We introduce CN-DHF (Compact Neural Double-Height-Field), a novel hybrid neural implicit 3D shape representation that is dramatically more compact than the current state of the art. Our representation leverages Double-Height-Field (DHF) geometries, defined as closed shapes bounded by a pair of oppositely oriented height-fields that share a common axis, and leverages the following key observations: DHFs can be compactly encoded as 2D neural implicits that capture the maximal and minimal heights along the DHF axis; and typical closed 3D shapes are well represented as intersections of a very small number (three or fewer) of DHFs. We represent input geometries as CNDHFs by first computing the set of DHFs whose intersection well approximates each input shape, and then encoding these DHFs via neural fields. Our approach delivers high-quality reconstructions, and reduces the reconstruction error by a factor of 2:5 on average compared to the state-of-the-art, given the same parameter count or storage capacity. Compared to the best-performing alternative, our method produced higher accuracy models on 94% of the 400 input shape and parameter count combinations tested.

翻译：我们提出CN-DHF（紧凑型神经双高度场），一种新颖的混合神经隐式三维形状表示方法，其紧凑性远超现有最优技术。该表示利用双高度场（DHF）几何结构——定义为由一对共享共同轴且方向相反的高度场边界所围成的封闭形状——并基于以下关键观察：双高度场可被紧凑编码为二维神经隐式函数，捕捉沿DHF轴的最大与最小高度；典型封闭三维形状可很好地表示为极少量（三个或更少）双高度场的交集。通过先计算能够良好近似每个输入形状的DHF交集集合，再借助神经场对这些DHF进行编码，我们将输入几何体表示为CNDHF。该方法实现了高质量重建，在同等参数数量或存储容量下，平均重建误差相比现有最优技术降低约2.5倍。与性能最佳的替代方法相比，我们的方法在测试的400种输入形状与参数数量组合中，有94%生成了更高精度的模型。