Abstract
After a brief review and description of the existing graph pyramids used for image processing, particularly stochastic (SP) and adaptive (AP) pyramids, we propose a new strategy to improve the final segmentation provided by such methods. The idea is to translate the image to be segmented into a minimal spanning tree (MST) before building the pyramid. It is shown that the use of an MST in this process improves the results of the pyramidal segmentation. Some experimental results are presented on synthetic and actual images. Finally, a filtering pyramidal algorithm is proposed, using the properties of the minimal spanning tree.
Similar content being viewed by others
References
M. Bister, J. Cornelis, and A. Rosenfeld, “A Critical view of Pyramid Segmentation algorithms,” Pattern Recognition Letters, Vol. 11, pp. 605–617, 1990.
A. Rosenfeld and A. Sher, “Detection and Dehneation of Compact Objects Using Intensity Pyramids,” Pattern Recognition, Vol. 21, pp. 147–151, 1988.
A. Rosenfeld, “Pyramid Algorithms for Finding Global Structures in Images,” Information Sciences, Vol. 50, pp. 23–34, 1990.
A. Rosenfeld, Multiresolution Image Processing and Analysis, Springer-Verlag, Berlin, 1984.
E.S. Baugher and A. Rosenfeld, “Boundary Localization in an Image Pyramid,” Pattern Recognition, Vol. 19, pp. 373–395, 1986.
T.H. Hong and A. Rosenfeld, “Compact Region Extraction using Weighted Pixel Linking in a Pyramid,” IEEE Trans. Pattern Anal. Machine Intell., Vol. 6, pp. 222–229, 1984.
P. Meer, “Stochastic Image Pyramids,” Computer Vision, Graphics and Image Processing, Vol. 45, pp. 269–294, 1989.
A. Montanvert, P. Meer, and A. Rosenfeld, “Hierarchical Image Analysis Using Irregular Tessellations,” IEEE Trans. Pattern Anal. Mach. Intelligence, Vol. 13, pp. 307–316, 1991.
J.M. Jolion and A. Montanvert, “The Adaptive Pyramid: a Framework for 2D Image Analysis,” Computer Vision, Graphics and Image Processing, Vol. 55, pp. 339–348, 1992.
M. Luby, “A simple parallel algorithm for the maximal independent set problem,” SIAM J. Computer, Vol. 15, No. 5, pp. 1036–1053, 1986.
A. Alj and R. Faure, “Guide de la Recherche Opérationnelle,” T.I “Les Fondements,” T.2 “Les Applications”, Masson, Paris, 1990.
N. Christofides, “Graph theory: an algorithmic approach,” Academic Press, London, 1975.
J.B. Kruskal, Jr., “On the Shortest Subtree of a Graph and the Traveling Salesman Problem,” Proceedings Am. Math. Soc., Vol. 7, pp. 48–50, 1956.
R.C. Prim, “Shortest Connection Networks,” The Bell System Technical Journal, Vol. 36, pp. 1389–1401, 1957.
R.S. Barr, R.V. Helgaon, and J.L. Kennington, “Minimal Spanning Trees: An empirical investigation of parallel algorithms,” Parallel Computing, Vol. 12. No. 1, pp. 45–52, 1989.
S. Choudhury and M.N. Murty, “A Divisive Scheme for Constructing Minimal Spanning Trees in Coordinate Space,” Pattern Recognition Letters, Vol. 11, pp. 385–389, 1990.
R. Miller and Q.F. Stout, “Data Movement Techniques for the Pyramid Computer,” SIAM Journal Computer, Vol. 16, No. 1, pp. 38–60, 1987.
O.J. Morris, M.J. Lee, and A.G. Constantinides, “Graph Theory for Image analysis: an Approach Based on the Shortest Spanning Tree,” IEE Proceedings F., Communications, Radar and Signal Processing, Vol. 133, pp. 146–152, April 1986.
K.S. Lau and G. Wade, “Spatial—Spectral Clustering using Recursive Spanning Trees,” IEE Proceedings—I. Communications, Speech and Vision, Vol. 138, No. 4, pp. 232–238, 1991.
C.E. Mathieu, “Segmentation d'images par pyramides souples: application—l'imagerie médicale multidimensionnelle,” Thése de Doctorat en Génie Biologique et Médical: INSA Lyon—France, pp. 217, 1993.
W.G. Krospatsh, C. Reither, D. Willersinn, and G. Wlaschitz, “The Dual Irregular Pyramid,” Proceedings of the 5th International Conference on Computer Analysis of Images and Patterns, Budapest, September 1993, pp. 31–40.
A. Montanvert and P. Bertolino, “Irregular pyramids for parallel image segmentation,” 16th Austrian Working Group for Pattern Recognition, Vienna, 6–8 May 1992, pp. 13–34.
Nacken and Toet, “Candidate Grouping for bottom-up segmentation,” Proceedings of NATO Workshop Shape in Picture, Driebergen, The Nederlands, September 1992.
Author information
Authors and Affiliations
Additional information
This work has been performed in accordance with the research topics of the group 134 of the CNRS (National Center for Scientific Research).
The authors are with the National Institute for Applied Sciences of Lyon, URA 1216, 69621 Villeurbanne, France.
Rights and permissions
About this article
Cite this article
Mathieu, C.E., Magnin, I.E. On the choice of the first level on graph pyramids. J Math Imaging Vis 6, 85–96 (1996). https://doi.org/10.1007/BF00127376
Issue Date:
DOI: https://doi.org/10.1007/BF00127376