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

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