# PKSS-Align: Robust Point Cloud Registration on Pre-Kendall Shape Space

arXiv: https://arxiv.org/abs/2508.04286 · HTML: https://mlsanity.com/paper/2508.04286/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 61 references that are in the map.
- First posted on arXiv 6 Aug 2025.

## Builds on (most cited first, 22 of 22)

- [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)
- [3DMatch: Learning Local Geometric Descriptors from RGB-D Reconstructions](https://mlsanity.com/paper/1603.08182/) (2016)
- [Deep Closest Point: Learning Representations for Point Cloud Registration](https://mlsanity.com/paper/1905.03304/) (2019)
- [PointNetLK: Robust & Efficient Point Cloud Registration using PointNet](https://mlsanity.com/paper/1903.05711/) (2019)
- [Deep Global Registration](https://mlsanity.com/paper/2004.11540/) (2020)
- [Geometric Transformer for Fast and Robust Point Cloud Registration](https://mlsanity.com/paper/2202.06688/) (2022)
- [RPM-Net: Robust Point Matching using Learned Features](https://mlsanity.com/paper/2003.13479/) (2020)
- [PRNet: Self-Supervised Learning for Partial-to-Partial Registration](https://mlsanity.com/paper/1910.12240/) (2019)
- [Robust Point Cloud Registration Framework Based on Deep Graph Matching](https://mlsanity.com/paper/2103.04256/) (2021)
- [3DRegNet: A Deep Neural Network for 3D Point Registration](https://mlsanity.com/paper/1904.01701/) (2019)
- [REGTR: End-to-end Point Cloud Correspondences with Transformers](https://mlsanity.com/paper/2203.14517/) (2022)
- [3D Registration with Maximal Cliques](https://mlsanity.com/paper/2305.10854/) (2023)
- [Rotation-Invariant Transformer for Point Cloud Matching](https://mlsanity.com/paper/2303.08231/) (2023)
- [Fast and Robust Iterative Closest Point](https://mlsanity.com/paper/2007.07627/) (2020)
- [PCRNet: Point Cloud Registration Network using PointNet Encoding](https://mlsanity.com/paper/1908.07906/) (2019)
- [SC^2-PCR: A Second Order Spatial Compatibility for Efficient and Robust Point Cloud Registration](https://mlsanity.com/paper/2203.14453/) (2022)
- [Unsupervised Deep Probabilistic Approach for Partial Point Cloud Registration](https://mlsanity.com/paper/2303.13290/) (2023)
- [Extend Your Own Correspondences: Unsupervised Distant Point Cloud Registration by Progressive Distance Extension](https://mlsanity.com/paper/2403.03532/) (2024)
- [Multiway Point Cloud Mosaicking with Diffusion and Global Optimization](https://mlsanity.com/paper/2404.00429/) (2024)
- [KSS-ICP: Point Cloud Registration based on Kendall Shape Space](https://mlsanity.com/paper/2211.02807/) (2022)
- [Geodesic analysis in Kendall's shape space with epidemiological applications](https://mlsanity.com/paper/1906.11950/) (2019)

## Abstract (arXiv)

Point cloud registration is a classical topic in the field of 3D Vision and Computer Graphics. Generally, the implementation of registration is typically sensitive to similarity transformations (translation, scaling, and rotation), noisy points, and incomplete geometric structures. Especially, the non-uniform scales and defective parts of point clouds increase probability of struck local optima in registration task. In this paper, we propose a robust point cloud registration PKSS-Align that can handle various influences, including similarity transformations, non-uniform densities, random noisy points, and defective parts. The proposed method measures shape feature-based similarity between point clouds on the Pre-Kendall shape space (PKSS), textcolorblackwhich is a shape measurement-based scheme and doesn't require point-to-point or point-to-plane metric. The employed measurement can be regarded as the manifold metric that is robust to various representations in the Euclidean coordinate system. Benefited from the measurement, the transformation matrix can be directly generated for point clouds with mentioned influences at the same time. The proposed method does not require data training and complex feature encoding. Based on a simple parallel acceleration, it can achieve significant improvement for efficiency and feasibility in practice. Experiments demonstrate that our method outperforms the relevant state-of-the-art methods.