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Segmentation and Skeletonization on Arbitrary Graphs Using Multiscale Morphology and Active Contours

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Innovations for Shape Analysis

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

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Abstract

In this chapter we focus on formulating and implementing on abstract domains such as arbitrary graphs popular methods and techniques developed for image analysis, in particular multiscale morphology and active contours. To this goal we extend existing work on graph morphology to multiscale dilation and erosion and implement them recursively using level sets of functions defined on the graph’s nodes. We propose approximations to the calculation of the gradient and the divergence of vector functions defined on graphs and use these approximations to apply the technique of geodesic active contours for object detection on graphs via segmentation. Finally, using these novel ideas, we propose a method for multiscale shape skeletonization on arbitrary graphs.

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Author information

Authors and Affiliations

  1. School of Electrical and Computer Engineering, National Technical University of Athens, Athens, 15773, Greece

    Petros Maragos

  2. Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139-4307, USA

    Kimon Drakopoulos

Authors
  1. Petros Maragos
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  2. Kimon Drakopoulos
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Correspondence to Petros Maragos .

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Editors and Affiliations

  1. , Inst. for Appl. Math.&Scient.Comp., Brandenburg Technical University, Platz der Deutschen Einheit 1, Cottbus, 03046, Germany

    Michael Breuß

  2. Department of Computer Science, Technion-Israel Institute of Technology, Haifa, 32000, Israel

    Alfred Bruckstein

  3. School of Electrical &, Computer Engineering, National Technical University of Athens, Athens, 15773, Greece

    Petros Maragos

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Maragos, P., Drakopoulos, K. (2013). Segmentation and Skeletonization on Arbitrary Graphs Using Multiscale Morphology and Active Contours. In: Breuß, M., Bruckstein, A., Maragos, P. (eds) Innovations for Shape Analysis. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34141-0_3

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