Introducing persistence homology in 3D point cloud processing for tree morphology characterization

Persistent homology (PH) is a well-established mathematical approach that has been increasingly used to measure plant morphology. Stemming from topological data analysis, PH was developed as a mathematical framework to characterize topological relationships between data points. Structures are found by tracking topological features that persist across scales, making it resistant to noise and invariant to orientation and size.  The great advantage of PH lies in its ability to integrate several morphological features into a single metric value. In this way, it captures multiple and comprehensive measurements better than uni- or multivariate systems.  Consequently, PH enables an accurate quantification of phenological variations, quantifying the complete morphology of a plant, including growing branching structures. 

Most studies that use PH for plant morphology quantification use 2D images for the task. This is despite the fact that plants are essentially three-dimensional objects and should be analysed in that space. Studies that have explored PH in 3D focus on classification of man-made objects (e.g., toys or furniture). However, point clouds of trees that were acquired in their natural environment present a bigger challenge. There, the collected data is unevenly distributed, includes occlusions and highly depends on the season (leafing stage). All of these can vastly influence the topological analysis, and lead to incorrect structures. Not only that, but also the platform used to acquire the data might greatly affect the quantification. This is due to the point of view (i.e., from the air or terrestrially), which documents different parts of the tree. 

In this work, we test the applicability of PH for tree morphology characterization. We show how such an analysis enables us to describe various branching topologies. We use PH on individual trees that were acquired by different laser scanning platforms (i.e., UAV-borne and terrestrial), with and without leaves. This enables us to evaluate the potential of PH for 3D tree morphology characterization, test its limits, and explore its application in tree species classification.