# Unsupervised Shape Completion via Deep Prior in the Neural Tangent Kernel Perspective

arXiv: https://arxiv.org/abs/2104.09023 · HTML: https://mlsanity.com/paper/2104.09023/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 87 references that are in the map.
- First posted on arXiv 19 Apr 2021.

## Builds on (most cited first, 30 of 38)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [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 Semantic Segmentation with Submanifold Sparse Convolutional Networks](https://mlsanity.com/paper/1711.10275/) (2017)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [Open3D: A Modern Library for 3D Data Processing](https://mlsanity.com/paper/1801.09847/) (2018)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [On Exact Computation with an Infinitely Wide Neural Net](https://mlsanity.com/paper/1904.11955/) (2019)
- [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)
- [Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion](https://mlsanity.com/paper/2003.01456/) (2020)
- [Deep Local Shapes: Learning Local SDF Priors for Detailed 3D Reconstruction](https://mlsanity.com/paper/2003.10983/) (2020)
- [What Do Single-view 3D Reconstruction Networks Learn?](https://mlsanity.com/paper/1905.03678/) (2019)
- [Shape Completion using 3D-Encoder-Predictor CNNs and Shape Synthesis](https://mlsanity.com/paper/1612.00101/) (2016)
- [Thingi10K: A Dataset of 10,000 3D-Printing Models](https://mlsanity.com/paper/1605.04797/) (2016)
- [Graph Neural Tangent Kernel: Fusing Graph Neural Networks with Graph Kernels](https://mlsanity.com/paper/1905.13192/) (2019)
- [Neural Tangents: Fast and Easy Infinite Neural Networks in Python](https://mlsanity.com/paper/1912.02803/) (2019)
- [Deep Decoder: Concise Image Representations from Untrained Non-convolutional Networks](https://mlsanity.com/paper/1810.03982/) (2018)
- [Finite Depth and Width Corrections to the Neural Tangent Kernel](https://mlsanity.com/paper/1909.05989/) (2019)
- ["Double-DIP": Unsupervised Image Decomposition via Coupled Deep-Image-Priors](https://mlsanity.com/paper/1812.00467/) (2018)
- [Deep Geometric Prior for Surface Reconstruction](https://mlsanity.com/paper/1811.10943/) (2018)
- [High-Resolution Shape Completion Using Deep Neural Networks for Global Structure and Local Geometry Inference](https://mlsanity.com/paper/1709.07599/) (2017)
- [SG-NN: Sparse Generative Neural Networks for Self-Supervised Scene Completion of RGB-D Scans](https://mlsanity.com/paper/1912.00036/) (2019)
- [Unsupervised Learning of 3D Structure from Images](https://mlsanity.com/paper/1607.00662/) (2016)

## Built on by (most cited first, 8 of 8)

- [Neural Kernel Surface Reconstruction](https://mlsanity.com/paper/2305.19590/) (2023)
- [Fluid Simulation on Neural Flow Maps](https://mlsanity.com/paper/2312.14635/) (2023)
- [LaS-Comp: Zero-shot 3D Completion with Latent-Spatial Consistency](https://mlsanity.com/paper/2602.18735/) (2026)
- [Learning Self-Prior for Mesh Inpainting Using Self-Supervised Graph Convolutional Networks](https://mlsanity.com/paper/2305.00635/) (2023)
- [Self-supervised Shape Completion via Involution and Implicit Correspondences](https://mlsanity.com/paper/2409.15939/) (2024)
- [SR-CurvANN: Advancing 3D Surface Reconstruction through Curvature-Aware Neural Networks](https://mlsanity.com/paper/2407.17896/) (2024)
- [Self-Supervised Implicit Attention Priors for Point Cloud Reconstruction](https://mlsanity.com/paper/2511.04864/) (2025)
- [Channel Estimation by Infinite Width Convolutional Networks](https://mlsanity.com/paper/2504.08660/) (2025)

## Abstract (arXiv)

We present a novel approach for completing and reconstructing 3D shapes from incomplete scanned data by using deep neural networks. Rather than being trained on supervised completion tasks and applied on a testing shape, the network is optimized from scratch on the single testing shape, to fully adapt to the shape and complete the missing data using contextual guidance from the known regions. The ability to complete missing data by an untrained neural network is usually referred to as the deep prior. In this paper, we interpret the deep prior from a neural tangent kernel (NTK) perspective and show that the completed shape patches by the trained CNN are naturally similar to existing patches, as they are proximate in the kernel feature space induced by NTK. The interpretation allows us to design more efficient network structures and learning mechanisms for the shape completion and reconstruction task. Being more aware of structural regularities than both traditional and other unsupervised learning-based reconstruction methods, our approach completes large missing regions with plausible shapes and complements supervised learning-based methods that use database priors by requiring no extra training data set and showing flexible adaptation to a particular shape instance.