A New Outlier Removal Strategy Based on Reliability of Correspondence Graph for Fast Point Cloud Registration

TL;DR

An intuitive method is used to describe the 6-DOF (degree of freedom) curtailment process in point cloud registration and an outlier removal strategy is proposed based on the reliability of the correspondence graph to obtain the global maximum consensus set.

Abstract

Registration is a basic yet crucial task in point cloud processing. In correspondence-based point cloud registration, matching correspondences by point feature techniques may lead to an extremely high outlier ratio. Current methods still suffer from low efficiency, accuracy, and recall rate. We use a simple and intuitive method to describe the 6-DOF (degree of freedom) curtailment process in point cloud registration and propose an outlier removal strategy based on the reliability of the correspondence graph. The method constructs the corresponding graph according to the given correspondences and designs the concept of the reliability degree of the graph node for optimal candidate selection and the reliability degree of the graph edge to obtain the global maximum consensus set. The presented method could achieve fast and accurate outliers removal along with gradual aligning parameters estimation. Extensive experiments on simulations and challenging real-world datasets demonstrate that the proposed method can still perform effective point cloud registration even the correspondence outlier ratio is over 99%, and the efficiency is better than the state-of-the-art. Code is available at https://github.com/WPC-WHU/GROR.

Figures (10)

• Figure 1: The process of three correspondences alignment.
• Figure 2: An example for computing the node reliability metric. (a) Ten correspondences for example, (b) undirected complete graph, (c) compact graph, and (d) adjacency matrix and degree of nodes.
• Figure 3: Two point pairs (correspondences) aligning process based on the correspondence graph. (a) Before aligning, and (b) after aligning.
• Figure 4: An example to explain that the constraint$\left\| \mathcal{E}_{ij}^{\mathcal{P}} \right\|=\left\| \mathcal{E}_{ij}^{Q} \right\|$ does not completely remove outliers. The orange and pink points in the figure represent inliers, and the black points represent outliers. All correspondence satisfies the constraint: $\left\| \vec{\mathcal{E}}_{_{ik}}^{\mathcal{P}} \right\|=\left\| \vec{\mathcal{E}}_{_{ik}}^{\mathcal{Q}} \right\|$ between the edges, but the outliers cannot satisfy the constraint: $\left| Pr{{j}_{\vec{\mathcal{E}}_{ij}^{\mathcal{P}}}}\vec{\mathcal{E}}_{ik}^{\mathcal{P}} \right|=\left| Pr{{j}_{\vec{\mathcal{E}}_{ij}^{\mathcal{Q}}}}\vec{\mathcal{E}}_{ik}^{\mathcal{Q}} \right|$.
• Figure 5: Calculation method of $\theta$. (a) Rotate the vector $\vec{\mathcal{E}}_{ij}^{\mathcal{P}\mathcal{Q}}$ to the Z-axis direction, and the correspondence to be aligned is $\left( \mathbf{p}_{k}^{z},\mathbf{q}_{k}^{z} \right)$, (b) calculate the angle interval that aligns $\left( \mathbf{p}_{k}^{z},\mathbf{q}_{k}^{z} \right)$, ${{d}_{k}}=\left| \mathbf{q}_{k}^{z}(3)-\mathbf{p}_{k}^{z}(3) \right|$,${{\delta }_{xy}}=\sqrt{{{\delta }^{2}}-d_{k}^{2}}$, and (c) the top view of (b), $\Omega =azi(\mathbf{p}_{k}^{z})-azi(\mathbf{q}_{k}^{z})$, $azi(\cdot )$is the coordinate azimuth, $\gamma =\arccos (\left\| \mathbf{q}_{k}^{z} \right\|_{xy}^{2}+\left\| \mathbf{p}_{k}^{z} \right\|_{xy}^{2}-{{\delta }_{xy}})/2{{\left\| \mathbf{q}_{k}^{z} \right\|}_{xy}}{{\left\| \mathbf{p}_{k}^{z} \right\|}_{xy}}$,${{\alpha }_{k}}=\Omega -\gamma$,${{\beta }_{k}}=\Omega +\gamma$.