Abstract
A quadtree-like representation for storing gridded elevation data is described. The data structure is a pyramid with each node containing two bits of data. The root of the pyramid has associated with it the minimum elevation for the corresponding grid and the maximum variance (the difference between the minimum and maximum values). The elevation value at any pixel is calculated by traversing a path from the root to the pixel, refining the local elevation value during the decent by interpreting the two bit codes stored with each node along the path. Since the total number of nodes in the pyramid is 4/3 the number of pixels required for the bottom level of the pyramid, the amortized storage cost is less than 3 bits per pixel, regardless of vertical resolution.This scheme is most appropriate for efficient secondary storage archival, such as on a CD-ROM. It allows efficient retrieval of complete elevation data from any sub-region, at multiple scales, within the entire elevation database. This is a lossless encoding when the difference between sibling pixels is not “too great”.
This work was partially supported by General Dynamics and by the Virginia Center for Innovative Technology.
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9. References
A.V. Aho, J.E. Hopcroft, and J.D. Ullman, Data Structures and Algorithms, Addison Wesley, Reading MA, 1960.
R. Antony and P.J. Emmerman, Spatial reasoning and knowledge representation, in Geographic Information Systems in Government, vol. 2, B.K. Opitz, Ed., A. Deepak Publishing, Hampton, VA, 795–813.
J.A. Cebrian, J.E. Mower, and D.M. Mark, Analysis and display and digital elevation models within a quadtree-based geographic information system, Proceedings, Auto-Carto 7, Washington, D.C., 1985, 55–65.
Z.T. Chen and W.R. Tobler, Quadtree representations of digital terrain, Proceedings of Auto-Carto London, Vol. 1, London, September 1986, 475–484.
G.H. Dutton, Efficient encoding of gridded surfaces, in Spatial algorithms for processing land data with a microcomputer, Cambridge MA: Lincoln Institute for Land Policy Monograph Series, 1983.
E. Fredkin, Trie memory, Communications of the ACM 3, 9(September 1960), 490–499.
I. Gargantini, An effective way to represent quadtrees, Communications of the ACM, 25 12(December 1982), 905–910.
D.M. Hardas and S.N. Srihari, Progressive refinement of 3-D images using coded binary trees: Algorithms and architecture, IEEE Transactions on Pattern Analysis and Machine Intelligence 6, 6(November 1984), 748–757.
F.S. Hill, Jr., W. Sheldon, Jr., and F. Gao, Interactive image query system using progressive transmission, Computer Graphics 17, 3(July 1983), 323–330.
E. Kawaguchi and T. Endo, On a method of binary picture representation and its application to data compression, IEEE Transactions on Pattern Analysis and Machine Intelligence 2, 1(January 1980), 27–35.
R.E. Kelly, E.P.H. McConnell, and S.J. Mildenberger, The Gestalt photomapping system, Photogramm. Engng Rem. Sens. 43, (11), 1407–1417.
K. Knowlton, Progressive transmission of grey-scale and binary pictures by simple, efficient, and lossless encoding schemes, Proceedings of the IEEE 68, 7(July 1980), 885–896.
L.A. Leifer and D.M Mark, Recursive approximation of topographic data using quadtrees and orthogonal polynomials, Proceedings of Auto-Carto 8, Baltimore, MD, 1987, 650–659.
B.B. Mandelbrot, The Fractal Geometry of Nature, Freeman, New York, 1982.
D.M. Mark and J.P. Lauzon, Approaches for quadtree-based geographic information systems at continental or global scales, Proceedings of Auto-Carto 7, Washington, D.C., 1985, 355–364.
G.M. Morton, A computer oriented geodetic data base and a new technique in file sequencing, IBM Canada, 1966.
J. Nievergelt, H. Hinterberger, and K.C. Sevcik, The grid file: an adaptable, symmetric multikey file structure, ACM Transactions on Database Systems 9, 1(March 1984), 38–71.
T.K. Peuker, R.J. Fowler, J.J. Little, and D.M. Mark, The triangulated irregular network, in Proceedings of the DTM Symposium, American Society of Photogrammetry — American Congress on Survey and Mapping, St. Louis, MO, 1978, 24–31.
— H. Samet, The quadtree and related hierarchical data structures, ACM Computing Surveys 16, 2(June 1984), 187–260.
H. Samet, A top-down quadtree traversal algorithm, IEEE Transactions on Pattern Analysis and Machine Intelligence 7, 1 (January 1985), 94–98.
H. Samet and R.E. Webber, Storing a collection of polygons using quadtrees, ACM Transactions on Graphics 4, 3(July 1985), 182–222.
— C.A. Shaffer, H. Samet, and R.C. Nelson, QUILT: a geographic information system based on quadtrees, University of Maryland TR 1885, July 1987.
C.A. Shaffer and H. Samet, An in-core hierarchical data structure organization for a geographic database, Computer Science TR 1886, University of Maryland, College Park, MD, July 1987.
C.A. Shaffer and H. Samet, Set operations for unaligned linear quadtrees, to appear in Computer Vision, Graphics, and Image Processing, also Department of Computer Science TR 88-31, Virginia Polytechnic Institute and State University, Blacksburg, VA, September 1988.
K.R. Sloan and S.L. Tanimoto, Progressive refinement of raster images, IEEE Transactions on Computers 28, 11(November 1979), 871–874.
M. Tamminen, The EXCELL method for efficient geometric access to data, Acta Polytechnica Scandinavia, Mathematics and Computer Science Series No. 34, Helsinki, 1981.
— M. Tamminen, Encoding trees, Computer Vision, Graphics, and Image Processing 28, 1(October 1984), 44–57.
S. Tanimoto and T. Pavlidis, A hierarchical data structure for picture processing, Computer Graphics and Image Processing 4, 2(1975), 104–119.
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Shaffer, C.A. (1990). A full resolution elevation representation requiring three bits per pixel. In: Buchmann, A.P., Günther, O., Smith, T.R., Wang, YF. (eds) Design and Implementation of Large Spatial Databases. SSD 1989. Lecture Notes in Computer Science, vol 409. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52208-5_21
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