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To date, the comparison of Statistical Shape Models (SSMs) is often solelyperformance-based, carried out by means of simplistic metrics such ascompactness, generalization, or specificity. Any similarities or differencesbetween the actual shape spaces can neither be visualized nor quantified. Inthis paper, we present a new method to qualitatively compare two linear SSMs indense correspondence by computing approximate intersection spaces andset-theoretic differences between the (hyper-ellipsoidal) allowable shapedomains spanned by the models. To this end, we approximate the distribution ofshapes lying in the intersection space using Markov chain Monte Carlo andsubsequently apply Principal Component Analysis (PCA) to the posterior samples,eventually yielding a new SSM of the intersection space. We estimatedifferences between linear SSMs in a similar manner; here, however, theresulting spaces are no longer convex and we do not apply PCA but instead usethe posterior samples for visualization. We showcase the proposed algorithmqualitatively by computing and analyzing intersection spaces and differencesbetween publicly available face models, focusing on gender-specific male andfemale as well as identity and expression models. Our quantitative evaluationbased on SSMs built from synthetic and real-world data sets provides detailedevidence that the introduced method is able to recover ground-truthintersection spaces and differences accurately.

Approximating Intersections and Differences Between Linear Statistical Shape Models Using Markov Chain Monte Carlo