# ESCAPE: Equivariant Shape Completion via Anchor Point Encoding

arXiv: https://arxiv.org/abs/2412.00952 · HTML: https://mlsanity.com/paper/2412.00952/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 56 references that are in the map.
- First posted on arXiv 1 Dec 2024.

## Builds on (most cited first, 30 of 36)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [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)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [VoxelNet: End-to-End Learning for Point Cloud Based 3D Object Detection](https://mlsanity.com/paper/1711.06396/) (2017)
- [Perceiver: General Perception with Iterative Attention](https://mlsanity.com/paper/2103.03206/) (2021)
- [PV-RCNN: Point-Voxel Feature Set Abstraction for 3D Object Detection](https://mlsanity.com/paper/1912.13192/) (2019)
- [PointCNN: Convolution On X-Transformed Points](https://mlsanity.com/paper/1801.07791/) (2018)
- [3D Semantic Segmentation with Submanifold Sparse Convolutional Networks](https://mlsanity.com/paper/1711.10275/) (2017)
- [PCT: Point cloud transformer](https://mlsanity.com/paper/2012.09688/) (2020)
- [PCN: Point Completion Network](https://mlsanity.com/paper/1808.00671/) (2018)
- [OmniObject3D: Large-Vocabulary 3D Object Dataset for Realistic Perception, Reconstruction and Generation](https://mlsanity.com/paper/2301.07525/) (2023)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [PoinTr: Diverse Point Cloud Completion with Geometry-Aware Transformers](https://mlsanity.com/paper/2108.08839/) (2021)
- [RPM-Net: Robust Point Matching using Learned Features](https://mlsanity.com/paper/2003.13479/) (2020)
- [SnowflakeNet: Point Cloud Completion by Snowflake Point Deconvolution with Skip-Transformer](https://mlsanity.com/paper/2108.04444/) (2021)
- [SpinNet: Learning a General Surface Descriptor for 3D Point Cloud Registration](https://mlsanity.com/paper/2011.12149/) (2020)
- [PPF-FoldNet: Unsupervised Learning of Rotation Invariant 3D Local Descriptors](https://mlsanity.com/paper/1808.10322/) (2018)
- [Robust Point Cloud Registration Framework Based on Deep Graph Matching](https://mlsanity.com/paper/2103.04256/) (2021)
- [SeedFormer: Patch Seeds based Point Cloud Completion with Upsample Transformer](https://mlsanity.com/paper/2207.10315/) (2022)
- [Rotation Invariant Convolutions for 3D Point Clouds Deep Learning](https://mlsanity.com/paper/1908.06297/) (2019)
- [Rotation-Invariant Transformer for Point Cloud Matching](https://mlsanity.com/paper/2303.08231/) (2023)
- [AdaPoinTr: Diverse Point Cloud Completion with Adaptive Geometry-Aware Transformers](https://mlsanity.com/paper/2301.04545/) (2023)
- [LatticeNet: Fast Point Cloud Segmentation Using Permutohedral Lattices](https://mlsanity.com/paper/1912.05905/) (2019)
- [Rotational Projection Statistics for 3D Local Surface Description and Object Recognition](https://mlsanity.com/paper/1304.3192/) (2013)
- [ConDor: Self-Supervised Canonicalization of 3D Pose for Partial Shapes](https://mlsanity.com/paper/2201.07788/) (2022)
- [Skeleton Merger: an Unsupervised Aligned Keypoint Detector](https://mlsanity.com/paper/2103.10814/) (2021)
- [RIGA: Rotation-Invariant and Globally-Aware Descriptors for Point Cloud Registration](https://mlsanity.com/paper/2209.13252/) (2022)

## Built on by (most cited first, 4 of 4)

- [Learning Generalizable Shape Completion with SIM(3) Equivariance](https://mlsanity.com/paper/2509.26631/) (2025)
- [Repurposing 2D Diffusion Models for 3D Shape Completion](https://mlsanity.com/paper/2512.13991/) (2025)
- [Wave-Former: Through-Occlusion 3D Reconstruction via Wireless Shape Completion](https://mlsanity.com/paper/2511.14152/) (2025)
- [REVNET: Rotation-Equivariant Point Cloud Completion via Vector Neuron Anchor Transformer](https://mlsanity.com/paper/2601.08558/) (2026)

## Abstract (arXiv)

Shape completion, a crucial task in 3D computer vision, involves predicting and filling the missing regions of scanned or partially observed objects. Current methods expect known pose or canonical coordinates and do not perform well under varying rotations, limiting their real-world applicability. We introduce ESCAPE (Equivariant Shape Completion via Anchor Point Encoding), a novel framework designed to achieve rotation-equivariant shape completion. Our approach employs a distinctive encoding strategy by selecting anchor points from a shape and representing all points as a distance to all anchor points. This enables the model to capture a consistent, rotation-equivariant understanding of the object's geometry. ESCAPE leverages a transformer architecture to encode and decode the distance transformations, ensuring that generated shape completions remain accurate and equivariant under rotational transformations. Subsequently, we perform optimization to calculate the predicted shapes from the encodings. Experimental evaluations demonstrate that ESCAPE achieves robust, high-quality reconstructions across arbitrary rotations and translations, showcasing its effectiveness in real-world applications without additional pose estimation modules.