METHODS

The basic idea is to relate only corresponding parts of the shape under investigation. A sample from the samples set is chosen as a common reference (atlas), and the other samples are landmarked and registered to it so that the corresponding points can be identified. The registration has three levels: alignment, rigid and elastic transformations.

To align two scapulae, we define a coordinate system, attach it to each scapula and align both systems. For this, we automatically locate three characteristic points on the scapula's surface. All samples are then scaled to the atlas and the rigid registration is determined by minimising the Euclidian distance between surfaces using Levenberg-Marquadt algorithm.

Afterwards, the samples are locally deformed toward the atlas using directly their landmarks (traditional approach). Unfortunately, landmarks-correspondences could be mismatched at some anatomically complex, “critical,” zones of the scapula. To overcome such a problem, we suggest to 3D-segment these “critical” zones using a 3D Watershed-based method.

Watershed is based on a physical concept of immersion, where it is achieved in a similar way to water filling geographic basins. We believe that this is a natural way to segment the surface of the scapula since it has two large “basins”: the glenoid and the subscapularis fossa. Watershed is followed by geometrical operations to establish eight separated zones on the surface of the scapula.

Once we have the zones, surface-to-surface correspondence is defined and the landmarks' point-to-point correspondences are obtained within each zone pair separately. The elastic registration is then applied on the whole surface via a multi-resolution B-Spline algorithm. The atlas is built through an iterative procedure to eliminate the bias to the initial choice and the correspondences are identified by a reverse registration. Finally, the statistical model can be constructed by performing Principle Component Analysis (PCA).