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

2025-05-07

AI Summary

To address the insufficient robustness of 3D point cloud registration under large rotational discrepancies and non-Gaussian noise, this paper proposes Exponential Similarity Matrix-driven ICP (ESM-ICP). Within the conventional ICP framework, ESM-ICP introduces a Gaussian-kernel-inspired exponential adaptive similarity matrix that dynamically weights point correspondences and jointly optimizes rotation and translation parameters—without requiring learned priors or supervision. Theoretical analysis, grounded in matrix exponentials and geometric optimization, guarantees convergence stability. Experiments demonstrate that ESM-ICP significantly outperforms classical ICP and multiple state-of-the-art learning-based methods under large-angle rotations and heavy outlier corruption, achieving substantial improvements in accuracy, robustness, and generalization. The source code is publicly available.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Learning with Manifolds
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

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

Problem

• Aligning 3D point sets with large rotational differences
• Improving registration accuracy under significant sensor noise
• Enhancing robustness in point cloud registration algorithms

Innovation

• Exponential Similarity Matrix ICP (ESM-ICP) for robust registration
• Gaussian-inspired exponential weighting scheme for dynamic adaptation
• Improved alignment of rotational and translational components