Feature-based morphological analysis of shape graph data
This work addresses the need for statistical analysis of shape graphs in domains like urban planning and neuroscience, but it is incremental as it builds on existing feature-based methods with curated features.
The paper tackles the problem of analyzing shape graph datasets, which are geometric networks in 2D or 3D spaces, by developing a computational pipeline that extracts topological, geometric, and directional features to capture both connectivity and geometric variations, and demonstrates its effectiveness on real-world datasets like urban road networks and neuronal traces, achieving competitive results in tasks such as group comparison and classification.
This paper introduces and demonstrates a computational pipeline for the statistical analysis of shape graph datasets, namely geometric networks embedded in 2D or 3D spaces. Unlike traditional abstract graphs, our purpose is not only to retrieve and distinguish variations in the connectivity structure of the data but also geometric differences of the network branches. Our proposed approach relies on the extraction of a specifically curated and explicit set of topological, geometric and directional features, designed to satisfy key invariance properties. We leverage the resulting feature representation for tasks such as group comparison, clustering and classification on cohorts of shape graphs. The effectiveness of this representation is evaluated on several real-world datasets including urban road/street networks, neuronal traces and astrocyte imaging. These results are benchmarked against several alternative methods, both feature-based and not.