Topological Classification of Firn Image Data

When snow persists yearly, previous layers of snowfall along with pockets of air are buried by fresh snow. As this cycle repeats, deeper layers of snow are put under increasing pressure until they solidify into glacial ice. Upper layers of granular snow that have not fully compressed into ice are called firn. The varying pressure causes changes in connectivity which motivates studying firn structure across multiple depths. Connectivity is well defined through homology, and we propose a classifier to determine depth as a function of topological features computed through techniques from persistent homology. This classifier is compared to benchmarks computed with convolutional neural networks, which are standard in computer vision tasks. The topological approach has comparable accuracy and advantages in terms of efficiency, generalizability, invariance against rigid transformations, and interpretability.