Abstract
Constrained connectivity relations partition the image definition domain into connected sets of maximal extent. The homogeneity and maximality of the resulting cells is subject to non-connective criteria that associate to logical predicates. The latter are based on attribute metrics, and are used to counter the leakage effect of the single-linkage clustering rule. Linkage is controlled by some dissimilarity measure and if unconstrained, may be used to generate regular connectivity classes. In this paper we introduce a hierarchical partition representation structure to map the evolution of components along the dissimilarity range in the absence of constraints. By contrast to earlier approaches, constraints may be put in place on the actual structure in the form of filters. This allows for custom and interactive segmentation of the image. Moreover, given an instance of the dissimilarity measure, one can retrieve all connected sets making up the corresponding connectivity class, directly from the hierarchy. The evolution of linkage relations with respect to the attributes on which the predicates are based on is used to compute a new type of pattern spectrum that is demonstrated on two real applications.
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
Braga-Neto, U.M., Goutsias, J.: Connectivity on complete lattices: New results. Computer Vision and Image Understanding 85(1), 22–53 (2002)
Breen, E.J., Jones, R.: Attribute openings, thinnings and granulometries. Computer Vision and Image Understanding 64(3), 377–389 (1996)
Buf, J.M.H.D., Bayer, M.M. (eds.): Automatic Diatom Identification. Series in Machine Perception and Artificial Intelligence. World Scientific Publishing Co., Singapore (2002)
Gueguen, L., Soille, P.: Frequent and dependent connectivities. In: Soille, P., Pesaresi, M., Ouzounis, G.K. (eds.) ISMM 2011. LNCS, vol. 6671, pp. 120–131. Springer, Heidelberg (2011) (in press)
Maragos, P.: Pattern spectrum and multiscale shape representation. IEEE Trans. Pattern Analysis and Machine Intelligence 11(7), 701–715 (1989)
Meyer, F., Maragos, P.: Nonlinear scale-space representation with morphological levelings. Journal Visual Communication and Image Representation 11(3), 245–265 (2000)
Nagao, M., Matsuyama, T., Ikeda, Y.: Region extraction and shape analysis in aerial photographs. Computer Graphics and Image Processing 10(3), 195–203 (1979)
Ouzounis, G.K., Soille, P.: Differential area profiles. In: 20th Int. Conf. on Pattern Recognition, ICPR 2010, Istanbul, Turkey, pp. 4085–4088 (August 2010)
Ouzounis, G.K., Soille, P.: Attribute constrained connectivity and the alpha-tree representation. IEEE Trans. on Image Processing (submitted, 2011)
Ouzounis, G.K., Soille, P., Pesaresi, M.: Rubble detection from VHR aerial imagery data using differential morphological profiles. In: 34th Int. Symp. Remote Sensing of the Environment, Sydney, Australia (April 2011) (in press)
Ouzounis, G.K., Wilkinson, M.H.F.: Mask-based second-generation connectivity and attribute filters. IEEE Trans. Pattern Analysis and Machine Intelligence 29(6), 990–1004 (2007)
Ouzounis, G.K., Wilkinson, M.H.F.: Partition-induced connections and operators for pattern analysis. Pattern Recognition 43(10), 3193–3207 (2010)
Pesaresi, M., Benediktsson, J.A.: A new approach for the morphological segmentation of high-resolution satellite imagery. IEEE Trans. Geoscience and Remote Sensing 39(2), 309–320 (2001)
Ronse, C.: Set-theoretical algebraic approaches to connectivity in continuous or digital spaces. Journal of Mathematical Imaging and Vision 8, 41–58 (1998)
Ronse, C.: Partial partitions, partial connections and connective segmentation. Journal of Mathematical Imaging and Vision 32(2), 97–125 (2008)
Salembier, P., Serra, J.: Flat zones filtering, connected operators, and filters by reconstruction. IEEE Trans. on Image Processing 4(8), 1153–1160 (1995)
Serra, J. (ed.): Image Analysis and Mathematical Morphology. Theoretical Advances, vol. II. Academic Press, London (1988)
Serra, J.: A lattice approach to image segmentation. Journal of Mathematical Imaging and Vision 24, 83–130 (2006)
Soille, P.: Constrained connectivity for hierarchical image partitioning and simplification. IEEE Trans. Pattern Analysis and Machine Intelligence 30(7), 1132–1145 (2008)
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)
Soille, P.: On genuine connectivity relations based on logical predicates. In: Int. Conf. Image Analysis and Processing (ICIAP), pp. 487–492 (2007)
Urbach, E.R., Roerdink, J.B.T.M., Wilkinson, M.H.F.: Connected shape-size pattern spectra for rotation and scale-invariant classification of gray-scale images. IEEE Trans. Pattern Analysis and Machine Intelligence 29(2), 272–285 (2007)
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
Ouzounis, G.K., Soille, P. (2011). Pattern Spectra from Partition Pyramids and Hierarchies. 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_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-21569-8_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21568-1
Online ISBN: 978-3-642-21569-8
eBook Packages: Computer ScienceComputer Science (R0)