nD statistical shape model building via recursive boundary subdivision
Sylvia Rueda, Jayaram K. Udupa · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2009
Landmark based statistical object modeling techniques, such as Active Shape Modeling, have proven useful in medical image analysis. Identification of the same homologous set of points in a training set of object shapes is the most crucial step in ASM, which has encountered challenges, the most crucial among these being (C1) defining and characterizing landmarks; (C2) ensuring homology; (C3) generalizing to n > 2 dimensions; (C4) achieving practical computations. In this paper, we propose a novel global-to-local strategy that attempts to address C3 and C4 directly and works in Rn. The 3D version of it attempts to address C1 and C2 indirectly by starting from three initial corresponding points determined in all training shapes via a method α, and subsequently by subdividing the shapes into connected boundary segments by a plane determined by these points. A shape analysis method β is applied on each segment to determine a landmark on the segment. This point introduces more triplets of points, the planes defined by which are used to further subdivide the boundary segments. This recursive boundary subdivision (RBS) process continues simultaneously on all training shapes, maintaining synchrony of the level of recursion, and thereby keeping correspondence among generated points automatically by the correspondence of the homologous shape segments in all training shapes. The process terminates when no subdividing planes are left to be considered that indicate (as per method β) that a point can continue to be selected on the associated segment. Several examples of α and β are provided as well as some preliminary results on 3D shapes.