OctField: Hierarchical Implicit Functions for 3D Modeling

Abstract

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.

3D Reconstruction Based on Iterative Optimization of Moving Least-Squares Function

“…The combination of the two has both local and global information, which can quickly and conveniently obtain sign distance values and improve reconstruction efficiency; latent partition implicit (LPI) [20] combined local regions into global shapes in implicit space, and the use of affinity vectors allowed the reconstruction results to include both local region features and cleverly integrate global information, resulting in currently outstanding reconstruction results; implicit functions in reconstruction and completion (IFRC) [21] proposed an implicit feature network that does not use a single vector to encode three-dimensional shapes. Instead, it extracts a learnable deep feature tensor for three-dimensional multi-scale deep features and aligns it with the original Euclidean space of the embedded shape, allowing the model to make decisions based on global and local shape structures; Octfield [22] proposed adaptive decomposition in 3D scenes, which only distributes local implicit functions around the surface of interest, connects the shape features of different layers, and possesses both local and global information, achieving excellent reconstruction accuracy. Learning consistency-aware unsigned distance functions (Learning CU) [23] used a cyclic optimization approach to reconstruct sparse point clouds into dense point clouds surrounding the shape, while maintaining the normal consistency of the point cloud; learning local pattern-specific deep implicit function (LP-DIF) [24] proposed a new local pattern-specific implicit function that simplifies the learning of fine geometric details by reducing the diversity of local regions seen by each decoder.…”