# Curvy: A Parametric Cross-section based Surface Reconstruction

arXiv: https://arxiv.org/abs/2409.00829 · HTML: https://mlsanity.com/paper/2409.00829/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 37 references that are in the map.
- First posted on arXiv 1 Sep 2024.

## Builds on (most cited first, 17 of 17)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [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)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [Shape As Points: A Differentiable Poisson Solver](https://mlsanity.com/paper/2106.03452/) (2021)
- [Learning Efficient Point Cloud Generation for Dense 3D Object Reconstruction](https://mlsanity.com/paper/1706.07036/) (2017)
- [Towards Deeper Graph Neural Networks with Differentiable Group Normalization](https://mlsanity.com/paper/2006.06972/) (2020)
- [Point Cloud Completion by Skip-attention Network with Hierarchical Folding](https://mlsanity.com/paper/2005.03871/) (2020)
- [Multi-Angle Point Cloud-VAE: Unsupervised Feature Learning for 3D Point Clouds from Multiple Angles by Joint Self-Reconstruction and Half-to-Half Prediction](https://mlsanity.com/paper/1907.12704/) (2019)
- [RL-GAN-Net: A Reinforcement Learning Agent Controlled GAN Network for Real-Time Point Cloud Shape Completion](https://mlsanity.com/paper/1904.12304/) (2019)
- [Topology-Aware Surface Reconstruction for Point Clouds](https://mlsanity.com/paper/1811.12543/) (2018)

## Abstract (arXiv)

In this work, we present a novel approach for reconstructing shape point clouds using planar sparse cross-sections with the help of generative modeling. We present unique challenges pertaining to the representation and reconstruction in this problem setting. Most methods in the classical literature lack the ability to generalize based on object class and employ complex mathematical machinery to reconstruct reliable surfaces. We present a simple learnable approach to generate a large number of points from a small number of input cross-sections over a large dataset. We use a compact parametric polyline representation using adaptive splitting to represent the cross-sections and perform learning using a Graph Neural Network to reconstruct the underlying shape in an adaptive manner reducing the dependence on the number of cross-sections provided.