Planar decomposition for quadtree data structure

Abstract The quadtree data structure is extensively used in representing 2-dimensional data in many applications like image processing, cartographic data processing. VLSL embedding, graphics, computer animation, computer-aided architecture, etc. The data structure employs the divide-and-conquer technique to recursively decompose the planar region. This paper addresses the problem of planar tessellation which yields the quadtree data structure. Arbitrary triangles and parallelograms have been used as basic cells and hyper-cellular structures corresponding to lower order k-gons have been shown to represent such data structures. Different tessellation schemes have been discussed using the notion of tessellation matrix. The performances of different tessellation schemes have been compared, introducing the concept of the neighborhood graph.

[1]  Chris L. Jackins,et al.  Oct-trees and their use in representing three-dimensional objects , 1980 .

[2]  Azriel Rosenfeld,et al.  Application of Hierarchical Data Structures to Geographical Information Systems. , 1983 .

[3]  Hanan Samet,et al.  An Algorithm for Converting Rasters to Quadtrees , 1981, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[4]  Nikitas A. Alexandridis,et al.  Picture decomposition, tree data-structures, and identifying directional symmetries as node combinations , 1978 .

[5]  Narendra Ahuja.  On approaches to polygonal decomposition for hierarchical image representation , 1983, Comput. Vis. Graph. Image Process..

[6]  Pinaki Mazumder.  Networks and embedding aspects of cellular structures for on-chip parallel processing in VLSI , 1985 .

[7]  Frank W. Barnes,et al.  Algebraic theory of brick packing I , 1982, Discret. Math..

[8]  Hanan Samet,et al.  Data structures for quadtree approximation and compression , 1985, CACM.

[9]  Ming Li,et al.  Normalized quadtrees with respect to translations , 1982, Comput. Graph. Image Process..

[10]  Gregory Michael Hunter,et al.  Efficient computation and data structures for graphics. , 1978 .

[11]  J. R. Woodward,et al.  The Explicit Quad Tree as a Structure for Computer Graphics , 1982 .

[12]  A. L. Loeb,et al.  Color and symmetry , 1972 .

[13]  Gregory M. Hunter,et al.  Computer animation survey , 1977, Comput. Graph..

[14]  Azriel Rosenfeld,et al.  Region representation: boundary codes from quadtrees , 1980, CACM.

[15]  A. Tanenbaum.  Computer recreations , 1973 .

[16]  Azriel Rosenfeld,et al.  Connectivity in Digital Pictures , 1970, JACM.

[17]  S. Golomb.  Tiling with polyominoes , 1966 .

[18]  David M. McKeown,et al.  Map-guided feature extraction from aerial imagery , 1984 .

[19]  Charles R. Dyer,et al.  Experiments on Picture Representation Using Regular Decomposition , 1976 .

[20]  Irene Gargantini,et al.  An effective way to represent quadtrees , 1982, CACM.

[21]  Azriel Rosenfeld,et al.  Adjacency in Digital Pictures , 1974, Inf. Control..

[22]  M. J. Jackson,et al.  Spatially referenced methods of processing raster and vector data , 1983, Image Vis. Comput..

[23]  Frank Thomson Leighton,et al.  Wafer-scale integration of systolic arrays , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[24]  Narendra Ahuja,et al.  Efficient planar embedding of trees for VLSI layouts , 1986, Comput. Vis. Graph. Image Process..

[25]  Hanan Samet,et al.  The Quadtree and Related Hierarchical Data Structures , 1984, CSUR.

[26]  Theodosios Pavlidis,et al.  A hierarchical data structure for picture processing , 1975 .

[27]  Y. Chien,et al.  Pattern classification and scene analysis , 1974 .

[28]  Makoto Nagao,et al.  A file organization for geographic information systems based on spatial proximity , 1983, Comput. Vis. Graph. Image Process..

[29]  Jake K. Aggarwal,et al.  A normalized quadtree representation , 1983, Comput. Vis. Graph. Image Process..

[30]  M. Shneier.  Calculations of geometric properties using quadtrees , 1981 .

[31]  Hannan Samet,et al.  Region representation: Quadtrees from binary arrays , 1980 .

[32]  Charles M. Eastman.  Representations for space planning , 1970, CACM.

[33]  Alfred V. Aho,et al.  The Design and Analysis of Computer Algorithms , 1974 .

[34]  E. Dubois,et al.  Digital picture processing , 1985, Proceedings of the IEEE.

[35]  Markku Tamminen.  Comment on Quad- and Octtrees , 1984, CACM.