Fig. 5

The proposed registration pipeline. Given two point clouds \(\mathcal {P}\) and \(\mathcal {Q}\), dense features are extracted on each point cloud, denoted by \(h(\mathcal {P})\) and \(g(\mathcal {Q})\). Assuming that the feature extraction function is SE(3)-invariant, the relation \(h({\textbf {p}}) = g(D_0({\textbf {q}}))\) holds for any pair of corresponding points \({\textbf {p}}\in \mathcal {P}\) and \({\textbf {q}}\in \mathcal {Q}\), where \(D_0\in SE(3)\) is the underlying, unknown transformation between the point clouds. Then L putative point correspondences are obtained using \(\ell _2\) distances between the extracted features, denoted by \(\{{\textbf {p}}_i\}_{i=1}^L\) and \(\{{\textbf {q}}_i\}_{i=1}^L\). The point clouds, extracted features, and putative matches are used as input for the RTUME hypothesis generation module described in Sect. 3.1.3, resulting in a set of hypothesized transformation estimates \(\mathcal {T} = \{\hat{D}_i\}_{i=1}^L\). Finally, \(\mathcal {T}\), the extracted features, point clouds, and putative matches, are used in the multiple consensus hypotheses evaluation to select the best hypothesis, and an estimate of the success probability of the registration procedure, as described in Sect. 3.2