, Volume 13, Issue 2, pp 175–191 | Cite as

From Curves to Trees: A Tree-like Shapes Distance Using the Elastic Shape Analysis Framework

  • A. Mottini
  • X. Descombes
  • F. Besse
Original Article


Trees are a special type of graph that can be found in various disciplines. In the field of biomedical imaging, trees have been widely studied as they can be used to describe structures such as neurons, blood vessels and lung airways. It has been shown that the morphological characteristics of these structures can provide information on their function aiding the characterization of pathological states. Therefore, it is important to develop methods that analyze their shape and quantify differences between their structures. In this paper, we present a method for the comparison of tree-like shapes that takes into account both topological and geometrical information. This method, which is based on the Elastic Shape Analysis Framework, also computes the mean shape of a population of trees. As a first application, we have considered the comparison of axon morphology. The performance of our method has been evaluated on two sets of images. For the first set of images, we considered four different populations of neurons from different animals and brain sections from the open database. The second set was composed of a database of 3D confocal microscopy images of three populations of axonal trees (normal and two types of mutations) of the same type of neurons. We have calculated the inter and intra class distances between the populations and embedded the distance in a classification scheme. We have compared the performance of our method against three other state of the art algorithms, and results showed that the proposed method better distinguishes between the populations. Furthermore, we present the mean shape of each population. These shapes present a more complete picture of the morphological characteristics of each population, compared to the average value of certain predefined features.


Elastic shape analysis Axonal morphology Neuron classification 



The authors would like to thank Anuj Srivastava, Sebastian Kurtek and Zhengwu Zhang (Department of Statistics, Florida State University) for providing their original code on ESA between curves. They would also like to thank Lars Relund Nielsen (Department of Economics and Business, University of Aarhus) for providing his code on ranked assignments and Darren Thomson (IBV) for proofreading the paper.

Conflict of interests

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.INRIA CRI-SAM, 2004 route des LuciolesSophia Antipolis CedexFrance
  2. 2.IBV, Faculté des SciencesNice Cedex 2France

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