Abstract
The nearest neighbor search algorithm is one of the major factors that influence the efficiency of grid interpolation. This paper introduces a KD-tree that is a two-dimensional index structure for use in grid interpolation. It also proposes an improved J-nearest neighbor search strategy based on “priority queue” and “neighbor lag” concepts. In the strategy, two types of J-nearest neighbor search algorithms can be used; these algorithms correspond to the consideration of a fixed number of points and a fixed radius. By using the KD-tree and proposed strategy, interpolation can be performed with methods such as Inverse Distance Weighting and Kriging. Experimental results show that the proposed algorithms has high operating efficiency, especially when the data amount is enormous, and high practical value for increasing the efficiency of grid interpolation.
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References
Bater CW, Coops NC (2009) Evaluating error associated with lidar-derived DEM interpolation. Comput Geosci 35(2):289–300
Bentley JL (1975) Multidimensional binary search trees used for associative searching. Commun ACM 18(9):509–517
Beutel A, Mølhave T, Agarwal PK (2010) Natural neighbor interpolation based grid DEM construction using a GPU. In: GISACM ’2010, pp 172–181
Chen M-B, Chuang T-R, Wu J-J (2006) Parallel divide-and-conquer scheme for 2D Delaunay triangulation. Concurr Comput Pract Exp 18(12):1595–1612
Dwyer RA (1987) A faster divide-and-conquer algorithm for constructing Delaunay triangulations. Algorithmica 2(1–4):137–151
Foley T, Sugerman J (2005) KD-tree acceleration structures for a GPU raytracer. Proceedings of the ACM SIGGRAPH/EUROGRAPHICS Conference on Graphics Hardware, pp 15–22
Goodsell G (2000) On finding p-th nearest neighbors of scattered points in two dimensions for small p. Comput Aided Geom Des 17(4):387–392
Lingli Z et al (2010) The research and implement of DEM interpolation method based on Voronoi K order adjacency. 2010 International Conference on Challenges in Environmental Science and Computer Engineering (CESCE), 6–7 March, vol 1, pp 386–389
Liu X, Zhang Z, Peterson J (2009) Evaluation of the performance of DEM interpolation algorithms for LiDAR data. Proceedings of the Surveying & Spatial Sciences Institute Biennial International Conference, Surveying & Spatial Sciences Institute, Adelaide, pp 771–780
Nene SA, Nayar SK (1997) A simple algorithm for nearest neighbor search in high dimensions. IEEE Trans Pattern Anal Mach Intell 19(9):989–1003
Piegl LA, Tiller W (2002) Algorithm for finding all k nearest neighbors. Comput Aided Des 34(2):167–172
Popov S, Günther J, Seidel H-P (2007) Stackless KD-tree traversal for high performance GPU ray tracing. EUROGRAPHICS 26(3):776–788
Silpa-Anan C, Hartley R (2008) Optimised KD-trees for fast image descriptor matching. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp 1–8
Wang P et al (2006) Effect of uncertainty of grid DEM on TOPMODEL: evaluation and analysis. Chin Geogr Sci 16(4):320–326
Wolberg G, Shin SY (1997) Scattered data interpolation with multilevel B-splines. IEEE Trans Vis Comput Graph 3(3):228–244
Xiao C, Liu M, Nie Y (2011) Fast exact nearest patch matching for patch-based image editing and processing. IEEE Trans Vis Comput Graph 17(8):1122–1134
Zhou K, Hou Q, Wang R, Guo B (2008) Real-time KD-tree construction on graphics hardware. ACM Trans Graph 27(5): Article 126
Acknowledgments
This work is supported by the project Priority Academic Program Development of Jiangsu and the project supported by the National Science and Technology Ministry (ID: 2012BAH28B02).
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Communicated by: H. A. Babaie
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Huang, H., Cui, C., Cheng, L. et al. Grid interpolation algorithm based on nearest neighbor fast search. Earth Sci Inform 5, 181–187 (2012). https://doi.org/10.1007/s12145-012-0106-y
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DOI: https://doi.org/10.1007/s12145-012-0106-y