Abstract
Generalized maps are widely used to model the topology of nD objects (such as images) by means of incidence and adjacency relationships between cells (vertices, edges, faces, volumes, ...). In this paper, we define a first error-tolerant distance measure for comparing generalized maps, which is an important issue for image processing and analysis. This distance measure is defined by means of the size of a largest common submap, in a similar way as a graph distance measure may be defined by means of the size of a largest common subgraph. We show that this distance measure is a metric, and we introduce a greedy randomized algorithm which allows us to efficiently compute an upper bound of it.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bunke, H., Shearer, K.: A graph distance metric based on the maximal common subgraph. PRL 19(3-4), 255–259 (1998)
Bunke, H.: On a relation between graph edit distance and maximum common subgraph. PRL 18, 689–694 (1997)
Damiand, G.: Topological model for 3d image representation: Definition and incremental extraction algorithm. CVIU 109(3), 260–289 (2008)
Damiand, G., Bertrand, Y., Fiorio, C.: Topological model for two-dimensional image representation: definition and optimal extraction algorithm. CVIU 93(2), 111–154 (2004)
Damiand, G., De La Higuera, C., Janodet, J.-C., Samuel, E., Solnon, C.: Polynomial algorithm for submap isomorphism: Application to searching patterns in images. In: Torsello, A., Escolano, F., Brun, L. (eds.) GbRPR 2009. LNCS, vol. 5534, pp. 102–112. Springer, Heidelberg (2009)
Lienhardt, P.: N-dimensional generalized combinatorial maps and cellular quasi-manifolds. International Journal of Computational Geometry and Applications 4(3), 275–324 (1994)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Combier, C., Damiand, G., Solnon, C. (2011). Measuring the Distance of Generalized Maps. In: Jiang, X., Ferrer, M., Torsello, A. (eds) Graph-Based Representations in Pattern Recognition. GbRPR 2011. Lecture Notes in Computer Science, vol 6658. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20844-7_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-20844-7_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-20843-0
Online ISBN: 978-3-642-20844-7
eBook Packages: Computer ScienceComputer Science (R0)