Statistical Model of Similarity Transformations: Building a Multi-Object Pose

In most of computational anatomy studies, pose is disregarded because pose information mainly depends on non relevant external factors. However, the relative pose among different objects belonging to a complex multi-object system may be useful for diagnosis, prognosis and monitoring. In this work a methodology to build statistical multi-object pose models (MOPM) is described. The methodology is based on Principal Geodesic Analysis because the space of similarity transformations does not form a vector space. Methods to compute statistics, namely averages and variation modes, are described in detail. Experimental results are performed on neuroanatomical structures such as the subcortical nuclei (caudate nucleus, hippocampus, amygdala, thalamus, putamen, pallidum) and lateral ventricles. We expect that multi-object pose models will be useful as a valuable a priori information about relative location, orientation and scale of each structure. This compact model will be relevant as a coarse initialization for segmentation, or regularization of segmentation and registration algorithms.