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.

本文提出一种可学习的、分层的隐式表示方法 OctField，通过引入一种自适应的八叉树结构，可以将离散的、可递归编码的八叉树结构和表面几何以可微分的方式编码和解码，从而优于其他方法在一系列形状建模和重建任务中展现了其价值。