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ICPR2012 Tutorials PM-03
Connectivity, Connected Filters, and Beyond: Theory and Applications for Fast Filtering and Object Recognition

Michael H.F. Wilkinson
Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen., the Netherlands



Connected filters have rapidly become one of the most important classes of morphological filters. They allow edge preserving image simplification using a variety of strategies, and can be applied to many different tasks, ranging from image de-noising at the low-level end of the spectrum, to object recognition at the high-level task. Besides their edge preserving nature, connected filters can model the Gestalt notion of perceptual grouping, by using more generalised notions of connectivity, allowing, e.g., a flock of birds to be viewed as a single entity. Furthermore, they allow very fast multi-scale analysis of images and volumes, and can be made scale or even affine invariant very easily. In this tutorial the foundations of connected filters and connectivity will be presented. The aim is to give participants insight into the properties of these methods, and how to apply them in practical problems.



Course description

From Basics to Multi-Scale
We will first cover the most important types of connected filters in the grey scale case. After a brief refresher on regular morphological filters, connected filters are introduced by the best known example, i.e. openings by reconstruction, and their extension to levelings [3]. We then move on to area openings [10] and attribute filters [2], which allow enhancement or suppression of objects based on a range of properties. We also introduce the graph-based data structures used for implementation of these filters, and the fast multi-scale analysis that can be performed with them. The methods will be illustrated by examples, such as fast multi-scale analysis of gigapixel images in remote sensing.

Connectivity and Colour
Next, we will extend the notion of connectivity beyond the usual graph-based forms, and move to so-called second-generation connectivity [1, 4, 8]. Applications including 3D medical imaging and visualisation, and astronomy will be used to illustrate the theory. We also extend the filters to colour and other vector images [6, 9], and show how these can be used in both remote sensing and video segmentation.

Beyond Connectivity
The third lecture will explore notions of hyperconnectivity [8, 12] and attribute-space connectivity [11], which expand the mathematical framework of these object-oriented filters, especially to dealing with overlapping structures. We show how these extensions provide greater flexibility and robustness in several cases, including astronomical images and historical document processing [5]. This work is very much at the cutting edge, and we will touch upon many open research questions in this area.


Relevant References:

[1] U.M. Braga-Neto and J. Goutsias. Connectivity on complete lattices: New results. Comp. Vis. Image Understand., 85:22–53, 2002.
[2] E. J. Breen and R. Jones. Attribute openings, thinnings and granulometries. Comp. Vis. Image Understand., 64(3):377–389, 1996.
[3] F. Meyer. Levelings, image simplification filters for segmentation. J. Math. Imag. Vis., 20(1–2):59–72, 2004.
[4] G. K. Ouzounis and M. H. F. Wilkinson. Mask-based second generation connectivity and attribute filters. IEEE Trans. Pattern Anal. Mach. Intell., 29:990–1004, 2007.
[5] G. K. Ouzounis and M. H. F. Wilkinson. Hyperconnected attribute filters based on k-flat zones. IEEE Trans. Pattern Anal. Mach. Intell., 33:224–239, 2011.
[6] P. Salembier and L. Garrido. Binary partition tree as an efficient representation for image processing, segmentation and information retrieval. IEEE Trans. Image Proc., 9(4):561–576, April,
[7] P. Salembier and M. H. F. Wilkinson. Connected operators: A review of region-based morphological image processing techniques. IEEE Signal Processing Magazine, 26(6):136–157, 2009.
[8] J. Serra. Connectivity on complete lattices. J. Math. Imag. Vis., 9(3):231–251, 1998.
[9] P. Soille. Constrained connectivity and connected filters. IEEE Trans. Pattern Anal. Mach.
Intell., 30(7):1132–1145, July 2008.
[10] L. Vincent. Morphological area openings and closings for grey-scale images. In Y.-L. O, A. Toet, D. Foster, H. J. A. M. Heijmans, and P. Meer, editors, Shape in Picture: Mathematical Description of Shape in Grey-level Images, pages 197–208. NATO, 1993.
[11] M. H. F. Wilkinson. Attribute-space connectivity and connected filters. Image Vis. Comput., 25:426–435, 2007.
[12] M. H. F. Wilkinson. An axiomatic approach to hyperconnectivity. In M. H. F. Wilkinson and J. B. T. M. Roerdink, editors, Proc. Int. Symp. Math. Morphology (ISMM) 2009, volume 5720 of LNCS, pages 35–46, 2009.
[13] Michael H.F. Wilkinson and Georgios K. Ouzounis. Advances in connectivity and connected attribute filters. In Peter W. Hawkes, editor, Advances in Imaging and Electron Physics, volume 161, pages 211 – 275. Elsevier, 2010.


About Lecturer:

Michael Wilkinson obtained an MSc in astronomy from the Kapteyn Laboratory, University of Groningen in 1993, after which he worked on image analysis of intestinal bacteria at the Department of Medical Microbiology, University of Groningen, obtaining a PhD at the Institute of Mathematics and Computing Science, also in Groningen, in 1995. He was appointed as researcher at the Centre for High Performance Computing in Groningen working on simulating the intestinal microbial ecosystem on parallel computers. During that time he edited the book “Digital Image Analysis of Microbes” (John Wiley, UK, 1998) together with Frits Schut. After this he worked as a researcher and lecturer at the Johann Bernoulli Institute for Mathematics and Computer Science (JBI) on image analysis of diatoms. He is currently senior lecturer at the JBI, working on morphological image analysis and especially connected morphology. At ICIP2008, he organised a special session on connected filters together with Philippe Salembier. He organised the 2009 International Symposium on Mathematical Morphology (ISMM) together with Jos Roerdink, is member of the ISMM Steering Committee, and has given several tutorials on connected filters at international conferences and summer schools. Is is co-author of two recent review papers on connected filters [7, 13].






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