A New Matching Algorithm Between Trees of Shapes and Its Application to Brain Tumor Segmentation

Many approaches exist to compute the distance between two trees in pattern recognition. These trees can be structures with or without values on their nodes or edges. However, none of these distances take into account the shapes possibly associated to the nodes of the tree. For this reason, we propose in this paper a new distance between two trees of shapes based on the Hausdorff distance. This distance allows us to make inexact tree matching and to compute what we call residual forests, representing where two trees differ. We will also see that thanks to these residual forests, we can obtain good preliminary results in matter of brain tumor segmentation. This segmentation not only provides a segmentation but also the tree of shapes corresponding to the segmentation and its depth map.