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

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 NeuroMorpho.org 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.