Analysis of Joint Shape Variation from Multi-Object Complexes

Shape correlation of multi-object complexes in the human body can have significant implications in understanding the development of disease. While there exist geometric and statistical methods that aim for multi-object shape analysis, very little research can effectively extract shape correlation. It is especially difficult to extract the correlation when the involved objects have different variability in separate non-Euclidean spaces. To address these difficulties, this paper proposes geometric and statistical methods to extract the shape correlation from multi-object complexes. In particular, we focus on the shape correlation of the hippocampus and the caudate subject to the development of autism. The proposed methods are designed (1) to capture objects’ shape features (2) to capture shape correlation regardless of different variability between the two objects and (3) to provide interpretable shape correlation in multi-object complexes. In our experiments on synthetic data and autism data, the quantitative results and the qualitative visualization suggest that our methods are effective and robust.