishi-8 Kita-ku Sapporo 060-8628, Japan;1. School of Mathematics and Statistics, UNSW Sydney, Sydney, NSW 2052, Australia;2. Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands;1. Department of Chemistry, Indiana University, 800 E. Kirkwood Ave., Bloomington, IN 47405, USA;2. Center for Exploration of Energy and Matter, Indiana University, 2401 Milo B. Sampson Ln., Bloomington, IN 47408, USA;3. Department of Physics, Indiana University, 727 E. 3rd St., Bloomington, IN 47405, USA |
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| Abstract: | Thales’ second theorem can be used for the automatic detection of the vanishing points of an image. This paper explores its reliability and accuracy according to the type of operator used for the detection of edges. An algorithm has been used which processes a photographic image according to the operator selected. The result is a point cloud which is then used to find the desired solution. The comparison between the four discrete gradient operators (Frei-Chen, Prewitt, Roberts and Sobel) has been made taking into account the resolution of the image and the number of vanishing points. The results obtained show that Frei-Chen’s operator shows good performance in determining vanishing points with respect to the spatial X axis, Sobel’s operator is the best for determining the vanishing point with respect to the spatial Y axis, Roberts’ operator gives good results for calculating vanishing points in both spatial axes, and Prewitt’s operator is not appropriate for processing this type of image. |
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