Multiview registration via graph diffusion of dual quaternions

Abstract

Surface registration is a fundamental step in the reconstruction of three-dimensional objects. While there are several fast and reliable methods to align two surfaces, the tools available to align multiple surfaces are relatively limited. In this paper we propose a novel multiview registration algorithm that projects several pairwise alignments onto a common reference frame. The projection is performed by representing the motions as dual quaternions, an algebraic structure that is related to the group of 3D rigid transformations, and by performing a diffusion along the graph of adjacent (i.e., pairwise alignable) views. The approach allows for a completely generic topology with which the pairwise motions are diffused. An extensive set of experiments shows that the proposed approach is both orders of magnitude faster than the state of the art, and more robust to extreme positional noise and outliers. The dramatic speedup of the approach allows it to be alternated with pairwise alignment resulting in a smoother energy profile, reducing the risk of getting stuck at local minima.

Dynamic Optimal Path Selection for 3D Triangulation with Multiple Cameras

“…Triangulation error is evaluated while perturbing the graph edges (left col.) and observations (right col.) for grid, hemisphere and line graph topologies (top to bottom). similar behaviour can be observed for [12] varying the network graph error σ r . Since [12] can only diffuse errors without discarding any edge, it suffers from large relative motion displacements that may happen during graph calibration.…”

“…4) we compared the reconstruction accuracy of our approach against "dual-quaternions" [12] and "SBA" [13]. The first method exploits properties of dual-quaternions to diffuse the camera network error and creates a new set of coherent motions to a common reference frame.…”

“…All the tests were performed by reconstructing a structure of 10 points. For [12], we considered the best triangulation in terms of re-projection error between all the graph paths with less than 3 vertices whereas, for [13], all the structure points were optimized at the same time. We can observe that SBA, even if it has the advantage of recomputing the camera poses while triangulating, mostly suffers from the observation errors.…”

“…4. Comparison between our method, dual-quaternions [12] and SBA [13]. Triangulation error is evaluated while perturbing the graph edges (left col.) and observations (right col.) for grid, hemisphere and line graph topologies (top to bottom).…”

“…Classic approaches use artificial targets with known geometry [10] to compute intrinsic parameters and simultaneously assess the relative pose of each camera [11]. Other methods perform pairwise calibrations that can be subsequently made consistent with respect to a reference world [12]. It is also very common to exploit the scene itself to obtain simultaneous extrinsic calibration ad structure reconstruction [13].…”