Comparing botanical trees requires considering both their branching structure and their three-dimensional shape, including branch lengths, orientations, and curvature.

This topic investigates similarity measures that combine these aspects, building on approaches such as tree edit distances, elastic shape analysis, and geometric matching. Existing methods have undesired failure cases, e.g. inducing a large distance when a branch is dropped (fused Gromov-Wasserstein) or massive penalization of a slightly off branching angle of a larger subtree (Chamfer).

Possible research directions include adapting existing measures, developing efficient approximations, and improving robustness to missing branches or differences in reconstruction resolution. The resulting methods would be evaluated on how well they capture meaningful differences between trees while remaining stable under irrelevant changes such as translation or rotation.

Starting literature:

• Fused Gromov-Wasserstein distance for structured objects: theoretical foundations and mathematical properties (2018)
• Elastic Shape Analysis of Tree-like 3D Objects Using Extended SRVF Representation (2024)