Title:	Function-trees: an efficient data structure for compact binary pictures
Authors:	Gallo, Giovanni Spampinato, Daria
Citation:	Journal of WSCG. 1997, vol. 5, no. 1-3, p. 144-152.
Issue Date:	1997
Publisher:	Václav Skala - UNION Agency
Document type:	článek article
URI:	http://wscg.zcu.cz/wscg1997/wscg97.htm http://hdl.handle.net/11025/15892
ISSN:	1213-6972 (print) 1213-6980 (CD-ROM) 1213-6964 (online)
Keywords:	struktura dat;3D krajina;trapézové regiony;algoritmy
Keywords in different language:	data structure;3D scene;trapezoidal regions;algorithms
Abstract in different language:	In the representation of binary images or of binary three-dimensional scenes two principal paradigms have been introduced: boundary representation and hierarchical decomposition. The data-structure introduced in this paper, called function-tree or function-octree for a 3D scene, is an elementary generalization of the standard quadtree and octree. It combines the compactness of a boundary representation of spatial data with the nice recursive properties of a tree representation. This is achieved by decomposing regularly an image into rectangular sub-images whose black regions are trapezoidal regions. A trapezoidal region (defined in detail in the paper) is a region below the graph of a function. Trapezoidal regions can be, in turn, efficiently encoded with a boundary representation. Efficient algorithms to construct the function-tree are described in the paper. The time complexities of such algorithms are O (n2) for a n × n binary picture and O (n3) for a n × n × n binary scene. The algorithms have been implemented. A final quick review of the possible applications of the proposed structures concludes the paper.
Rights:	© Václav Skala - UNION Agency
Appears in Collections:	Volume 5, number 1-3 (1997)

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