Simplification of 2D shapes with equivalent rectangles

• Autorzy: Kwinta Andrzej , Bac-Bronowicz Joanna

Identyfikatory

DOI

10.24425/gac.2022.141167

• Języki publikacji: EN

Abstrakty

EN

Real objects in horizontal projection often have a complex geometry. Their irregular shape causes issues during analyses and calculations that consider their geometry. The paper proposes the replacement of real-world objects with equivalent rectangles (ER). The paper also defines the geometric criteria of ER as well as ER parameters and methods for calculating them. The paper also demonstrates the difference in the duration of calculations for different types of rectangles (equivalent rectangle with the same area, surrounding rectangle with the smallest area, inscribed rectangle with the largest area). The presented approach has been illustrated with three case studies. The first one is the application of ER to underground mining cavities to determine post-mining deformations of the ground surface. In the second study, an ER was applied to analyse the geometry of agricultural parcels in a selected part of a rural settlement. ER can help assess whether the spatial layout is faulty and if a planning intervention is necessary. The third example describes a building’s geometry with an ER. Regarding the simplification of building’s geometry, it is crucial to replace a simplified building with a model that has the same centroid location and the same area. It is the perfect solution for rapid analyses of displaying objects on maps in various scales.

Słowa kluczowe

EN

equivalent rectangle; geometry simplification; underground mining cavities; agricultural parcels; building geometry

PL

działka rolna; podziemne wyrobisko górnicze; układ przestrzenny zabudowy

• Wydawca: Komitet Geodezji PAN
• Czasopismo: Advances in Geodesy and Geoinformation
• Rocznik: 2022
• Tom: Vol. 71, no. 1
• Strony: art. no. e14, 2022
• Opis fizyczny: Bibliogr. 57 poz., rys., tab., wykr.

Twórcy

autor

Kwinta Andrzej

• University of Agriculture in Krakow, Krakow, Poland

• https://orcid.org/0000-0002-2003-7703

autor

Bac-Bronowicz Joanna

• Wroclaw University of Sciences and Technology, Wroclaw, Poland

• https://orcid.org/0000-0001-9038-1131

Bibliografia

• [1] Alt, H., de Berg, M., and Knauer, C. (2017). Approximating minimum-area rectangular and convex containers for packing convex polygons. J Comput. Geom., 8(1), 1–10. DOI: 10.1007/978-3-662- 48350-3_3.
• [2] Bac, S. (1928). Contribution to research on the change in the position of arable loess soils. Rocz. Nauk Rol. i Leś., 19(3), 463–499. Poznań.
• [3] Bac-Bronowicz, J., Dygaszewicz, J., and Grzempowski, P. (2009). Contribute data from cadastral database to multiresolution topographic database. Geomat. Environ. Eng., 3(1/1), 45–58.
• [4] Bac-Bronowicz, J., Dygaszewicz, J., Grzempowski, P. et al. (2010). Reference databases as a source of power and updating of building layers in a multi-resolution topographic database. Annals of Geomatics, VIII, 5(41). Warszawa.
• [5] Bac-Bronowicz, J., and Wojciechowska, G. (2016). The status of work on development of the database of architectural industrial heritage in Wrocław. Annals of Geomatics, 14(5), 537–548.
• [6] Bahuguna, P.P., Srivastava, A.M.C., and Saxena, N.C. (1991). A critical review of mine subsidence prediction methods. Min. Sci. and Technol., 13, 369–382.
• [7] Baranska, A., Bac-Bronowicz, J., Dejniak, D. et al. (2021). Unified Methodology for the Generalisation of the Geometry of Features. ISPRS Int. J. Geo.-Inf., 10(3), 107.
• [8] Bielecka, E. (2015) Geographical data sets fitness of use evaluation. Geodetski Vestnik, 59(2), 335–348.
• [9] Bunge, W. (1966) Theoretical geography. Royal University of Lund. Dept. of Geography; Gleerup.
• [10] Buttenfield, B., and McMaster, R. (1991). Map Generalization: Making Rules for Knowledge Representation. Longman: London.
• [11] Chaudhuri, D., Kushwaha, N. K., Sharif, I. et al. (2012). Finding best-fitted rectangle for regions using a bisection method. Mach. Vis. Appl., 23(6), 1263–1271. DOI: 10.1007/s00138-011-0348-6.
• [12] Chrobak, T., Szombara, S., Koziol, K. et al. (2017). A method for assessing generalized data accuracy with linear object resolution verification. Geocarto Int., 32(3), 238–256. DOI: 10.1080/ 10106049.2015.14133721.
• [13] Chugh, Y.P., Hao, Q.W., and Zhu., F.S. (1989). State of the art. in mine subsidence prediction. In “Land Subsidence 1989” Publ. Balkema.
• [14] Demetriou, D., Stillwell, J., and See. L. (2013). A new methodology for measuring land fragmentation. Comput. Environ. Urban Syst., 39, 71–80. DOI: 10.1016/j.compenvurbsys.2013.02.001.
• [15] Díaz-Fernández, M.E., Álvarez-Fernández, M.I., and Álvarez-Vigil, A.E. (2010). Computation of influence functions for automatic mining subsidence prediction. Comput. Geosci., 14(1), 83–103. DOI: 10.1007/s10596-009-9134-1.
• [16] Ghaffarian, S. (2014). Automatic building detection based on supervised classification using high resolution Google Earth images. The International Archives of Photogrammetry. Remote Sens. Spatial Inf. Sci., 40(3), 101–106. DOI: 10.5194/isprsarchives-XL-3-101-2014.
• [17] Gibbs, J.P. (1961). Urban research methods. New York.
• [18] Hanus, P., Peska-Siwik, A., and Szewczyk, R. (2018). Spatial analysis of the accuracy of the cadastral parcel boundaries. Comput. Electron. Agric., 144, 9–15. DOI: 10.1016/j.compag.2017.11.031.
• [19] Hartvigsen, M. (2014). Land reform and land fragmentation in Central and Eastern Europe. Land Use Policy, 36, 330–341.
• [20] Hejmanowski, R., and Kwinta, A. (2010). Modeling continuous deformation of terrain in variable conditions of deposition. Mineral Resources Management, 26(3), 141–153.
• [21] Hejmanowski, R., Malinowska, A., Kwinta, A. et al. (2018). Modeling of land subsidence caused by salt cavern convergence applying Knothe’s theory. Prace Instytutu Mechaniki Górotworu PAN (Transactions of the Strata Mechanics Research Institute), 20(2), 87–94.
• [22] Hu, M.K. (1962). Visual pattern recognition by moment invariants. computer methods in image analysis. IEEE Trans. Inf. Theory, 8, 179–187. DOI: 10.1109/TIT.1962.1057692.
• [23] Huertas, A., and Nevatia, R. (1988). Detecting buildings in aerial images. Computer Vision. Graphics. and Image Processing, 41(2), 131–152.
• [24] INSPIRE (2007). Directive 2007/2/ EC of the European Parliament and of the Council of 14 March 2007. Known as the INSPIRE Directive.
• [25] Janus, J., and Taszakowski, J. (2015). The idea of ranking of setting priorities for land consolidation works. Geomatics. Landmanagement and Landscape. Publ. University of Agriculture in Krakow, 1, 31–43.
• [26] Józefaciuk, Cz., and Józefaciuk, A. (1987). Study on anti-erosion utilization system of utilization of agricultural lands on upland areas. Soil Science Annual, XXXVIII, 1, 59-76.
• [27] King, R., and Burton, S. (1982) Land fragmentation: notes on fundamental rural spatial problem. Progress in Human Geography, 5(6), 475–494.
• [28] Kohl, J.G. (1850). Der Verkehr und die Aussiedlungen der Menschen in ihrer Abhängigkeit von der Gestaltung der Erdoberfläche. Leipzig.
• [29] Kosturbiec, B. (1972). Analysis of concentration phenomena in settlement network. Polish Academy of Sciences. Geographical Studies, 93.
• [30] Kratzsch, H. (1983). Mining Subsidence Engineering. New York: Springer-Verlag Berlin Heidelberg.
• [31] Kwinta, A., and Gniadek, J. (2017). The description of parcel geometry and its application in terms of land consolidation planning. Comput. Electron. Agric., 136, 117–124. DOI: 10.1016/j.compag. 2017.03.006.
• [32] Kwinta, A., and Gradka, R. (2018). Mining exploitation influence range. Nat. Hazard, 94(3), 979–997.
• [33] Kwinta, A., and Bac-Bronowicz, J. (2020). Regular polygons in 2D objects shape description. Geomatics. Landmanagement and Landscape, 4, 43–61.
• [34] Kwinta, A., and Gradka, R. (2020). Analysis of the damage influence range generated by underground mining. Int. J Rock Mec., 128, 104263.
• [35] Len, P. (2018). An algorithm for selecting groups of factors for prioritization of land consolidation in rural areas. Comput. Electron. Agric., 144, 216–221. DOI: 10.1016/j.compag.2017.12.014.
• [36] Li, H.Z., Zhao, B.C., Guo, G.L. et al. (2018). The influence of an abandoned goaf on surface subsidence in an adjacent working coal face: a prediction method. Bulletin of Engineering Geology and the Environment, 77, 305–315.
• [37] Liu, W., Zhang, X., Li, S. et al. (2010). Reasoning about cardinal directions between extended objects. Artif. Intell., 174(12-13), 951–983.
• [38] Mackaness, W.A., Ruas, A., and Sarjakoski, L.T. (2011). Generalisation of Geographic Information: Cartographic Modelling and Applications. Elsevier.
• [39] Maling, D.H. (2016). Measurements from Maps: Principles and Methods of Cartometry. Butterworth Heinemann.
• [40] Manjunatha, A., Anik, A.R., Speelman, S. et al. (2013). Impact of land fragmentation. farm size. Land ownership and crop diversity on profit and efficiency of irrigated farms in India. Land Use Policy, 31, 397–405.
• [41] Molano, R., Rodríguez, P.G., Caro, A. et al. (2012). Finding the largest area rectangle of arbitrary orientation in a closed contour. Appl. Math. Comput., 218(19), 9866–9874.
• [42] Müller, J.C., Lagrange, J.P., and Weibel, R. (1995). GIS and generalization. Methodology and practice. London: Taylor and Francis.
• [43] Peng, S.S. (1986). Coal mine ground control. John Wiley & Sons.
• [44] Peura, M., and Iivarinen, J. (1997). Efficiency of Simple Shape Descriptors. In: 3rd International Workshop on Visual Form. Capri. Italy.
• [45] Pilkey, W.D. (1993). Formulas for Stress. Strain. and Structural Matrices. New York: John Wiley & Sons.
• [46] Prokop, J. and Reeves, A.P. (1992). A survey of moment-based techniques for unoccluded object representation and recognition. Computer Vision. Graphics and Image Processing. 54(5), 438–460.
• [47] Rosin, P.L. (1999). Measuring rectangularity. Mach. Vis. Appl., 11(4), 191–196.
• [48] Rosin, P.L. (2003). Measuring shape: ellipticity, rectangularity and triangularity. Mach. Vis. Appl., 14(3), 172–184.
• [49] Salishchev, K.A. (1976). Kartovedeniye. Moscow University.
• [50] Sarkar, A., Biswas, A., Dutt, M. et al. (2018). Finding a largest rectangle inside a digital object and rectangularization. J. Comput. Syst. Sci., 95, 204–217. DOI: 10.1016/j.jcss.2017.05.006.
• [51] Smith, J.R., and Chang, S.F. (1996). VisualSEEk: a fully automated content-based image query system. In Proceedings of the fourth ACM international conference on Multimedia. Boston. Massachusetts. USA, 87–98.
• [52] Touya, G. (2019). Finding the Oasis in the Desert Fog? Understanding Multi- Scale Map Reading. Proceedings of the ICA workshop on abstraction, scale and perception. Tokyo, Japan.
• [53] Wawer, R., and Nowocień, E. (2018). Water and wind erosion in Poland. Studia i Raporty IUNG-PIB. Vol. 58(12) pp. 57–79.
• [54] Weibel, R. (1997). Generalization of spatial data: Principles and selected algorithms. In eds. van Kreveld, M., Nievergelt, J., Roos, T., Widmayer, P.. Algorithmic Foundations of Geographic Information Systems. Lecture Notes in Computer Science, 1340. Springer.
• [55] White, C. L., and Renner, G. T. (1957). Natural environment and human Society. New York, 590–599.
• [56] Woch, F. (2008). Soil protection from erosion in countryside development in Poland. Nat. Environ. Monitoring, 9, 79–87.
• [57] Zandonadi, R.S., Luck, J.D., Stombaugh, T.S. et al. (2013). Evaluating field shape descriptors for estimating off-target application area in agricultural fields. Comput. Electron. Agric., 96, 216–226.

Uwagi

PL

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)