# 3D Shapes Local Geometry Codes Learning with SDF arXiv: https://arxiv.org/abs/2108.08593 ยท HTML: https://mlsanity.com/paper/2108.08593/ ## Key facts - Cited by 10 papers in the map (data through 14 Oct 2026). - Builds on 22 of its 26 references that are in the map. - First posted on arXiv 19 Aug 2021. ## Builds on (most cited first, 22 of 22) - [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016) - [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016) - [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017) - [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019) - [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020) - [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016) - [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018) - [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018) - [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020) - [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021) - [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019) - [Local Implicit Grid Representations for 3D Scenes](https://mlsanity.com/paper/2003.08981/) (2020) - [Deep Local Shapes: Learning Local SDF Priors for Detailed 3D Reconstruction](https://mlsanity.com/paper/2003.10983/) (2020) - [Generating 3D faces using Convolutional Mesh Autoencoders](https://mlsanity.com/paper/1807.10267/) (2018) - [Learning Shape Templates with Structured Implicit Functions](https://mlsanity.com/paper/1904.06447/) (2019) - [SALD: Sign Agnostic Learning with Derivatives](https://mlsanity.com/paper/2006.05400/) (2020) - [MeshSDF: Differentiable Iso-Surface Extraction](https://mlsanity.com/paper/2006.03997/) (2020) - [Neural 3D Morphable Models: Spiral Convolutional Networks for 3D Shape Representation Learning and Generation](https://mlsanity.com/paper/1905.02876/) (2019) - [DualSDF: Semantic Shape Manipulation using a Two-Level Representation](https://mlsanity.com/paper/2004.02869/) (2020) - [PatchNets: Patch-Based Generalizable Deep Implicit 3D Shape Representations](https://mlsanity.com/paper/2008.01639/) (2020) - [Fully Convolutional Mesh Autoencoder using Efficient Spatially Varying Kernels](https://mlsanity.com/paper/2006.04325/) (2020) - [Deep Implicit Volume Compression](https://mlsanity.com/paper/2005.08877/) (2020) ## Built on by (most cited first, 10 of 10) - [Neural Points: Point Cloud Representation with Neural Fields for Arbitrary Upsampling](https://mlsanity.com/paper/2112.04148/) (2021) - [Surface Reconstruction from Point Clouds: A Survey and a Benchmark](https://mlsanity.com/paper/2205.02413/) (2022) - [Latent Partition Implicit with Surface Codes for 3D Representation](https://mlsanity.com/paper/2207.08631/) (2022) - [PRIF: Primary Ray-based Implicit Function](https://mlsanity.com/paper/2208.06143/) (2022) - [PolyGNN: Polyhedron-based Graph Neural Network for 3D Building Reconstruction from Point Clouds](https://mlsanity.com/paper/2307.08636/) (2023) - [F-INR: Functional Tensor Decomposition for Implicit Neural Representations](https://mlsanity.com/paper/2503.21507/) (2025) - [Adaptive Local Basis Functions for Shape Completion](https://mlsanity.com/paper/2307.08348/) (2023) - [Isomorphic mesh generation from point clouds with multilayer perceptrons](https://mlsanity.com/paper/2210.14157/) (2022) - [Theoretical and Empirical Analysis of a Fast Algorithm for Extracting Polygons from Signed Distance Bounds](https://mlsanity.com/paper/2111.05778/) (2021) - [Taylor3DNet: Fast 3D Shape Inference With Landmark Points Based Taylor Series](https://mlsanity.com/paper/2201.06845/) (2022) ## Abstract (arXiv) A signed distance function (SDF) as the 3D shape description is one of the most effective approaches to represent 3D geometry for rendering and reconstruction. Our work is inspired by the state-of-the-art method DeepSDF that learns and analyzes the 3D shape as the iso-surface of its shell and this method has shown promising results especially in the 3D shape reconstruction and compression domain. In this paper, we consider the degeneration problem of reconstruction coming from the capacity decrease of the DeepSDF model, which approximates the SDF with a neural network and a single latent code. We propose Local Geometry Code Learning (LGCL), a model that improves the original DeepSDF results by learning from a local shape geometry of the full 3D shape. We add an extra graph neural network to split the single transmittable latent code into a set of local latent codes distributed on the 3D shape. Mentioned latent codes are used to approximate the SDF in their local regions, which will alleviate the complexity of the approximation compared to the original DeepSDF. Furthermore, we introduce a new geometric loss function to facilitate the training of these local latent codes. Note that other local shape adjusting methods use the 3D voxel representation, which in turn is a problem highly difficult to solve or even is insolvable. In contrast, our architecture is based on graph processing implicitly and performs the learning regression process directly in the latent code space, thus make the proposed architecture more flexible and also simple for realization. Our experiments on 3D shape reconstruction demonstrate that our LGCL method can keep more details with a significantly smaller size of the SDF decoder and outperforms considerably the original DeepSDF method under the most important quantitative metrics.