We propose an efficient algorithm for discovering the high-level topological structure of a collection of 3-dimensional trajectories. In particular, our algorithm computes a sparse graph representing the latent “bundling” and “unbundling” structure of the trajectory data. This graph can serve both as a compact signature of the trajectory data set as well as a tool for efficient comparison among different data sets. Our problem formulation and the algorithms are broadly applicable and general-purpose but we focus on a particu- lar neuroscience application to highlight the key features. In particular, our motivation stems from the emerging area of brain tractography, which aims to construct the connectome of human brain white matter fibers. These fibers can be inferred noninvasively using magnetic resonance imaging (MRI) diffusion scans of the brain interior and modeled abstractly as a set of time-independent geometric trajectories in a three-dimensional brain space. Real neuronal fiber pathways exhibit complex but natural bundling struc- tures, which elude existing MRI reconstruction techniques, but are easily captured by our algorithm. We validate our algorithms both theoretically (uniqueness of the graph repre- sentation and provably efficient algorithms) and empirically (using both synthetic and real scanned brain data sets).
Proceedings of the International Conference on Advances in Geographic Information Systems
Date: November, 2015