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.

我们提出了一个框架，用于从现有点云为生物树创建形状空间。我们的方法允许通过计算由我们的度量得出的测地线上的任意点来自由探索给定输入树之间的形状。在建立分支和单个输入点之间的对应关系后，我们的高效公式允许在线性时间内为形状空间中的给定点计算几何 3D 树模型，从而实现交互式探索。由于我们的度量以自然的方式捕获分支属性，例如长度、方向和半径，因此可以探索输入树及其测地线形成的凸包之外的形状空间。我们的方法直接适用于点云，可以使用远程传感设备获取，并且不依赖于中间网格表示。