- Global Registration of Multiple 3D Point Sets via Optimization-on-a-Manifold
- Shankar Krishnan, Pei Lee, John Moore, and Suresh Venkatasubramanian
- Symposium on Geometry Processing pp. 187-196, 2005.
PDF (662K)
- Abstract
We propose a novel algorithm to register multiple 3D point sets within a
common reference frame using an manifold optimization approach. The
point sets are obtained with multiple laser scanners or a mobile
scanner. Unlike most prior algorithms, our approach performs an explicit
optimization on the manifold of rotations, allowing us to formulate the
registration problem as an unconstrained minimization on a
constrained manifold. This approach exploits the Lie group
structure of SO_3 and the simple representation of its associated Lie
algebra so_3 in terms of R^3.
Our contributions are threefold. We present a new analytic method based
on singular value decompositions that yields a closed-form solution for
simultaneous multiview registration in the noise-free
scenario. Secondly, we use this method to derive a good initial estimate
of a solution in the noise-free case. This initialization step may be of
use in any general iterative scheme. Finally, we present an iterative
scheme based on Newton's method on SO_3 that has locally quadratic
convergence. We demonstrate the efficacy on our scheme on scan data
taken both from the Digital Michelangelo project and from scans
extracted from models, and compare it to some of the other well known
schemes for multiview registration. In all cases, our algorithm
converges much faster than the other approaches, (in some cases orders
of magnitude faster), and generates consistently higher quality
registrations.
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