  To date, the comparison of Statistical Shape Models (SSMs) is often solely
performance-based, carried out by means of simplistic metrics such as
compactness, generalization, or specificity. Any similarities or differences
between the actual shape spaces can neither be visualized nor quantified. In
this paper, we present a new method to qualitatively compare two linear SSMs in
dense correspondence by computing approximate intersection spaces and
set-theoretic differences between the (hyper-ellipsoidal) allowable shape
domains spanned by the models. To this end, we approximate the distribution of
shapes lying in the intersection space using Markov chain Monte Carlo and
subsequently apply Principal Component Analysis (PCA) to the posterior samples,
eventually yielding a new SSM of the intersection space. We estimate
differences between linear SSMs in a similar manner; here, however, the
resulting spaces are no longer convex and we do not apply PCA but instead use
the posterior samples for visualization. We showcase the proposed algorithm
qualitatively by computing and analyzing intersection spaces and differences
between publicly available face models, focusing on gender-specific male and
female as well as identity and expression models. Our quantitative evaluation
based on SSMs built from synthetic and real-world data sets provides detailed
evidence that the introduced method is able to recover ground-truth
intersection spaces and differences accurately.
