Approximating Intersections and Differences Between Statistical Shape Models

To date, the comparison of Statistical Shape Models (SSMs) is often solely performance-based and 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 first method to compare two SSMs in dense correspondence by computing approximate intersection spaces and set-theoretic differences between the affine vector spaces spanned by the models. To this end, we approximate the distribution of shapes lying in the intersection space using Markov Chain Monte Carlo, and then apply Principal Component Analysis (PCA) to its samples. By representing the resulting spaces again as an SSM, our method enables an easy and intuitive analysis of similarities between two model's shape spaces. We estimate differences between SSMs in a similar manner; here, however, the resulting shape spaces are not linear vector spaces anymore 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. Finally, we demonstrate that the proposed algorithm can be easily adapted to also compute intersections and differences between color spaces.