4-points congruent sets for robust pairwise surface registration

Abstract

We introduce 4PCS, a fast and robust alignment scheme for 3D point sets that uses wide bases, which are known to be resilient to noise and outliers. The algorithm allows registering raw noisy data, possibly contaminated with outliers, without pre-filtering or denoising the data. Further, the method significantly reduces the number of trials required to establish a reliable registration between the underlying surfaces in the presence of noise, without any assumptions about starting alignment. Our method is based on a novel technique to extract all coplanar 4-points sets from a 3D point set that are approximately congruent, under rigid transformation, to a given set of coplanar 4-points. This extraction procedure runs in roughly O(n 2 + k) time, where n is the number of candidate points and k is the number of reported 4-points sets. In practice, when noise level is low and there is sufficient overlap, using local descriptors the time complexity reduces to O(n + k). We also propose an extension to handle similarity and affine transforms. Our technique achieves an order of magnitude asymptotic acceleration compared to common randomized alignment techniques. We demonstrate the robustness of our algorithm on several sets of multiple range scans with varying degree of noise, outliers, and extent of overlap.

Landmark-free posture invariant human shape correspondence

“…Approaches that solve the correspondence problem by aligning two shapes using a transformation that is approximately rigid [1,16,24] are not suitable to align a set of human shapes in varying posture due to nonrigid shape and posture changes. Hence, we focus our attention on approaches that take nonrigid transformations into account.…”

A new robust markerless method for automatic image-to-patient registration in image-guided neurosurgery system

“…The TREs show that the method was accurate enough for IGNS. Again, two examples ( Figure 6(e)) show that the previously described 4PCS method [3,16] was not robust for facial registration.…”

“…As shown in Figure 4, the registration accuracy was stable across different downsampling resolutions and different support radii. Furthermore, the proposed method was compared with another coarse registration method: 4-point congruent sets (4PCS) [16] used in [3] for spatial registration in IGNS, which was a heuristic method with certain contingency. More concretely, the method was compared with the original 4PCS algorithm [16], whose source code was publicly available.…”

“…Furthermore, the proposed method was compared with another coarse registration method: 4-point congruent sets (4PCS) [16] used in [3] for spatial registration in IGNS, which was a heuristic method with certain contingency. More concretely, the method was compared with the original 4PCS algorithm [16], whose source code was publicly available. The 4PCS method could not always return acceptable coarse registrations between a facial region and the whole head.…”

Variations of the soft tissue thicknesses external to the ribs in Pectus Excavatum patients

“…In order to evaluate the SCIA and VOI, these two meshes were first aligned using an affine surface registration method [14]. This method determines the translations and/ or rotations in the 3D space that best align each other.…”