GERA: Geometric Embedding for Efficient Point Registration Analysis

TL;DR

This work tackles real-time point cloud registration under limited computational resources by introducing GERA, a lightweight pipeline that replaces raw 3D coordinates with offline geometric encodings fed into a simple MLP. The geometric representations are built as offline, fully connected neighbor graphs, with per-point edge-length features and MMD-based analysis showing superior stability and generalization over coordinate-only inputs. The architecture concatenates geometric embeddings with coordinates and decodes a displacement field, achieving fast inference and strong accuracy on MedShapeNet organ datasets, including challenging small bowel scenarios. The results suggest that offline geometric encoding can substantially improve efficiency and robustness for registration tasks in robotics and surgical guidance, with potential extension to scene flow applications.

Abstract

Point cloud registration aims to provide estimated transformations to align point clouds, which plays a crucial role in pose estimation of various navigation systems, such as surgical guidance systems and autonomous vehicles. Despite the impressive performance of recent models on benchmark datasets, many rely on complex modules like KPConv and Transformers, which impose significant computational and memory demands. These requirements hinder their practical application, particularly in resource-constrained environments such as mobile robotics. In this paper, we propose a novel point cloud registration network that leverages a pure MLP architecture, constructing geometric information offline. This approach eliminates the computational and memory burdens associated with traditional complex feature extractors and significantly reduces inference time and resource consumption. Our method is the first to replace 3D coordinate inputs with offline-constructed geometric encoding, improving generalization and stability, as demonstrated by Maximum Mean Discrepancy (MMD) comparisons. This efficient and accurate geometric representation marks a significant advancement in point cloud analysis, particularly for applications requiring fast and reliability.

Figures (5)

• Figure 1: In robot-assisted surgery, real-time analysis and registration of target organs are required, which presents new challenges for robustness and efficiency.
• Figure 2: Perform MMD analysis on the liver dataset using a batch size of 32 for both absolute position encoding and geometric encoding
• Figure 3: The ovearll structure of GERA. The raw point cloud coordinate information is processed by an offline geometric constructor, resulting in encoded geometric information. This encoded data is passed through an MLP-based encoder, extracting $\mathcal{F}^{\mathit{geo}}_{\mathbf{P}_\mathcal{S}}$ and $\mathcal{F}^{\mathit{geo}}_{\mathbf{P}_\mathcal{T}}$. Subsequently, the original coordinates are concatenated with the geometric information, yielding a fully populated feature map $\mathcal{F}_\mathbf{full}^{\mathit{geo}} \in \mathbb{R}^{d \times n}$. Finally, the $\mathcal{F}_\mathbf{full}^{\mathit{geo}}$ is fed into a decoder, to obtain the displacement matrix.
• Figure 4: The qualitative registration results on the dataset where the two point sets exhibit pure deformation. The blue and red point sets represent the source and target point clouds, respectively. For both Case 1 and Case 2, the maximum noise magnitude is 2 mm, and the deformation magnitude is 18 mm.
• Figure 5: The qualitative registration results on the dataset show that the two point sets exhibit pure deformation. The red and blue point sets represent the source and target point clouds, respectively. The deformation magnitude is 114.19 mm. On the right side of the figure, four randomly selected samples from the small intestine dataset are displayed, with yellow boxes marking breakpoints and noise locations.