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Selected Publications:
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da Silva, N. P. and
Costeira, J. P..
" The Normalized Subspace Inclusion: Robust Clustering of Motion Subspaces",
The Twelfth IEEE International Conference on Conputer Vision (ICCV),
Kyoto, Japan, September, 2009.
The Normalized Subspace Inclusion (NSI) is a criterion for linear subspace clustering. It remains geometrically consistent
where most of the previous proposed criteria fail to do so, because it is invariant to both the orthogonal and inclusion relationship between subspaces. By clustering the GMC geometric solution (see the CVPR'08 paper), using the
NSI similarity, we get a rigid motion interpretation for the linear subspaces underlying the different groups of image trajectories.
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da Silva, N. P. and
Costeira, J. P..
" Subspace segmentation with outliers: a Grassmannian approach to the maximum consensus subspace",
IEEE Computer Society Conference on Conputer Vision and Pattern Recognition (CVPR),
Anchorage, Alaska, USA, June, 2008.
Here we present sufficient conditions defining the intrinsic maximum consensus statistic on Smooth Manifolds. In particular, we explore the riemannian
structure of the Grassmann manifold, using a geometric optimization algorithm, to built the Grassmannian Maximum Consensus (GMC): a new
maximum consensus
based method for robust linear subspace segmentation, avoiding random search and voting procedures, rank estimation, and with quadratic convergence
rate near the optima. Also, the subspace dimension arises as a byproduct of the segmentation method.
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Education:
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2010
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Ph.D. Degree in Electrical and Computer Engineering at Instituto Superior Técnico, Portugal.
The final dissertation Robust
Nonmetric Perception of Moving Rigid Bodies
(June, 2010) addresses the problem of perceiving rigid motion in
dynamic scenes.
It proves constructively the existence of the Smooth Maximum Consensus
(SMC) map, thus providing a tool for intrinsic robust
fitting on Riemannian Manifolds. It develops the Grassmannian Maximum
Consensus (GMC) method for robust linear subspace segmentation, the Normalized Subspace Inclusion (NSI) criterion for
subspace clustering and a new algorithm for Planar Factorization.
2005
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Master Degree in Electrical and Computer Engineering at Instituto Superior Técnico, Portugal.
The final dissertation Global Robust Image
Registration (June, 2005) (June, 2005) addresses two concepts
of robustness in global image registration: (i) robustness to outliers (proposed solution: the IGLOS methodology) and (ii) robustness to the uncertainty in
the model of the image transformations (proposed solution: the L-infinity algorithm).
2002
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