Interactive optimization of 3D shape and 2D correspondence using multiple geometric constraints via POCS. Sun, Z.; Tekalp, A.; Navab, N; and Ramesh, V IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, 24(4):562-569, APR, 2002.
doi  abstract   bibtex   
The traditional approach of handling motion tracking and structure from motion (SFM) independently in successive steps exhibits inherent limitations in terms of achievable precision and incorporation of prior geometric constraints about the scene. This paper proposes a projections onto convex sets (POCS) framework for iterative refinement of the measurement matrix in the well-known factorization method to incorporate multiple geometric constraints about the scene, thereby improving the accuracy of both 2D feature point tracking and 3D structure estimates. Regularities in the scene, such as points on line and plane and parallel lines and planes, that can be interactively identified and marked at each POCS iteration, enforce rank and parallelism constraints on appropriately defined local measurement matrices, one for each constraint. The POCS framework allows for the integration of the information in each of these local measurement matrices into a single measurement matrix that is ``closest'' to the initial observed measurement matrix in Frobenius norm, which is then factored in the usual manner. Experimental results demonstrate that the proposed interactive POCS framework consistently improves both 2D correspondences and 3D shape/motion estimates and similar results can not be achieved by enforcing these constraints as either post or preprocessing.
@article{ ISI:000174574100012,
Author = {Sun, ZH and Tekalp, AM and Navab, N and Ramesh, V},
Title = {{Interactive optimization of 3D shape and 2D correspondence using
   multiple geometric constraints via POCS}},
Journal = {{IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE}},
Year = {{2002}},
Volume = {{24}},
Number = {{4}},
Pages = {{562-569}},
Month = {{APR}},
Abstract = {{The traditional approach of handling motion tracking and structure from
   motion (SFM) independently in successive steps exhibits inherent
   limitations in terms of achievable precision and incorporation of prior
   geometric constraints about the scene. This paper proposes a projections
   onto convex sets (POCS) framework for iterative refinement of the
   measurement matrix in the well-known factorization method to incorporate
   multiple geometric constraints about the scene, thereby improving the
   accuracy of both 2D feature point tracking and 3D structure estimates.
   Regularities in the scene, such as points on line and plane and parallel
   lines and planes, that can be interactively identified and marked at
   each POCS iteration, enforce rank and parallelism constraints on
   appropriately defined local measurement matrices, one for each
   constraint. The POCS framework allows for the integration of the
   information in each of these local measurement matrices into a single
   measurement matrix that is ``closest{''} to the initial observed
   measurement matrix in Frobenius norm, which is then factored in the
   usual manner. Experimental results demonstrate that the proposed
   interactive POCS framework consistently improves both 2D correspondences
   and 3D shape/motion estimates and similar results can not be achieved by
   enforcing these constraints as either post or preprocessing.}},
DOI = {{10.1109/34.993563}},
ISSN = {{0162-8828}},
Unique-ID = {{ISI:000174574100012}},
}
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