Exploring shape spaces of 3D tree point clouds

Abstract

We propose a framework for creating a shape space for biological trees from existing point clouds. Our method allows to freely explore the shapes between given input trees by computing arbitrary points on the geodesics induced by our metric. After establishing correspondences between branches and individual input points, our efficient formulation allows to compute the geometric 3D tree model for a given point in shape space in linear time, allowing an interactive exploration. As our metric captures branch attributes such as length, orientation, and radius, in a natural way, it is possible to explore the shape space beyond the convex hull formed by the input trees and their geodesics. Our method works directly on point clouds, which can be acquired using ranged sensing devices, and does not rely on an intermediate mesh representation.