Repairing Binary Images Through the 2D Diamond Grid
A 2D binary image is well-composed if it does not contain a $$2\times 2$$ configuration of two diagonal black and two diagonal white squares. We propose a simple repairing algorithm to construct two well-composed images $$I_4$$ and $$I_8$$ starting from an image I, and we prove that $$I_4$$ and $$I_...
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| Published in | Combinatorial Image Analysis Vol. 12148; pp. 183 - 198 |
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| Main Authors | , |
| Format | Book Chapter |
| Language | English |
| Published |
Switzerland
Springer International Publishing AG
2020
Springer International Publishing |
| Series | Lecture Notes in Computer Science |
| Subjects | |
| Online Access | Get full text |
| ISBN | 9783030510015 3030510018 |
| ISSN | 0302-9743 1611-3349 |
| DOI | 10.1007/978-3-030-51002-2_13 |
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| Summary: | A 2D binary image is well-composed if it does not contain a $$2\times 2$$ configuration of two diagonal black and two diagonal white squares. We propose a simple repairing algorithm to construct two well-composed images $$I_4$$ and $$I_8$$ starting from an image I, and we prove that $$I_4$$ and $$I_8$$ are homotopy equivalent to I with 4- and 8-adjacency, respectively. This is achieved by passing from the original square grid to another one, rotated by $$\pi /4$$ , whose pixels correspond to the original pixels and to their vertices. The images $$I_4$$ and $$I_8$$ are double in size with respect to the image I. Experimental comparisons and applications are also shown. |
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| Bibliography: | Original Abstract: A 2D binary image is well-composed if it does not contain a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2\times 2$$\end{document} configuration of two diagonal black and two diagonal white squares. We propose a simple repairing algorithm to construct two well-composed images \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$I_4$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$I_8$$\end{document} starting from an image I, and we prove that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$I_4$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$I_8$$\end{document} are homotopy equivalent to I with 4- and 8-adjacency, respectively. This is achieved by passing from the original square grid to another one, rotated by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi /4$$\end{document}, whose pixels correspond to the original pixels and to their vertices. The images \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$I_4$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$I_8$$\end{document} are double in size with respect to the image I. Experimental comparisons and applications are also shown. |
| ISBN: | 9783030510015 3030510018 |
| ISSN: | 0302-9743 1611-3349 |
| DOI: | 10.1007/978-3-030-51002-2_13 |