![](bg9.png)
faces, a largely global transformation between them,
local deformation on the entire surface as well as sen-
sor noise (around the hand area). Figure. 8(c) shows
the source surface before and after deformation and il-
lustrates that our method overcomes all the challenges
of this data to deform correctly the source surface to-
ward the target surface. Final alignment between the
deformed surface and the target surface is shown in
Figure. 8(d).
5 CONCLUSIONS
We have presented an efficient non-rigid registra-
tion algorithm to align two partially overlapping sur-
faces. Contrarily to other algorithms which nor-
mally require prior knowledge to obtain final align-
ment, our method is implemented automatically with-
out any user-intervention for constraining the defor-
mation and without making other assumptions. To
achieve this, the algorithm is divided into two phases.
While the first phase provides initial correspondences
to constrain the optimization, the strategy of the sec-
ond phase is performed in two steps in which the first
step aims to move the source surface close to the tar-
get surface and the second step forces the two surfaces
to coincide accurately. The experimental results prove
that our algorithm can be applied to data sets where
the deformation between the two surfaces is severe
and prior knowledge is not available.
We are also aware of some limitations of our al-
gorithm. Currently, all initial correspondences are
treated equally in phase 1 without considering how
accurate they are. We need to consider the contri-
bution of each correspondence by using contribution
weights before using it in phase 2. This change may
increase convergence speed of the optimization pro-
cess in phase 2. Another limitation is related to the
deformation model. Because this model determines
the influence area of affine transformations based on
Euclidean distance, this property can create strange
deformations when two nodes are close with respect
to Euclidean distance but far away with respect to
geodesic distance (two nodes of two close fingers, for
example). This limitation should be considered in fu-
ture work. Once these limitations are resolved, we
plan to develop the algorithm so it can be applied for
global registration including several surfaces in order
to reconstruct a completely deformable object.
ACKNOWLEDGEMENTS
We are grateful to Myronenko et al for providing
the CPD implementation and the GRAIL laboratory-
University of Washington for providing the 3D
data. This research was supported by the NSERC-
Creaform Industrial Research Chair on 3D Scanning.
REFERENCES
Allen, B., Curless, B., and Popovi
´
c, Z. (2002). Articulated
body deformation from range scan data. ACM Trans.
Graph., 21(3):612–619.
Allen, B., Curless, B., and Popovi
´
c, Z. (2003). The space
of human body shapes: reconstruction and param-
eterization from range scans. ACM Trans. Graph.,
22(3):587–594.
Amberg, B., Romdhani, S., and Vetter, T. (2007). Optimal
step nonrigid icp algorithms for surface registration.
In Computer Vision and Pattern Recognition, 2007.
CVPR ’07. IEEE Conference on, pages 1–8.
Anguelov, D., Srinivasan, P., Pang, H.-C., Koller, D., Thrun,
S., and Davis, J. (2004). The correlated correspon-
dence algorithm for unsupervised registration of non-
rigid surfaces. In NIPS’04, pages –1–1.
Besl, P. and McKay, N. D. (1992). A method for regis-
tration of 3-d shapes. Pattern Analysis and Machine
Intelligence, IEEE Transactions on, 14(2):239–256.
Brown, B. J. and Rusinkiewicz, S. (2007). Global non-rigid
alignment of 3-d scans. ACM Trans. Graph., 26(3).
Chang, W. and Zwicker, M. (2008). Automatic registration
for articulated shapes. In Proceedings of the Sympo-
sium on Geometry Processing, SGP ’08, pages 1459–
1468, Aire-la-Ville, Switzerland, Switzerland. Euro-
graphics Association.
Chen, Y. and Medioni, G. (1991). Object modeling by reg-
istration of multiple range images. In Robotics and
Automation, 1991. Proceedings., 1991 IEEE Interna-
tional Conference on, pages 2724–2729 vol.3.
Chui, H. and Rangarajan, A. (2003). A new point match-
ing algorithm for non-rigid registration. Comput. Vis.
Image Underst., 89(2-3):114–141.
DeVore, J. (2008). Probability and Statistics for Engineer-
ing and the Sciences: Enhanced [With Glossary of
Symbols Booklet]. Available 2010 Titles Enhanced
Web Assign Series. Brooks/Cole, Cengage Learning.
Frome, A., Huber, D., Kolluri, R., Blow, T., and Malik, J.
(2004). Recognizing objects in range data using re-
gional point descriptors. In EUROPEAN CONFER-
ENCE ON COMPUTER VISION, pages 224–237.
Huang, Q.-X., Adams, B., Wicke, M., and Guibas, L. J.
(2008). Non-rigid registration under isometric defor-
mations. In Proceedings of the Symposium on Geom-
etry Processing, SGP ’08, pages 1449–1457, Aire-la-
Ville, Switzerland, Switzerland. Eurographics Associ-
ation.
Jian, B. and Vemuri, B. C. (2011). Robust point set regis-
tration using gaussian mixture models. IEEE Trans.
Pattern Anal. Mach. Intell., 33(8):1633–1645.
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