Locally Adaptive Hierarchical Cluster Termination With Application To Individual Tree Delineation

A clustering termination procedure which is locally adaptive (with respect to the hierarchical tree of sets representative of the agglomerative merging) is proposed, for agglomerative hierarchical clustering on a set equipped with a distance function. It represents a multi-scale alternative to conventional scale dependent threshold based termination criteria. We trim the tree at specific locations by studying cumulative extreme values of rates of change of parameters along paths of the agglomeration hierarchy, each path representing the ”history” of successive merges with respect to an initial set. Thus the method considers the smallest localities. Moreover, a cumulative extreme value of the rate of a parameter indicates the parameter is changing more rapidly than it has yet changed, which, in the context of geometric parameters we interpret to mean: the geometry at that merging step is changing more drastically than at any preceding step. We refer to this qualitative phenomenon as geometric ”paradigm shift”. The method is sensitive to extreme changes in geometry that may happen at any scale. The proposed termination is presented in the context of a motivating example in forest mapping. Automated approaches for delineating Individual Tree Crowns (ITCs) from high resolution imagery offer the possibility of improving mapping consistency, accuracy, and effectiveness. The Individual Tree Crown (ITC) methods of Gougeon et al. [1], [2] distinguish individual tree crowns by following the darker ”valley” material between them. Such is a highly effective modus operandi for conically shaped trees (softwoods). Hardwood trees, on the other hand, are of greater structural complexity resulting in less distinction between internal and external shadow, hence oversegmentation may result. As a possible avenue for remediating this exceptional situation, the proposed termination method offers assistance in detecting instances of oversegmentation by proposing geometrically meaningful candidate groups of segments, from hierarchical clustering using an appropriate ”distance”. After developing the approach in this motivating context, we rank the resulting clusters of segments by a scale-independent dispersion measure.