Medial axis based statistical shape model (MASSM): Applications to 3D prostate segmentation on MRI

In this paper, we present a novel methodology for computing statistical shape models (SSM's) by leveraging the medial axis model to determine shape variations between objects. Landmark based SSM's (LSSM's) are a popular approach to describing valid shape variation in an object of interest by applying principal component analysis to a set of landmarks on the surface of the object. However, defining landmarks which capture important shape variations can be difficult. Additionally, establishing landmark correspondences across different shapes is a challenging problem. In this work we utilize the medial axis to define the shape of the object, thereby enabling superior characterization of the underlying shape variations compared to the landmark based approach. Locations on the medial axis (medial atoms) are utilized to generate a SSM, one that we refer to as a medial axis based SSM (MASSM). The aim of the MASSM is to capture variations in the local symmetry of an object across different studies. We show analytically that reconstructing a shape using medial atoms yields a lower average error compared to reconstructing a shape using triangulations of landmarks on the boundary of a 2D object. We experimentally validate the ability of the MASSM to better reconstruct a 3D prostate volume, and to better segment that prostate compared to an LSSM on 34 3D T2-weighted endorectal Magnetic Resonance images. The accuracy of the LSSM in reconstructing the prostate was highly dependent on the number of landmarks N, while the accuracy of the MASSM was quite robust to the number of medial atoms N. In addition, in a segmentation test, the results showed an average Dice overlap of 0.93 for the MASSM while the LSSM showed an average Dice overlap of 0.88.