Abstract
Regions in an image graph can be described by their spanning tree. A graph pyramid is a stack of image graphs at different granularities. Integral features capture important properties of these regions and the associated trees. We compute the depth of a rooted tree, its diameter and the center which becomes the root in the top-down decomposition of a region. The integral tree is an intermediate representation labeling each vertex of the tree with the integral feature(s) of the subtree. Parallel algorithms efficiently compute the integral trees for subtree depth and diameter enabling local decisions with global validity in subsequent top-down processes.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Viola, P., Jones, M.: Robust Real-time Face Detection. International Journal of Computer Vision 57, 137–154 (2004)
Beleznai, C., Frühstück, B., Bischof, H., Kropatsch, W.G.: Detecting Humans in Groups using a Fast Mean Shift Procedure. OCG-Schriftenreihe 179, 71–78 (2004)
Kropatsch, W.G.: Building Irregular Pyramids by Dual Graph Contraction. IEE-Proc. Vision, Image and Signal Processing 142, 366–374 (1995)
Christofides, N.: The Traveling Salesman Problem. John Wiley and Sons, Chichester (1985)
Graham, S.M., Joshi, A., Pizlo, Z.: The Travelling Salesman Problem: A Hierarchical Model. Memory & Cognition 28, 1191–1204 (2000)
Pizlo, Z., Li, Z.: Graph Pyramids as Models of Human Problem Solving. In: Proc. of SPIE-IS&T Electronic Imaging, Computational Imaging, vol. 5299, pp. 205–215 (2004)
Humphrey, G.: Directed Thinking. Dodd, Mead (1948)
Pizlo, Z.: Perception Viewed as an Inverse Problem. Vis. Res. 41, 3145–3161 (2001)
Pizlo, Z., Rosenfeld, A., Epelboim, J.: An Exponential Pyramid Model of the Time-course of Size Processing. Vision Research 35, 1089–1107 (1995)
Koffka, K.: Principles of Gestalt Psychology. Harcourt, New York (1935)
Borgefors, G.: Distance Transformation in Arbitrary Dimensions. Computer Vision, Graphics, and Image Processing 27, 321–345 (1984)
Borgefors, G.: Distance Transformation in Digital Images. Computer Vision, Graphics, and Image Processing 34, 344–371 (1986)
Kropatsch, W.G.: Equivalent Contraction Kernels to Build Dual Irregular Pyramids. Advances in Computer Vision, pp. 99–107. Springer, Heidelberg (1997)
Kropatsch, W.G., Saib, M., Schreyer, M.: The Optimal Height of a Graph Pyramid. OCG-Schriftenreihe 160, 87–94 (2002)
Kropatsch, W.G., Haxhimusa, Y., Pizlo, Z.: Integral Trees: Subtree Depth and Diameter. Technical Report No. 92, PRIP, Vienna University of Technology (2004)
Bister, M., Cornelis, J., Rosenfeld, A.: A Critical View of Pyramid Segmentation Algorithms. Pattern Recognition Letters 11, 605–617 (1990)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kropatsch, W.G., Haxhimusa, Y., Pizlo, Z. (2004). Integral Trees: Subtree Depth and Diameter. In: Klette, R., Žunić, J. (eds) Combinatorial Image Analysis. IWCIA 2004. Lecture Notes in Computer Science, vol 3322. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30503-3_6
Download citation
DOI: https://doi.org/10.1007/978-3-540-30503-3_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23942-0
Online ISBN: 978-3-540-30503-3
eBook Packages: Computer ScienceComputer Science (R0)