# Cloud Sphere: A 3D Shape Representation via Progressive Deformation

arXiv: https://arxiv.org/abs/2112.11133 · HTML: https://mlsanity.com/paper/2112.11133/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 36 references that are in the map.
- First posted on arXiv 21 Dec 2021.

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

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [PointDAN: A Multi-Scale 3D Domain Adaption Network for Point Cloud Representation](https://mlsanity.com/paper/1911.02744/) (2019)
- [Point2Sequence: Learning the Shape Representation of 3D Point Clouds with an Attention-based Sequence to Sequence Network](https://mlsanity.com/paper/1811.02565/) (2018)
- [Multiresolution Tree Networks for 3D Point Cloud Processing](https://mlsanity.com/paper/1807.03520/) (2018)
- [SyncSpecCNN: Synchronized Spectral CNN for 3D Shape Segmentation](https://mlsanity.com/paper/1612.00606/) (2016)
- [3D Shape Segmentation with Projective Convolutional Networks](https://mlsanity.com/paper/1612.02808/) (2016)
- [3DN: 3D Deformation Network](https://mlsanity.com/paper/1903.03322/) (2019)
- [VoxSegNet: Volumetric CNNs for Semantic Part Segmentation of 3D Shapes](https://mlsanity.com/paper/1809.00226/) (2018)
- [SurfNet: Generating 3D shape surfaces using deep residual networks](https://mlsanity.com/paper/1703.04079/) (2017)
- [ShapeFlow: Learnable Deformations Among 3D Shapes](https://mlsanity.com/paper/2006.07982/) (2020)
- [A Survey on Deep Geometry Learning: From a Representation Perspective](https://mlsanity.com/paper/2002.07995/) (2020)

## Abstract (arXiv)

In the area of 3D shape analysis, the geometric properties of a shape have long been studied. Instead of directly extracting representative features using expert-designed descriptors or end-to-end deep neural networks, this paper is dedicated to discovering distinctive information from the shape formation process. Concretely, a spherical point cloud served as the template is progressively deformed to fit the target shape in a coarse-to-fine manner. During the shape formation process, several checkpoints are inserted to facilitate recording and investigating the intermediate stages. For each stage, the offset field is evaluated as a stage-aware description. The summation of the offsets throughout the shape formation process can completely define the target shape in terms of geometry. In this perspective, one can derive the point-wise shape correspondence from the template inexpensively, which benefits various graphic applications. In this paper, the Progressive Deformation-based Auto-Encoder (PDAE) is proposed to learn the stage-aware description through a coarse-to-fine shape fitting task. Experimental results show that the proposed PDAE has the ability to reconstruct 3D shapes with high fidelity, and consistent topology is preserved in the multi-stage deformation process. Additional applications based on the stage-aware description are performed, demonstrating its universality.