Group-wise Shape Correspondence of Variable and Complex Objects.

We present a group-wise shape correspondence method for analyzing variable and complex objects in a population study. The proposed method begins with the standard spherical harmonics (SPHARM) point distribution models (PDM) with their spherical mappings. In case of complex and variable objects, the equal area spherical mapping based SPHARM correspondence is imperfect. For such objects, we present here a novel group-wise correspondence. As an example dataset, we use 12 second mandibular molars representing 6 living or fossil euarchontan species. To improve initial correspondence of the SPHARM-PDM representation, we first apply a rigid transformation on each subject using five well-known landmarks (molar cusps). We further enhance the correspondence by optimizing landmarks (local) and multidimensional geometric property (global) over each subject with spherical harmonic representation. The resulting average shape model better captures sharp landmark representation in quantitative evaluation as well as a nice separation of different species compared with that of the SPHARM-PDM method.