This Article 
 Bibliographic References 
 Add to: 
Efficient Component Labeling of Images of Arbitrary Dimension Represented by Linear Bintrees
July 1988 (vol. 10 no. 4)
pp. 579-586

An algorithm is presented to perform connected-component labeling of images of arbitrary dimension that are represented by a linear bintree. The bintree is a generalization of the quadtree data structure that enables dealing with images of arbitrary dimension. The linear bintree is a pointerless representation. The algorithm uses an active border which is represented by linked lists instead of arrays. This results in a significant reduction in the space requirements, thereby making it feasible to process three- and higher-dimensional images. Analysis of the execution time of the algorithm shows almost linear behavior with respect to the number of leaf nodes in the image, and empirical tests are in agreement. The algorithm can be modified easily to compute a (d-1)-dimensional boundary measure (e.g. perimeter in two dimensions and surface area in three dimensions) with linear performance.

[1] C. R. Dyer, "Computing the Euler number of an image from its quadtree,"Comput. Graphics Image Processing, vol. 13, pp. 270-276, July 1980.
[2] I. Gargantini, "An Effective Way to Represent Quadtrees,"CACM, Dec. 1982, pp. 905-910.
[3] G.M. Hunter, "Efficient Computation and Data Structures for Graphics," doctoral dissertation, Princeton Univ., Princeton, N.J., 1978.
[4] C. L. Jackins, and S. L. Tanimoto, "Oct-trees and their use in representing three-dimensional objects,"Comput. Graphics Image Processing, vol. 14, pp. 249-270, Nov. 1980.
[5] C. L. Jackins, and S. L. Tanimoto, "Quad-trees, oct-trees, andk-trees-A generalized approach to recursive decomposition of Euclidean space,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-5, pp. 533-539, Sept. 1983.
[6] E. Kawaguchi and T. Endo, "On the method of binary picture representation and its application to data compression,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-2, pp. 27-35, Jan. 1980.
[7] A. Klinger, "Patterns and search statistics," inOptimizing Methods in Statistics, J. S. Rustagi, Ed. New York: Academic, 1971, pp. 303-337.
[8] R. Lumina, "A new three-dimensional connected components algorithm,"Comput. Vision, Graphics, Image Processing, vol. 23, pp. 207-217, Aug. 1983.
[9] D. Meagher, "Geometric modeling using octree encoding,"Comput. Graphics Image Processing, vol. 19, pp. 129-147, June 1982.
[10] M. Minsky and S. Papert,Perceptrons: An Introduction to Computational Geometry. Cambridge, MA: M.I.T. Press, 1969.
[11] A. Rosenfeld and J. Pfaltz, "Sequential operations in digital picture processing,"J. ACM, vol. 4, 1966.
[12] H. Samet, "Connected component labeling using quadtrees,"J. ACM, vol. 28, pp. 487-501, July 1981.
[13] H. Samet, "The quadtree and related hierarchical data structures,"Comput. Surveys, vol. 16, pp. 187-260, 1984.
[14] H. Samet, "A top-down quadtree traversal algorithm,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-7, Jan. 1985; also, Univ. Maryland, College Park, Comput. Sci. TR-1237.
[15] H. Samet and M. Tamminen, "Computing geometric properties of images represented by linear quadtrees,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-7, Mar. 1985.
[16] H. Samet and M. Tamminen, "An improved approach to connected component labeling of images," inProc. CVPR86 Conf., Miami Beach, FL, June 1986, pp. 312-318.
[17] M. Tamminen, "Comment on Quad- and Octtrees,"CACM, Mar. 1984, pp. 248-249.
[18] M. Tamminen and H. Samet, "Effective octree conversion by connectivity labeling," inProc. SIGGRAPH '84 Conf., Minneapolis, MN, July 1984, pp. 43-51.
[19] R. E. Tarjan, "Efficiency of a good but non linear set union algorithm,"J. ACM, vol. 22, pp. 215-225, 1975.
[20] R. E. Tarjan and J. van Leeuwen, "Worst-case analysis of set union algorithms,"J. ACM, vol. 31, pp. 245-281, Apr. 1984.
[21] M. Yau and S. N. Srihari, "A hierarchical data structure for multi-dimensional digital images,"Commun. ACM, vol. 26, pp. 504-515, July 1983.

Index Terms:
image analysis; computerised pattern recognition; computerised picture processing; component labeling; linear bintrees; quadtree data structure; pointerless representation; computerised pattern recognition; computerised picture processing; data structures; trees (mathematics)
H. Samet, M. Tamminen, "Efficient Component Labeling of Images of Arbitrary Dimension Represented by Linear Bintrees," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 10, no. 4, pp. 579-586, July 1988, doi:10.1109/34.3918
Usage of this product signifies your acceptance of the Terms of Use.