Abstract
A dissimilarity measure between adjacent pixels of an image is usually determined by the intensity values of these pixels and therefore does not depend on statistics computed over the whole image domain. In this paper, new dissimilarity measures exploiting image statistics are proposed. This is achieved by introducing the notion of dissimilarity function defined for every possible pair of intensity values. Necessary conditions for generating a valid dissimilarity function are provided and a series of functions integrating image statistics are presented. For example, the joint probability of adjacent pixel values leads to the notion of frequent connectivity while the notion of dependent connectivity relies on the local mutual information. The usefulness of the proposed approach is demonstrated by a series of experiments on satellite image data.
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References
Sneath, P.: The application of computers in taxonomy. Journal of General Microbiology 17, 201–226 (1957)
Nagao, M., Matsuyama, T., Ikeda, Y.: Region extraction and shape analysis in aerial photographs. Computer Graphics and Image Processing 10(3), 195–223 (1979)
Baraldi, A., Parmiggiani, F.: Single linkage region growing algorithms based on the vector degree of match. IEEE Transactions on Geoscience and Remote Sensing 34(1), 137–148 (1996)
Meyer, F., Maragos, P.: Morphological scale-space representation with levelings. In: Nielsen, M., Johansen, P., Fogh Olsen, O., Weickert, J. (eds.) Scale-Space 1999. LNCS, vol. 1682, pp. 187–198. Springer, Heidelberg (1999)
Zanoguera, F., Meyer, F.: On the implementation of non-separable vector levelings. In: Talbot, H., Beare, R. (eds.) Proc. of VIth ISMM, Sydney, CSIRO, pp. 369–377 (2002)
Soille, P.: Constrained connectivity for hierarchical image partitioning and simplification. IEEE Transactions on Pattern Analysis and Machine Intelligence 30(7), 1132–1145 (2008)
Kruskal, J.: On the shortest spanning subtree of a graph and the traveling salesman problem. Proc. Am. Math. Soc. 7(1), 48–50 (1956)
Gower, J., Ross, G.: Minimum spanning trees and single linkage cluster analysis. Applied statistics 18(1), 54–64 (1969)
Serra, J.: Mathematical morphology for Boolean lattices. In: Serra, J. (ed.) Image Analysis and Mathematical Morphology. Theoretical Advances, vol. 2, pp. 37–58. Academic Press, London (1988)
Serra, J.: A lattice approach to image segmentation. Journal of Mathematical Imaging and Vision 24, 83–130 (2006)
Akçay, G., Aksoy, S., Soille, P.: Hierarchical segmentation of complex structures. In: Proc. of 20th Int. Conf. on Pattern Recognition, Istanbul, pp. 1120–1123. IEEE, Los Alamitos (2010)
Haralick, R., Shanmugam, K., Dinstein, I.: Textural features for image classification. IEEE Transactions on Systems, Man, and Cybernetics 3(6), 610–621 (1973)
Cover, T., Thomas, J.: Elements of Information Theory, 2nd edn. Wiley & Sons, Chichester (2006)
Gueguen, L., Datcu, M.: Mixed information measure: Application to change detection in earth observation. In: MultiTemp 2009: The Fifth International Workshop on the Analysis of Multi-temporal Remote Sensing Images, Connecticut, USA (June 2009)
Soille, P.: On genuine connectivity relations based on logical predicates. In: Proc. of 14th Int. Conf. on Image Analysis and Processing, Modena, Italy, pp. 487–492. IEEE Computer Society Press, Los Alamitos (2007)
Panjwani, D.K., Healey, G.: Markov random field models for unsupervised segmentation of textured color images. IEEE Transactions on Pattern Analysis and Machine Intelligence 17(10), 939–954 (1995)
Soille, P.: Preventing chaining through transitions while favouring it within homogeneous regions. In: Soille, P., Pesaresi, M., Ouzounis, G.K. (eds.) ISMM 2011. LNCS, vol. 6671, pp. 96–107. Springer, Heidelberg (2011)
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Gueguen, L., Soille, P. (2011). Frequent and Dependent Connectivities. In: Soille, P., Pesaresi, M., Ouzounis, G.K. (eds) Mathematical Morphology and Its Applications to Image and Signal Processing. ISMM 2011. Lecture Notes in Computer Science, vol 6671. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21569-8_11
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DOI: https://doi.org/10.1007/978-3-642-21569-8_11
Publisher Name: Springer, Berlin, Heidelberg
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