# Local Deep Implicit Functions for 3D Shape

arXiv: https://arxiv.org/abs/1912.06126 · HTML: https://mlsanity.com/paper/1912.06126/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Dec 2019.

## Built on by (most cited first, 18 of 18)

- [NeRV: Neural Representations for Videos](https://mlsanity.com/paper/2110.13903/) (2021)
- [A-SDF: Learning Disentangled Signed Distance Functions for Articulated Shape Representation](https://mlsanity.com/paper/2104.07645/) (2021)
- [CaDeX: Learning Canonical Deformation Coordinate Space for Dynamic Surface Representation via Neural Homeomorphism](https://mlsanity.com/paper/2203.16529/) (2022)
- [Learning Signal-Agnostic Manifolds of Neural Fields](https://mlsanity.com/paper/2111.06387/) (2021)
- [NeUDF: Leaning Neural Unsigned Distance Fields with Volume Rendering](https://mlsanity.com/paper/2304.10080/) (2023)
- [Topology-Preserving Shape Reconstruction and Registration via Neural Diffeomorphic Flow](https://mlsanity.com/paper/2203.08652/) (2022)
- [Exploring Differential Geometry in Neural Implicits](https://mlsanity.com/paper/2201.09263/) (2022)
- [3D Equivariant Graph Implicit Functions](https://mlsanity.com/paper/2203.17178/) (2022)
- [SCI: A Spectrum Concentrated Implicit Neural Compression for Biomedical Data](https://mlsanity.com/paper/2209.15180/) (2022)
- [Semi-supervised 3D shape segmentation with multilevel consistency and part substitution](https://mlsanity.com/paper/2204.08824/) (2022)
- [LightSAL: Lightweight Sign Agnostic Learning for Implicit Surface Representation](https://mlsanity.com/paper/2103.14273/) (2021)
- [Capturing Longitudinal Changes in Brain Morphology Using Temporally Parameterized Neural Displacement Fields](https://mlsanity.com/paper/2504.09514/) (2025)
- [Enhancing Surface Neural Implicits with Curvature-Guided Sampling and Uncertainty-Augmented Representations](https://mlsanity.com/paper/2306.02099/) (2023)
- [Exploring Kernel Transformations for Implicit Neural Representations](https://mlsanity.com/paper/2504.04728/) (2025)
- [A Simple Plugin for Transforming Images to Arbitrary Scales](https://mlsanity.com/paper/2210.03417/) (2022)
- [A Compact Implicit Neural Representation for Efficient Storage of Massive 4D Functional Magnetic Resonance Imaging](https://mlsanity.com/paper/2312.00082/) (2023)
- [Dynamic Neural Graph Encoding of Inference Processes in Deep Weight Space](https://mlsanity.com/paper/2607.02166/) (2026)
- [Splat-based 3D Scene Reconstruction with Extreme Motion-blur](https://mlsanity.com/paper/2607.16926/) (2026)

## Abstract (arXiv)

The goal of this project is to learn a 3D shape representation that enables accurate surface reconstruction, compact storage, efficient computation, consistency for similar shapes, generalization across diverse shape categories, and inference from depth camera observations. Towards this end, we introduce Local Deep Implicit Functions (LDIF), a 3D shape representation that decomposes space into a structured set of learned implicit functions. We provide networks that infer the space decomposition and local deep implicit functions from a 3D mesh or posed depth image. During experiments, we find that it provides 10.3 points higher surface reconstruction accuracy (F-Score) than the state-of-the-art (OccNet), while requiring fewer than 1 percent of the network parameters. Experiments on posed depth image completion and generalization to unseen classes show 15.8 and 17.8 point improvements over the state-of-the-art, while producing a structured 3D representation for each input with consistency across diverse shape collections.