Gianfranco Doretto / Research / Project
3D Object Modeling
Euclidean and affine registration in the frequency domain
Description
We study the problem of aligning 3D range data in the frequency domain. We
derive a technique that gives robust estimates of the motion parameters and
that can be used as initialization for more accurate space domain alignment
techniques like ICP.
Three-dimensional models of rigid objects, built by aligning sets of
range data containing partially overlapping patches of surface,
traditionally use optimization techniques, like ICP, to perform the
registration of the data. While these techniques provide great
accuracy of the estimate, their convergence to the global minimum is
not guaranteed unless the optimization is well initialized. This
motivates the need to have tools to robustly initialize these
optimization techniques.
If we consider the alignment problem in the frequency domain, it is
possible to decouple the estimation of the rotation from the
estimation of the translation. This leads to an efficient algorithm
that robustly converges to the solution of the alignment problem. When
accuracy is the main concern (e.g. in industrial prototyping), the
estimate can subsequently be refined by spatial domain optimization
techniques like ICP.
The main contributions of our approach are:
- A new frequency domain technique to perform 3D range data registration that incorporates the estimation of the scaling factor.
- A range data registration technique that converges robustly to the global solution, and that can be used as initialization to other spatial domain alignment techniques, like ICP, for a more accurate registration.
- A frequency domain framework that can be extended to perform estimation of affine 3D motion, and to include texture information to further improve robustness.
Results
Range data of a Moai statue
This example depicts the range data of a Moai statue in its
"normal" position on the left. On the right, the range data
are rotated according to the following angles (54.0, 112.5, 26.5)
degrees, translated according to a translation vector of (2, -5, -10)
voxels, and scaled by a factor of 0.72. The alignment algorithm
returns the following estimate: rotation (53.2, 113.5, 26.5) degrees,
translation (2, -5, -10) voxels, scaling 0.71997. This estimate could
be used to initialize the ICP algorithm to rapidly refine the
registration.
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Related publications
- Cortelazzo, G. M., Doretto, G., and Lucchese, L.
Free-form textured surfaces registration by a frequency domaintechnique. In Proceedings of IEEE International Conference on Image Processing, pp. 813–817, Chicago, IL, USA, October 1998.
Details BibTeX PDF (270.5kB ) - Lucchese, L., Doretto, G., and Cortelazzo, G. M.
A frequency domain technique for range data registration. IEEE Transactions on Pattern Analysis and Machine Intelligence, 24(11):1468–1484, November 2002.
Details BibTeX PDF (3.3MB )