The medial axis transform (MAT) of a 3D shape includes the set of centers and radii of the maximally inscribed spheres, and is a complete shape descriptor that can be used to reconstruct the original shape. It is a compact representation that jointly describes geometry, topology, and symmetry properties of a given shape. In this work, we present P2MAT-NET, a neural network which learns the pattern of sparse point clouds and transform them into spheres approximating MAT. The experimental results illustrate that P2MAT-NET demonstrates better performance than state-of-the-art methods in computing MAT from point clouds, in terms of MAT quality to approximate the 3D shapes. The computed MAT can be used as an intermediate descriptor for downstream applications such as 3D shape recognition from point clouds. Our results show that it can achieve competitive performance in recognition with state-of-the-art methods.

3D形状的中间轴变换（MAT）包括最大内切球体的中心和半径的集合，并且是可用于重构原始形状的完整形状描述符。它是一个紧凑的表示形式，可以共同描述给定形状的几何形状，拓扑和对称属性。在这项工作中，我们提出了P2MAT-NET，这是一个神经网络，可学习稀疏点云的模式并将其转换为近似MAT的球体。实验结果表明，在从点云计算MAT方面，P2MAT-NET在逼近3D形状方面表现出比最新技术更好的性能。计算出的MAT可用作下游应用程序的中间描述符，例如来自点云的3D形状识别。