Abstract
It is a challenge work to propose new models for calculating spatial similarity degrees between objects in multiscale map spaces. In this chapter, ten new models are proposed. Three models are for individual objects and the other seven models are for object groups. To be exact, the former comprises the models for individual point objects, individual linear objects, and individual areal objects, and the latter comprises the models for point clouds, parallel line clusters, intersected line networks, tree-like networks, discrete polygon groups, connected polygon groups, and maps.
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References
Alt H, Godau M (1995) Computing the Fréchet distance between two polygonal curves. Int J Comput Geom Appl 5:75–91
Alt H, Fuchs U, Rote G, Weber G (1998) Matching convex shapes with respect to the symmetric difference. Algorithmica 21:89–103
Aurenhammer F (1991) Voronoi Diagram—a survey of a fundamental geometric data structure. ACM Comput Surv 23(3):345–405
Bader M, Weibel R (1997) Detecting and resolving size and proximity conflicts in the generalisation of polygon maps. In: Proceedings of the 18th International cartographic conference, Stockholm, Sweden, pp 1525–1532
Bader M, Barrault M, Weibel R (2005) Building displacement over a ductile truss. Int J Geogr Inform Sci 19(8–9):915–936
Barber P (2005) The map book, London: Weidenfeld and Nicolson. pp 232, 250
Berry JK (1993) Beyond mapping: concepts, algorithms and issues in GIS. Wiley, New York, 246 pp
Bjørke JT (2004) Topological relations between fuzzy regions: derivation of verbal terms. Fuzzy Set Syst 141(3):449–467
Boffet A, Rocca Serra S (2001) Identification of spatial structures within urban blocks for town characterization. In: Proceedings of the 20th international cartographic conference, Beijing, China. (CD-ROM)
Boots B, Csillag F (2006) Categorical maps, comparisons, and confidence. J Geogr Syst 8:109–118
Butler LK, Ries L, Bisson I, Hayden TJ, Wikelski MM, Romero LM (2013) Opposite but analogous effects of road density on songbirds with contrasting habitat preferences. Anim Conservat 16(1):77–85
Chen J, Li C, Li Z, Gold C (2001) A Voronoi-based 9-Intersection model for spatial relations. Int J Geogr Inform Sci 15(3):201–220
Christophe S, Ruas A (2002) Detecting building alignments for generalisation purposes. In: Richardson DE, van Oosterom P (eds) Proceedings of the 10th international symposium on spatial data handling. Springer, Berlin, pp 419–432
Clementini E, Sharma J, Egenhofer MJ (1994) Modeling topological spatial relations: strategies for query processing. Comput Graph 18(6):815–822
Csillag F, Boots B (2004) Toward comparing maps as spatial processes. In: Fisher P (ed) Developments in spatial data handling. Springer, Heidelberg, p 641
de Serres B, Roy A (1990) Flow direction and branching geometry at junctions in Dendritic river networks. Prof Geogr 42(2):149–201
Douglas D, Peucker T (1973) Algorithms for the reduction of the number of points required to represent a digitized line or its caricature. The Canadian Cartographer 10(2):112–122
Du S, Qin Q, Wang Q, Ma H (2008) Evaluating structural and topological consistency of complex regions with broad boundaries in multi-resolution spatial databases. Inform Sci 178(1):52–68
Egenhofer MJ, Clementini E, Di Felice P (1994) Topological relations between regions with holes. Int J Geogr Inform Syst 8(2):129–144
Formica A, Pourabbas E, Rafanelli M (2013) Constraint relaxation of the polygon-polyline topological relation for geographic pictorial query languages. Comput Sci Inf Syst 10(3):1053–1075
Goyal RK (2000) Similarity assessment for cardinal directions between extended spatial objects. PhD Thesis, The University of Maine, USA
Gustafson EJ (1998) Quantifying landscape spatial pattern: what is the state of the art? Ecosystems 1:143–156
Hagen A (2003) Fuzzy set approach to assessing similarity of categorical maps. Int J Geogr Inform Sci 17:235–249
Harvey PDA (1980) The history of topographical maps: symbols, pictures and surveys. Thames and Hudson, London, p 9
Hong J (1994) Qualitative distance and direction reasoning in geographic space. PhD Thesis, University of Maine, USA
Horton H (1945) Erosional development of streams and their drainage basins—hydrophysical approach to quantitative morphology. Bull Geol Soc Am 56:275–370
Knuth D (1997) The art of computer programming: fundamental algorithms, 3rd edn. Addison-Wesley, Reading, pp 308–423, Section 2.3: Trees
La Barbera P, Rosso R (1989) On the fractal dimensions of stream network. Water Resour Res 25(4):735–741
Li C, Chen J, Li Z (1999) A raster-based method for computing Voronoi Diagrams of spatial objects using dynamic distance transformation. Int J Geogr Inform Sci 13(3):209–225
Li Z, Yan H, Ai T, Chen J (2004) Automated building generalization based on urban morphology and gestalt theory. Int J Geogr Inform Sci 18(5):513–534
Liu YL (2002) Categorical database generalization in GIS. PhD Thesis, Utrecht University, The Netherlands
Milenkovic VJ (1998) Rotational polygon overlap minimization and compaction. Comput Geom: Theor Appl 10(4):305–318
Mokhtarian F, Mackworth AK (1992) A theory of multi-scale, curvature-based representation for planar curves. IEEE Trans Pattern Anal Mach Intell 14(8):789–805
Palmer SE (1992) Common region: a new principle of perceptual grouping. Cogn Psychol 24(2):436–447
Peuquet D, Zhan CX (1987) An algorithm to determine the directional relation between arbitrarily-shaped polygons in the plane. Pattern Recogn 20(1):65–74
Rainsford D, Mackaness W (2002) Template matching in support of generalization of rural buildings. In: Richardson DE, van Oosterom P (eds) Proceedings of the 10th international symposium on spatial data handling. Springer, Berlin, pp 137–151
Regnauld N (2001) Contextual building typification in automated map generalization. Algorithmica 30(2):312–333
Remmel TK, Fortin MJ (2013) Categorical, class-focused map patterns: characterization and comparison. Landsc Ecol 28:1587–1599
Rock I (1996) Indirect perception. MIT Press, London
Ross R (1999) Fractal relation of mainstream length to catchment area in river networks. Water Resour Res 27(3):381–387
Ruas A (1998) A method for building displacement in automated map generalization. Int J Geogr Inform Sci 12(8):789–803
Sadahiro Y (1997) Cluster perception in the distribution of point objects. Cartographica 34:49–61
Sadahiro Y (2012) Exploratory analysis of polygons distributed with overlap. Geogr Anal 44(4):350–367
Thomson R, Brooks R (2002) Exploiting perceptual grouping for map analysis, understanding and generalization: the case of road and river networks. In: Blostein D, Tobler WR (1970) A computer movie simulating urban growth in the Detroit region. Econ Geogr 46:234–240
Tobler WR (1970) A computer movie simulating urban growth in the Detroit region. Econ Geogr 46:234–240
Uuemaa E, Antrop M, Roosaare J, Mander U (2009) Landscape metrics and indices: an overview of the use in landscape research. Living Rev Landscape Res 3:1–28
Yan HW (2010) Fundamental theories of spatial similarity relations in multi-scale map spaces. Chin Geogr Sci 20(1):18–22
Yan HW, Chu YD, Li ZL, Guo RZ (2006) A quantitative direction description model based on direction groups. Geoinformatica 10(2):177–196
Zhang QN (2006) Generalization of drainage network with density differences. Acta Geodaetica et Cartographica Sinica 35(2):191–196
Zhang Q, Wang J, Peng X, Gong P, Shi P (2002) Urban built-up land change detection with road density and spectral information from multi-temporal Landsat TM data. Int J Rem Sens 23(15):3057–3078
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Yan, H., Li, J. (2015). Models for Calculating Spatial Similarity Degrees in Multiscale Map Spaces. In: Spatial Similarity Relations in Multi-scale Map Spaces. Springer, Cham. https://doi.org/10.1007/978-3-319-09743-5_4
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DOI: https://doi.org/10.1007/978-3-319-09743-5_4
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