# Registration of 3D Point Sets Using Exponential-based Similarity Matrix

arXiv: https://arxiv.org/abs/2505.04540 · HTML: https://mlsanity.com/paper/2505.04540/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 49 references that are in the map.
- First posted on arXiv 7 May 2025.

## Builds on (most cited first, 18 of 18)

- [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)
- [Deep Closest Point: Learning Representations for Point Cloud Registration](https://mlsanity.com/paper/1905.03304/) (2019)
- [TEASER: Fast and Certifiable Point Cloud Registration](https://mlsanity.com/paper/2001.07715/) (2020)
- [RPM-Net: Robust Point Matching using Learned Features](https://mlsanity.com/paper/2003.13479/) (2020)
- [Go-ICP: A Globally Optimal Solution to 3D ICP Point-Set Registration](https://mlsanity.com/paper/1605.03344/) (2016)
- [PRNet: Self-Supervised Learning for Partial-to-Partial Registration](https://mlsanity.com/paper/1910.12240/) (2019)
- [DeepGMR: Learning Latent Gaussian Mixture Models for Registration](https://mlsanity.com/paper/2008.09088/) (2020)
- [A comprehensive survey on point cloud registration](https://mlsanity.com/paper/2103.02690/) (2021)
- [Fast and Robust Iterative Closest Point](https://mlsanity.com/paper/2007.07627/) (2020)
- [KISS-Matcher: Fast and Robust Point Cloud Registration Revisited](https://mlsanity.com/paper/2409.15615/) (2024)
- [KSS-ICP: Point Cloud Registration based on Kendall Shape Space](https://mlsanity.com/paper/2211.02807/) (2022)
- [DICP: Doppler Iterative Closest Point Algorithm](https://mlsanity.com/paper/2201.11944/) (2022)
- [Lidar-Monocular Visual Odometry with Genetic Algorithm for Parameter Optimization](https://mlsanity.com/paper/1903.02046/) (2019)
- [Deep Learning-Based Point Cloud Registration: A Comprehensive Survey and Taxonomy](https://mlsanity.com/paper/2404.13830/) (2024)
- [Securing a UAV Using Individual Characteristics From an EEG Signal](https://mlsanity.com/paper/1704.04574/) (2017)
- [SemICP: Semantic Non-Rigid Point Cloud Registration with Elastic Energy Regularization](https://mlsanity.com/paper/2503.00972/) (2025)

## Abstract (arXiv)

Point cloud registration is a fundamental problem in computer vision and robotics, involving the alignment of 3D point sets captured from varying viewpoints using depth sensors such as LiDAR or structured light. In modern robotic systems, especially those focused on mapping, it is essential to merge multiple views of the same environment accurately. However, state-of-the-art registration techniques often struggle when large rotational differences exist between point sets or when the data is significantly corrupted by sensor noise. These challenges can lead to misalignments and, consequently, to inaccurate or distorted 3D reconstructions. In this work, we address both these limitations by proposing a robust modification to the classic Iterative Closest Point (ICP) algorithm. Our method, termed Exponential Similarity Matrix ICP (ESM-ICP), integrates a Gaussian-inspired exponential weighting scheme to construct a similarity matrix that dynamically adapts across iterations. This matrix facilitates improved estimation of both rotational and translational components during alignment. We demonstrate the robustness of ESM-ICP in two challenging scenarios: (i) large rotational discrepancies between the source and target point clouds, and (ii) data corrupted by non-Gaussian noise. Our results show that ESM-ICP outperforms traditional geometric registration techniques as well as several recent learning-based methods. To encourage reproducibility and community engagement, our full implementation is made publicly available on GitHub. https://github.com/aralab-unr/ESM_ICP