3D Curves Reconstruction Based on Deformable Models

by: Catalina Sbert, Andreas F Solé

Journal of Mathematical Imaging and Vision, Vol. 18, No. 3. (21 May 2003), pp. 211-223.

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Abstract

We present a new method, based on curve evolution, for the reconstruction of a 3D curve from two different projections. It is based on the minimization of an energy functional. Following the work on geodesic active contours by Caselles et al. (in Int. Conf. on Pattern Recognition, 1996, Vol. 43, pp. 693–737), we then transform the problem of minimizing the functional into a problem of geodesic computation in a Riemann space. The Euler-Lagrange equation of this new functional is derived and its associated PDE is solved using the level set formulation, giving the existence and uniqueness results. We apply the model to the reconstruction of a vessel from a biplane angiography.

@article{citeulike:2946180, abstract = {We present a new method, based on curve evolution, for the reconstruction of a 3D curve from two different projections. It is based on the minimization of an energy functional. Following the work on geodesic active contours by Caselles et al. (in Int. Conf. on Pattern Recognition, 1996, Vol. 43, pp. 693–737), we then transform the problem of minimizing the functional into a problem of geodesic computation in a Riemann space. The Euler-Lagrange equation of this new functional is derived and its associated PDE is solved using the level set formulation, giving the existence and uniqueness results. We apply the model to the reconstruction of a vessel from a biplane angiography.}, author = {Sbert, Catalina and Sol\'{e}, Andreas F. }, citeulike-article-id = {2946180}, doi = {10.1023/A:1022821409482}, journal = {Journal of Mathematical Imaging and Vision}, keywords = {mathematics}, month = {May}, number = {3}, pages = {211--223}, posted-at = {2008-07-01 02:12:20}, priority = {0}, title = {3D Curves Reconstruction Based on Deformable Models}, url = {http://dx.doi.org/10.1023/A:1022821409482}, volume = {18}, year = {2003} }

RIS record

TY - JOUR ID - citeulike:2946180 L3 - citeulike-article-id:2946180 TI - 3D Curves Reconstruction Based on Deformable Models JF - Journal of Mathematical Imaging and Vision VL - 18 IS - 3 SP - 211 EP - 223 N2 - We present a new method, based on curve evolution, for the reconstruction of a 3D curve from two different projections. It is based on the minimization of an energy functional. Following the work on geodesic active contours by Caselles et al. (in Int. Conf. on Pattern Recognition, 1996, Vol. 43, pp. 693–737), we then transform the problem of minimizing the functional into a problem of geodesic computation in a Riemann space. The Euler-Lagrange equation of this new functional is derived and its associated PDE is solved using the level set formulation, giving the existence and uniqueness results. We apply the model to the reconstruction of a vessel from a biplane angiography. KW - mathematics AU - Sbert, Catalina AU - Solé, Andreas PY - 2003/05/21/ UR - http://dx.doi.org/10.1023/A:1022821409482 ER -

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