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Open AccessArticle

Fourier-Based Automatic Transformation between Mapping Shapes—Cadastral and Land Registry Applications

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Departamento de Expresión Gráfica Arquitectónica y en la Ingeniería, Universidad de Granada, 18071 Granada, Spain
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Departamento de Ciencias de la Computación e Inteligencia Artificial, Universidad de Granada, 18071 Granada, Spain
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Departamento de Cartografia, Universidade Federal de Minas Gerais, 31270 Belo Horizonte, Brazil
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Author to whom correspondence should be addressed.
ISPRS Int. J. Geo-Inf. 2020, 9(8), 482; https://doi.org/10.3390/ijgi9080482
Received: 29 June 2020 / Revised: 31 July 2020 / Accepted: 3 August 2020 / Published: 6 August 2020
Sometimes it is necessary to know the transformation to apply to a mapping shape in order to locate its true place. Such an operation can be computed if a corresponding reference object exists and we can identify corresponding points in both shapes. Nevertheless our approach does not need to match any corresponding point beforehand. The method proposed defines a polygon in the frequency domain—two periodic functions are derived from a polygonal or polygon. According to the theory of elliptic Fourier descriptors those two periodic functions can be expressed by Fourier expansions. The transformation can be computed using the coefficients of the harmonics from the corresponding shapes without taking into account where each polygon vertex is placed in the spatial domain. The transformation parameters will be derived by a least squares approach. The geomatics and geosciences applications of this method go from photogrammetry, geographic information system, computer vision, to cadaster and real estates. View Full-Text
Keywords: fourier descriptors; closed cartographic shapes; automation; cadaster fourier descriptors; closed cartographic shapes; automation; cadaster
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Reinoso-Gordo, J.F.; Romero-Zaliz, R.; León-Robles, C.; Mataix-SanJuan, J.; Antonio Nero, M. Fourier-Based Automatic Transformation between Mapping Shapes—Cadastral and Land Registry Applications. ISPRS Int. J. Geo-Inf. 2020, 9, 482.

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