# Learning Continuous Mesh Representation with Spherical Implicit Surface

arXiv: https://arxiv.org/abs/2301.04695 · HTML: https://mlsanity.com/paper/2301.04695/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 30 references that are in the map.
- First posted on arXiv 11 Jan 2023.

## Builds on (most cited first, 19 of 19)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [3D-R2N2: A Unified Approach for Single and Multi-view 3D Object Reconstruction](https://mlsanity.com/paper/1604.00449/) (2016)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [Learning Category-Specific Mesh Reconstruction from Image Collections](https://mlsanity.com/paper/1803.07549/) (2018)
- [Generating 3D faces using Convolutional Mesh Autoencoders](https://mlsanity.com/paper/1807.10267/) (2018)
- [Volumetric and Multi-View CNNs for Object Classification on 3D Data](https://mlsanity.com/paper/1604.03265/) (2016)
- [Learning a Predictable and Generative Vector Representation for Objects](https://mlsanity.com/paper/1603.08637/) (2016)
- [3D-CODED : 3D Correspondences by Deep Deformation](https://mlsanity.com/paper/1806.05228/) (2018)
- [Nonlinear 3D Face Morphable Model](https://mlsanity.com/paper/1804.03786/) (2018)
- [Unsupervised Training for 3D Morphable Model Regression](https://mlsanity.com/paper/1806.06098/) (2018)
- [Body2Hands: Learning to Infer 3D Hands from Conversational Gesture Body Dynamics](https://mlsanity.com/paper/2007.12287/) (2020)
- [Parallelizable global conformal parameterization of simply-connected surfaces via partial welding](https://mlsanity.com/paper/1903.12359/) (2019)
- [Learning Local Neighboring Structure for Robust 3D Shape Representation](https://mlsanity.com/paper/2004.09995/) (2020)

## Built on by (most cited first, 3 of 3)

- [CAD-Llama: Leveraging Large Language Models for Computer-Aided Design Parametric 3D Model Generation](https://mlsanity.com/paper/2505.04481/) (2025)
- [Spectrum AUC Difference (SAUCD): Human-aligned 3D Shape Evaluation](https://mlsanity.com/paper/2403.01619/) (2024)
- [SUGAR: Spherical Ultrafast Graph Attention Framework for Cortical Surface Registration](https://mlsanity.com/paper/2307.00511/) (2023)

## Abstract (arXiv)

As the most common representation for 3D shapes, mesh is often stored discretely with arrays of vertices and faces. However, 3D shapes in the real world are presented continuously. In this paper, we propose to learn a continuous representation for meshes with fixed topology, a common and practical setting in many faces-, hand-, and body-related applications. First, we split the template into multiple closed manifold genus-0 meshes so that each genus-0 mesh can be parameterized onto the unit sphere. Then we learn spherical implicit surface (SIS), which takes a spherical coordinate and a global feature or a set of local features around the coordinate as inputs, predicting the vertex corresponding to the coordinate as an output. Since the spherical coordinates are continuous, SIS can depict a mesh in an arbitrary resolution. SIS representation builds a bridge between discrete and continuous representation in 3D shapes. Specifically, we train SIS networks in a self-supervised manner for two tasks: a reconstruction task and a super-resolution task. Experiments show that our SIS representation is comparable with state-of-the-art methods that are specifically designed for meshes with a fixed resolution and significantly outperforms methods that work in arbitrary resolutions.