Recent advances in localized implicit functions have enabled neural implicit representation to be scalable to large scenes.However, the regular subdivision of 3D space employed by these approaches fails to take into account the sparsity of the surface occupancy and the varying granularities of geometric details. As a result, its memory footprint grows cubically with the input volume, leading to a prohibitive computational cost even at a moderately dense decomposition. In this work, we present a learnable hierarchical implicit representation for 3D surfaces, coded OctField, that allows high-precision encoding of intricate surfaces with low memory and computational budget. The key to our approach is an adaptive decomposition of 3D scenes that only distributes local implicit functions around the surface of interest. We achieve this goal by introducing a hierarchical octree structure to adaptively subdivide the 3D space according to the surface occupancy and the richness of part geometry. As octree is discrete and non-differentiable, we further propose a novel hierarchical network that models the subdivision of octree cells as a probabilistic process and recursively encodes and decodes both octree structure and surface geometry in a differentiable manner. We demonstrate the value of OctField for a range of shape modeling and reconstruction tasks, showing superiority over alternative approaches.

In this supplemental material, we provide more details on network architecture and more visualization results, including shape reconstruction/comparison, shape Generation, and shape Interpolations. Furthermore, some results on scene reconstruction and comparison with Local Implicit Grid [3] are presented to demonstrate our superiority on large data representation thanks to the hierarchical tree structure of our proposed OctField representation. All sections are listed as follows: Section 1 provides the details of network architecture and training. Section 2, Section 3 and Section 4 provide more visualization results on a number of 3D modeling tasks, including shape reconstruction, generation and interpolation. Section 5 conducts four ablation studies, including with or without overlapping of adjacent octants, the training strategy, the distinction of latent codes and the subdivision parameter τ .