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# The 'gas of circles' model and its application to tree crown extraction

1 ARIANA - Inverse problems in earth monitoring
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - SIS - Signal, Images et Systèmes
Abstract : We present the gas of circles (GOC) model, which is a tool to describe a set of circles with an approximately fixed radius. The model is based on the recently introduced higher-order active contour'(HOAC) framework. For certain ranges of the parameters, the model creates stable circles with an approximately fixed radius instead of networks. We show how to determine this set of parameters. The general gas of circle model has many potential applications in varied domains, but it suffers from a drawback: the local minima corresponding to circles can trap the gradient descent algorithm, thus producing phantom circles even with no supporting data. We solve the problem of phantom circles by calculating, via a Taylor expansion of the energy, parameter values that make the circles into inflection points rather than minima. It is possible to create an alternative formulation of HOAC models, based on the phase field' framework. We address the tree crown extraction problem by constructing a phase field model of a `gas of circles'. The available images are color-infrared (CIR) and panchromatic images. We introduce two data models. The first describes the use of only one band of the three available bands. The model is based on the image gradient and on Gaussian distributions. Our second data model makes use of all three bands in the CIR images. Experiments show that the models outperform other traditional methods. The models can also be applied to the detection of other circular objects.
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https://tel.archives-ouvertes.fr/tel-00507418
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Submitted on : Friday, July 30, 2010 - 11:44:07 AM
Last modification on : Monday, October 12, 2020 - 10:30:12 AM
Long-term archiving on: : Thursday, November 4, 2010 - 10:24:03 AM

### Identifiers

• HAL Id : tel-00507418, version 1

### Citation

Peter Horvath. The 'gas of circles' model and its application to tree crown extraction. Human-Computer Interaction [cs.HC]. Université Nice Sophia Antipolis, 2007. English. ⟨tel-00507418⟩

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