An Improved ‘Gas of Circles’ Higher-Order Active Contour Model and Its Application to Tree Crown Extraction

  • Péter Horváth
  • Ian H. Jermyn
  • Zoltan Kato
  • Josiane Zerubia
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4338)


A central task in image processing is to find the region in the image corresponding to an entity. In a number of problems, the region takes the form of a collection of circles, e.g. tree crowns in remote sensing imagery; cells in biological and medical imagery. In [1], a model of such regions, the ‘gas of circles’ model, was developed based on higher-order active contours, a recently developed framework for the inclusion of prior knowledge in active contour energies. However, the model suffers from a defect. In [1], the model parameters were adjusted so that the circles were local energy minima. Gradient descent can become stuck in these minima, producing phantom circles even with no supporting data. We solve this problem by calculating, via a Taylor expansion of the energy, parameter values that make circles into energy inflection points rather than minima. As a bonus, the constraint halves the number of model parameters, and severely constrains one of the two that remain, a major advantage for an energy-based model. We use the model for tree crown extraction from aerial images. Experiments show that despite the lack of parametric freedom, the new model performs better than the old, and much better than a classical active contour.


Active Contour Gradient Descent Algorithm Local Energy Minimum Marked Point Process Phantom Region 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Péter Horváth
    • 1
    • 2
  • Ian H. Jermyn
    • 2
  • Zoltan Kato
    • 1
  • Josiane Zerubia
    • 2
  1. 1.Institute of InformaticsUniversity of SzegedSzegedHungary
  2. 2.Ariana (joint research group CNRS/INRIA/UNSA), InriaSophia AntipolisFrance

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