Multi-object statistical pose plus shape models

Region of interest (ROI) analysis is a very common procedure for morphometry studies of brain structures, where each structure is usually isolated from the rest of the brain and aligned to a reference shape. In the allignment process all pose information is disregarded. However, considering the brain as a multi-object system formed by several structures, the relative pose among different structures may provide clinically relevant information. A methodology to build multi-object statistical pose+shape models is given in this work. The pose features for each structure are given by the parameters of a similarity transformation and the shape features are given by the coordinates of corresponding landmarks on the boundary. As pose and shape features do not live in an Euclidean vector space but in a Riemmanian manifold, the methodology is based on performing standard multivariate statistical tools (such as PCA) on the tangent space. Experimental results are performed on brain structures such as the subcortical nuclei (caudate nucleus, hippocampus, amygdala, thalamus, putamen, pallidum) and lateral ventricles.