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

TL;DR

This work tackles robust fine rigid pairwise 3D point cloud registration in the presence of density differences, noise, holes, and partial overlap, where Euclidean-distance-based methods struggle due to non-commutativity. It introduces Iterative Differential Entropy Minimization (IDEM), a differential-entropy-based objective that defines $q_{tot}$ from neighborhood entropies, yielding commutativity and a clear minimum at alignment. IDEM shows superior robustness across diverse scenarios and is analyzed via a ROI around peak regions, with a sensitivity study confirming stability under noise. The approach offers a principled alternative to RMSE, Chamfer, and Hausdorff metrics and can serve as the core criterion for iterative fine registration, with potential integration into learning-based pipelines.

Abstract

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.

Figures (18)

• Figure 1: Demonstration that the calculation of the Euclidean distance between two point clouds is not commutative.
• Figure 2: 2D representation of the identification of the neighborhood $\rho$, radius $r$, and the set $p_k$.
• Figure 3: Point cloud ($B_0$) used as an example for the experiments.
• Figure 4: Behavior of $q_{tot}$ (translation along the X-axis) as the parameter $a$ varies.
• Figure 5: Behavior of $q_{tot}$ (rotation around the centroids Z-axis) as the parameter $a$ varies.