This Article 
 Bibliographic References 
 Add to: 
Hierarchical Image Analysis Using Irregular Tessellations
April 1991 (vol. 13 no. 4)
pp. 307-316

A novel multiresolution image analysis technique based on hierarchies of irregular tessellations generated in parallel by independent stochastic processes is presented. Like traditional image pyramids these hierarchies are constructed in a number of steps on the order of log(image-size) steps. However, the structure of a hierarchy is adapted to the image content and artifacts of rigid resolution reduction are avoided. Two applications of these techniques are presented: connected component analysis of labeled images and segmentation of gray level images. In labeled images, every connected component is reduced to a separate root, with the adjacency relations among the components also extracted. In gray level images the output is a segmentation of the image into a small number of classes as well as the adjacency graph of the classes.

[1] E.H. Adelson, E. Simoncelli, and R. Hingorani, "Orthogonal pyramid transforms for image coding," inVisual Communications and Image Processing II, SPIE Proc., vol. 845, pp. 50-58, 1987.
[2] N. Ahuja, "On approaches to polygonal decomposition for hierarchical image representation,"Comput. Graphics Image Processing, vol. 24, pp. 200-214, 1983.
[3] D. H. Ballard, "Cortical connections and parallel processing: Structure and function,"Behavioral Brain Sci., vol. 9, pp. 67-120, 1986.
[4] S. Baronti, A. Casini, F. Lotti, L. Favaro, and V. Roberto, "Variable pyramid structure for image segmentation,"Comput. Vision Graphics Image Processing, vol. 49, pp. 346-356, 1990.
[5] M. Bister, "A critical view on pyramid segmentation algorithms," Inform. Retrieval and Interpretation Sci. Lab., Vrije Univ., Brussels, Belgium, Tech. Rep. IRIS-TR-0006, 1989.
[6] P. J. Burt, "Tree and pyramid structures for coding hexagonally sampling binary images,"Comput. Graphics Image Processing, vol. 14, pp. 171-180, 1980.
[7] P. J. Burt, "Fast filter transforms for image processing,"Comput. Graphics Image Processing, vol. 16, pp. 20-51, 1981.
[8] V. Cantoni and S. Levialdi, Eds.,Pyramidal Systems for Computer Vision. Berlin: Springer-Verlag, 1986.
[9] J. M. Chassery and A. Montanvert, "A segmentation method in a Voronoi diagram environment,"Proc. Sixth Scandinavian Conf. Image Processing, Oulu, Finland, June 19-22, 1989, pp. 408-415.
[10] J. Cibulskis and C. R. Dyer, "Node linking strategies in pyramids for image segmentation," inMultiresolution Image Processing and Analysis, A. Rosenfeld, Ed. Berlin: Springer-Verlag, 1984, pp. 109-120.
[11] J. L. Crowley and R. M. Stern, "Fast computation of the difference of low-pass transform,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-6, pp. 212-222, 1984.
[12] L. S. Davis and A. Rosenfeld, "Noise cleaning by iterated local averaging,"IEEE Trans Syst., Man, Cybern, vol. SMC-8, pp. 705-710, 1978.
[13] A. D. Gross and A. Rosenfeld, "Multiresolution object detection and delineation,"Comput. Vision Graphics Image Processing, vol. 39, pp. 102-115, 1987.
[14] N. P. Hartman and S. L. Tanimoto, "A hexagonal pyramid data structure for image processing,"IEEE Trans. Syst., Man, Cybern., vol. SMC-14, pp. 247-255, 1984.
[15] D. Harwood. M. Subbarao, H. Hakalahti, and L. S. Davis, "A new class of edge-preserving smoothing filters,"Pattern Recognition Lett., vol. 6, pp. 115-162, 1987.
[16] T.H. Hong and A. Rosenfeld, "Compact region extraction using, weighted pixel linking in a pyramid,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-6, pp. 222-229, 1984.
[17] J. M. Jolion and A. Montanvert, "La pyramide adaptive: construction et utilisation pour l'analyse de scenes 2D," inProc. Seventh RFIA Conf., Paris, Nov. 1989, pp. 197-206.
[18] W. G. Kropatsch, "A pyramid that grows by powers of 2,"Pattern Recogni. Lett., vol. 3, pp. 315-322, 1985.
[19] W. G. Kropatsch, "Curve representation in multiple resolutions,"Pattern Recognition Lett., vol. 6, pp. 179-184, 1987.
[20] M. Li, W. I. Grosky, and R. Jain, "Normalized quadtrees with respect to translations,"Comput. Graphics Image Processing, vol. 20. pp. 72-81, 1982.
[21] M. Luby, "A simple parallel algorithm for the maximal independent set problem," inProc. Seventeenth Annu. ACM Symp. Theory of Computing, 1985, pp. 1-10.
[22] P. Meer, "Stochastic image pyramids,"Comput. Vision Graphics Image Processing, vol. 45, pp. 269-294, 1989.
[23] P. Meer and S. Connelly, "A fast parallel method for synthesis of random patterns,"Pattern Recognition, vol. 22, pp. 189-204, 1989.
[24] P. Meer, E. S. Baugher, and A. Rosenfeld, "Frequency domain analysis and synthesis of image pyramid generating kernels,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-9, pp. 512-522, 1987.
[25] R. Miller and Q. F. Stout, "Data movement techniques for the pyramid computer,"SIAM J. Comput., vol. 16, pp. 38-60, 1987.
[26] R. Miller and Q. F. Stout, "Simulating essential pyramids," inProc. IEEE Comput. Soc. Conf. Computer Vision and Pattern Recognition, Ann Arbor, MI, June 5-9, 1988, pp. 912-917.
[27] M. L. Minsky and S. A. Papert,Perceptrons, expanded ed. Cambridge, MA: MIT Press, 1988.
[28] S. Peleg, O. Federbusch, and R. Hummel, "Custom-made pyramids," inParallel Computer Vision, L. Uhr, Ed. New York: Academic, 1987, pp. 125-146.
[29] H. Rom and S. Peleg, "Image representation using Voronoi tessellation: Adaptive and secure," inProc. IEEE Comput. Soc. Conf. Computer Vision and Pattern Recognition, Ann Arbor, MI, June 5-9, 1988, pp. 282-285.
[30] C. Ronse and P.A. Devijver,Connected Components in Binary Images: The Detection Problem. Letchworth, England: Research Studies Press, 1984.
[31] A. Rosenfeld, Ed.,Multiresolution Image Processing and Analysis. Berlin: Springer-Verlag, 1984.
[32] A. Rosenfeld, "Recognizing unexpected objects: A proposed approach,"Int. J. Pattern Recognition Artificial Intell., vol. 1, pp. 71-84, 1987.
[33] P. K. Sahoo, S. Soltani, and A. K. C. Wong, "A survey of thresholding techniques,"Comput. Vision Graphics Image Processing, vol. 41, pp. 233-260, 1988.
[34] H. Samet, "The quadtree and related hierarchical data structures,"Comput. Surveys, vol. 16, pp. 187-260, 1984.
[35] C.A. Shaffer, "A formula for computing the number of quadtree node fragments created by a shift,"Pattern Recognition Lett., vol. 7, pp. 45-49, 1988.
[36] S. Tanimoto, "Pictorial feature distortion in a pyramid,"Comput. Graphics Image Processing, vol. 5, pp. 333-352, 1976.
[37] L. Uhr, Ed.,Parallel Computer Vision. New York: Academic, 1987.

Index Terms:
hierarchical structure; picture processing; irregular tessellations; multiresolution image analysis; stochastic processes; segmentation; gray level images; picture processing; stochastic processes
A. Montanvert, P. Meer, A. Rosenfeld, "Hierarchical Image Analysis Using Irregular Tessellations," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 4, pp. 307-316, April 1991, doi:10.1109/34.88566
Usage of this product signifies your acceptance of the Terms of Use.