Interactive optimization of 3D shape and 2D correspondence using multiple geometric constraints via POCS. Sun, Z., Tekalp, A., Navab, N, & 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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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","bibtex":"@article{ ISI:000174574100012,\nAuthor = {Sun, ZH and Tekalp, AM and Navab, N and Ramesh, V},\nTitle = {{Interactive optimization of 3D shape and 2D correspondence using\n multiple geometric constraints via POCS}},\nJournal = {{IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE}},\nYear = {{2002}},\nVolume = {{24}},\nNumber = {{4}},\nPages = {{562-569}},\nMonth = {{APR}},\nAbstract = {{The traditional approach of handling motion tracking and structure from\n motion (SFM) independently in successive steps exhibits inherent\n limitations in terms of achievable precision and incorporation of prior\n geometric constraints about the scene. This paper proposes a projections\n onto convex sets (POCS) framework for iterative refinement of the\n measurement matrix in the well-known factorization method to incorporate\n multiple geometric constraints about the scene, thereby improving the\n accuracy of both 2D feature point tracking and 3D structure estimates.\n Regularities in the scene, such as points on line and plane and parallel\n lines and planes, that can be interactively identified and marked at\n each POCS iteration, enforce rank and parallelism constraints on\n appropriately defined local measurement matrices, one for each\n constraint. The POCS framework allows for the integration of the\n information in each of these local measurement matrices into a single\n measurement matrix that is ``closest{''} to the initial observed\n measurement matrix in Frobenius norm, which is then factored in the\n usual manner. 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