# Iterative Differential Entropy Minimization (IDEM) method for fine rigid pairwise 3D Point Cloud Registration: A Focus on the Metric

arXiv: https://arxiv.org/abs/2601.09601 · HTML: https://mlsanity.com/paper/2601.09601/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 63 references that are in the map.
- First posted on arXiv 14 Jan 2026.

## Builds on (most cited first, 12 of 12)

- [Geometric Transformer for Fast and Robust Point Cloud Registration](https://mlsanity.com/paper/2202.06688/) (2022)
- [D3Feat: Joint Learning of Dense Detection and Description of 3D Local Features](https://mlsanity.com/paper/2003.03164/) (2020)
- [Go-ICP: A Globally Optimal Solution to 3D ICP Point-Set Registration](https://mlsanity.com/paper/1605.03344/) (2016)
- [KISS-ICP: In Defense of Point-to-Point ICP -- Simple, Accurate, and Robust Registration If Done the Right Way](https://mlsanity.com/paper/2209.15397/) (2022)
- [Robust Point Cloud Registration Framework Based on Deep Graph Matching](https://mlsanity.com/paper/2103.04256/) (2021)
- [DeepICP: An End-to-End Deep Neural Network for 3D Point Cloud Registration](https://mlsanity.com/paper/1905.04153/) (2019)
- [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)
- [SC^2-PCR: A Second Order Spatial Compatibility for Efficient and Robust Point Cloud Registration](https://mlsanity.com/paper/2203.14453/) (2022)
- [Iterative Global Similarity Points : A robust coarse-to-fine integration solution for pairwise 3D point cloud registration](https://mlsanity.com/paper/1808.03899/) (2018)
- [CorAl -- Are the point clouds Correctly Aligned?](https://mlsanity.com/paper/2109.09820/) (2021)
- [PointDifformer: Robust Point Cloud Registration With Neural Diffusion and Transformer](https://mlsanity.com/paper/2404.14034/) (2024)

## Abstract (arXiv)

Point cloud registration is a central theme in computer vision, with alignment algorithms continuously improving for greater robustness. Commonly used methods evaluate Euclidean distances between point clouds and minimize an objective function, such as Root Mean Square Error (RMSE). However, these approaches are most effective when the point clouds are well-prealigned and issues such as differences in density, noise, holes, and limited overlap can compromise the results. Traditional methods, such as Iterative Closest Point (ICP), require choosing one point cloud as fixed, since Euclidean distances lack commutativity. When only one point cloud has issues, adjustments can be made, but in real scenarios, both point clouds may be affected, often necessitating preprocessing. The authors introduce a novel differential entropy-based metric, designed to serve as the objective function within an optimization framework for fine rigid pairwise 3D point cloud registration, denoted as Iterative Differential Entropy Minimization (IDEM). This metric does not depend on the choice of a fixed point cloud and, during transformations, reveals a clear minimum corresponding to the best alignment. Multiple case studies are conducted, and the results are compared with those obtained using RMSE, Chamfer distance, and Hausdorff distance. The proposed metric proves effective even with density differences, noise, holes, and partial overlap, where RMSE does not always yield optimal alignment.