Recognition and Analysis of Image Patterns Based on Latin Squares by Means of Computational Algebraic Geometry
With the particular interest of being implemented in cryptography, the recognition and analysis of image patterns based on Latin squares has recently arisen as an efficient new approach for classifying partial Latin squares into isomorphism classes. This paper shows how the use of a Computer Algebra...
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doaj-a3c29676b6e549eaaeaeb21a59830b972021-03-22T00:00:44ZengMDPI AGMathematics2227-73902021-03-01966666610.3390/math9060666Recognition and Analysis of Image Patterns Based on Latin Squares by Means of Computational Algebraic GeometryRaúl M. Falcón0Department of Applied Mathematics I, University of Seville, 41012 Sevilla, SpainWith the particular interest of being implemented in cryptography, the recognition and analysis of image patterns based on Latin squares has recently arisen as an efficient new approach for classifying partial Latin squares into isomorphism classes. This paper shows how the use of a Computer Algebra System (CAS) becomes necessary to delve into this aspect. Thus, the recognition and analysis of image patterns based on these combinatorial structures benefits from the use of computational algebraic geometry to determine whether two given partial Latin squares describe the same affine algebraic set. This paper delves into this topic by focusing on the use of a CAS to characterize when two partial Latin squares are either partial transpose or partial isotopic.https://www.mdpi.com/2227-7390/9/6/666image pattern recognitionpartial Latin squareaffine algebraic setisomorphismpartial transposepartial isotopic |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Raúl M. Falcón |
spellingShingle |
Raúl M. Falcón Recognition and Analysis of Image Patterns Based on Latin Squares by Means of Computational Algebraic Geometry Mathematics image pattern recognition partial Latin square affine algebraic set isomorphism partial transpose partial isotopic |
author_facet |
Raúl M. Falcón |
author_sort |
Raúl M. Falcón |
title |
Recognition and Analysis of Image Patterns Based on Latin Squares by Means of Computational Algebraic Geometry |
title_short |
Recognition and Analysis of Image Patterns Based on Latin Squares by Means of Computational Algebraic Geometry |
title_full |
Recognition and Analysis of Image Patterns Based on Latin Squares by Means of Computational Algebraic Geometry |
title_fullStr |
Recognition and Analysis of Image Patterns Based on Latin Squares by Means of Computational Algebraic Geometry |
title_full_unstemmed |
Recognition and Analysis of Image Patterns Based on Latin Squares by Means of Computational Algebraic Geometry |
title_sort |
recognition and analysis of image patterns based on latin squares by means of computational algebraic geometry |
publisher |
MDPI AG |
series |
Mathematics |
issn |
2227-7390 |
publishDate |
2021-03-01 |
description |
With the particular interest of being implemented in cryptography, the recognition and analysis of image patterns based on Latin squares has recently arisen as an efficient new approach for classifying partial Latin squares into isomorphism classes. This paper shows how the use of a Computer Algebra System (CAS) becomes necessary to delve into this aspect. Thus, the recognition and analysis of image patterns based on these combinatorial structures benefits from the use of computational algebraic geometry to determine whether two given partial Latin squares describe the same affine algebraic set. This paper delves into this topic by focusing on the use of a CAS to characterize when two partial Latin squares are either partial transpose or partial isotopic. |
topic |
image pattern recognition partial Latin square affine algebraic set isomorphism partial transpose partial isotopic |
url |
https://www.mdpi.com/2227-7390/9/6/666 |
work_keys_str_mv |
AT raulmfalcon recognitionandanalysisofimagepatternsbasedonlatinsquaresbymeansofcomputationalalgebraicgeometry |
_version_ |
1724209728708411392 |