Point Set Topology Extraction for Branch and Crown-level Species Classification

Abstract

Contextually-based distance and proximity functions derived from the axioms of point set topology are applied at the branch and crown-level for species differentiation between eastern hemlock (Tsuga canadensis) and eastern white pine (Pinus strobus). Point set topology is a branch of mathematics that offers methods to describe the connectivity and orientation of spatial objects and therefore allows object grouping based on spatial characteristic metrics unlike traditional fixed distance measures imposed from a global metric. Local neighborhood membership functions based on topological space are robust to variation in object sizes within a fixed image resolution and are therefore useful for describing spatial characteristics in highly variable objects such as tree morphology. We investigated the utility of topological space for describing branch-level needle orientations and crown-level patterns of high and low spectral intensity clusters. Branch-level measures of orientations within topologically-derived neighborhoods resulted in a classification accuracy of 96 percent for hemlock and pine; this represents a 23 percentage point (pp) improvement over traditional spectral feature classification. A crown-level species feature extraction and classification methodology that incorporated a local Getis (Gi *) statistic contour analysis produced species discrimination results that were improved by 8 pp for an overall accuracy of 85 percent over traditional color and shape-based feature classification.