An efficient incremental algorithm for generating the characteristic shape of a dynamic set of points in the plane

ABSTRACT Several algorithms have been proposed to generate a polygonal ‘footprint’ to characterize the shape of a set of points in the plane. One widely used type of footprint is the χ-shape. Based on the Delaunay triangulation (DT), χ-shapes guaranteed to be simple (Jordan) polygons. This paper presents for the first time an incremental χ-shape algorithm, capable of processing point data streams. Our incremental χ-shape algorithm allows both insertion and deletion operations, and can handle streaming individual points and multiple point sets. The experimental results demonstrated that the incremental algorithm is significantly more efficient than the existing, batch χ-shape algorithm for processing a wide variety of point data streams.

[1]  Dani Lischinski.  Incremental Delaunay Triangulation , 1994, Graphics Gems.

[2]  Ray A. Jarvis,et al.  On the Identification of the Convex Hull of a Finite Set of Points in the Plane , 1973, Inf. Process. Lett..

[3]  Leysia Palen,et al.  Microblogging during two natural hazards events: what twitter may contribute to situational awareness , 2010, CHI.

[4]  Antony Galton,et al.  What Is the Region Occupied by a Set of Points? , 2006, GIScience.

[5]  David G. Kirkpatrick,et al.  On the shape of a set of points in the plane , 1983, IEEE Trans. Inf. Theory.

[6]  Marc Vigo Anglada,et al.  An improved incremental algorithm for constructing restricted delaunay triangulations , 1997, Comput. Graph..

[7]  Yutaka Matsuo,et al.  Earthquake shakes Twitter users: real-time event detection by social sensors , 2010, WWW '10.

[8]  Byung Suk Lee,et al.  Incremental causal network construction over event streams , 2014, Inf. Sci..

[9]  Ramanathan Muthuganapathy,et al.  A non-parametric approach to shape reconstruction from planar point sets through Delaunay filtering , 2015, Comput. Aided Des..

[10]  Onur Seref,et al.  Recursive voids for identifying a nonconvex boundary of a set of points in the plane , 2013, Pattern Recognit..

[11]  Dave Yates,et al.  Emergency knowledge management and social media technologies: A case study of the 2010 Haitian earthquake , 2011, Int. J. Inf. Manag..

[12]  David Maier,et al.  Semantics and evaluation techniques for window aggregates in data streams , 2005, SIGMOD '05.

[13]  Michael F. Goodchild,et al.  Please Scroll down for Article International Journal of Digital Earth Crowdsourcing Geographic Information for Disaster Response: a Research Frontier Crowdsourcing Geographic Information for Disaster Response: a Research Frontier , 2022 .

[14]  S. Cox,et al.  Citizen-based sensing of crisis events: sensor web enablement for volunteered geographic information , 2013 .

[15]  Bidyut Baran Chaudhuri,et al.  A split and merge procedure for polygonal border detection of dot pattern , 1999, Image Vis. Comput..

[16]  L. Manovich,et al.  Trending: The Promises and the Challenges of Big Social Data , 2012 .

[17]  Michèle Sebag,et al.  Data Stream Clustering With Affinity Propagation , 2014, IEEE Transactions on Knowledge and Data Engineering.

[18]  Robert P. Anderson,et al.  Maximum entropy modeling of species geographic distributions , 2006 .

[19]  Maribel Yasmina Santos,et al.  Concave hull: A k-nearest neighbours approach for the computation of the region occupied by a set of points , 2007, GRAPP.

[20]  D. Dransch,et al.  Volunteered Geographic Information for Disaster Management with Application to Rapid Flood Damage Estimation , 2019 .

[21]  Zeynep Tufekci,et al.  Big Questions for Social Media Big Data: Representativeness, Validity and Other Methodological Pitfalls , 2014, ICWSM.

[22]  Mahmoud Melkemi,et al.  Computing the shape of a planar points set , 2000, Pattern Recognit..

[23]  Antony Galton,et al.  Efficient generation of simple polygons for characterizing the shape of a set of points in the plane , 2008, Pattern Recognit..

[24]  Silvia Nittel,et al.  Scaling clustering algorithms for massive data sets using data streams , 2004, Proceedings. 20th International Conference on Data Engineering.

[25]  Anthony Stefanidis,et al.  #Earthquake: Twitter as a Distributed Sensor System , 2013, Trans. GIS.

[26]  Walid G. Aref,et al.  Continuous Query Processing of Spatio-Temporal Data Streams in PLACE , 2005, GeoInformatica.

[27]  J. Busby.  BIOCLIM - a bioclimate analysis and prediction system , 1991 .

[28]  Jennifer Widom,et al.  Query Processing, Resource Management, and Approximation ina Data Stream Management System , 2002 .

[29]  Harith Alani,et al.  Voronoi-based region approximation for geographical information retrieval with gazetteers , 2001, Int. J. Geogr. Inf. Sci..

[30]  Hans-Peter Kriegel,et al.  Incremental Clustering for Mining in a Data Warehousing Environment , 1998, VLDB.

[31]  Michèle Sebag,et al.  Data Streaming with Affinity Propagation , 2008, ECML/PKDD.

[32]  Özgür Ulusoy,et al.  Processing count queries over event streams at multiple time granularities , 2006, Inf. Sci..

[33]  Allison Kealy,et al.  Stream Kriging: Incremental and recursive ordinary Kriging over spatiotemporal data streams , 2016, Comput. Geosci..

[34]  Matt Duckham,et al.  Real-time estimation of wildfire perimeters from curated crowdsourcing , 2016, Scientific Reports.

[35]  Leonidas J. Guibas,et al.  Randomized incremental construction of Delaunay and Voronoi diagrams , 1990, Algorithmica.

[36]  Maggi Kelly,et al.  Support vector machines for predicting distribution of Sudden Oak Death in California , 2005 .

[37]  Michael J. Franklin,et al.  Streaming Queries over Streaming Data , 2002, VLDB.

[38]  Avi Arampatzis,et al.  Web-based delineation of imprecise regions , 2006, Comput. Environ. Urban Syst..

[39]  Jonathon K. Parker,et al.  Footprint generation using fuzzy-neighborhood clustering , 2013, GeoInformatica.

[40]  T. Hastie,et al.  Using multivariate adaptive regression splines to predict the distributions of New Zealand ’ s freshwater diadromous fish , 2005 .

[41]  Bidyut Baran Chaudhuri,et al.  A Novel Approach to Computation of the Shape of a Dot Pattern and Extraction of Its Perceptual Border , 1997, Comput. Vis. Image Underst..

[42]  Mahmoud Melkemi.  A-shapes of a finite point set , 1997, SCG '97.

[43]  Jennifer Widom,et al.  Models and issues in data stream systems , 2002, PODS.