Homomorphic Sensing of Subspace Arrangements

Homomorphic sensing is a recent algebraic-geometric framework that studies the unique recovery of points in a linear subspace from their images under a given collection of linear maps. It has been successful in interpreting such a recovery in the case of permutations composed by coordinate projections, an important instance in applications known as unlabeled sensing, which models data that are out of order and have missing values. In this paper, we provide tighter and simpler conditions that guarantee the unique recovery for the single-subspace case, extend the result to the case of a subspace arrangement, and show that the unique recovery in a single subspace is locally stable under noise. We specialize our results to several examples of homomorphic sensing such as real phase retrieval and unlabeled sensing. In so doing, in a unified way, we obtain conditions that guarantee the unique recovery for those examples, typically known via diverse techniques in the literature, as well as novel conditions for sparse and unsigned versions of unlabeled sensing. Similarly, our noise result also implies that the unique recovery in unlabeled sensing is locally stable.Comment: 18 page

Unsupervised Deep Epipolar Flow for Stationary or Dynamic Scenes

Unsupervised deep learning for optical flow computation has achieved promising results. Most existing deep-net based methods rely on image brightness consistency and local smoothness constraint to train the networks. Their performance degrades at regions where repetitive textures or occlusions occur. In this paper, we propose Deep Epipolar Flow, an unsupervised optical flow method which incorporates global geometric constraints into network learning. In particular, we investigate multiple ways of enforcing the epipolar constraint in flow estimation. To alleviate a "chicken-and-egg" type of problem encountered in dynamic scenes where multiple motions may be present, we propose a low-rank constraint as well as a union-of-subspaces constraint for training. Experimental results on various benchmarking datasets show that our method achieves competitive performance compared with supervised methods and outperforms state-of-the-art unsupervised deep-learning methods.Comment: CVPR 201

Leveraging feature uncertainty in the PnP problem

Trabajo presentado a la 25th British Machine Vision Conference (BMVC), celebrada en Nottingham (UK) del 1 al 5 de septiembre de 2014.-- Este ítem (excepto textos e imágenes no creados por el autor) está sujeto a una licencia de Creative Commons: Attribution-NonCommercial-NoDerivs 3.0 Spain.We propose a real-time and accurate solution to the Perspective-n-Point (PnP) problem --estimating the pose of a calibrated camera from n 3D-to-2D point correspondences-- that exploits the fact that in practice the 2D position of not all 2D features is estimated with the same accuracy. Assuming a model of such feature uncertainties is known in advance, we reformulate the PnP problem as a maximum likelihood minimization approximated by an unconstrained Sampson error function, which naturally penalizes the most noisy correspondences. The advantages of this approach are clearly demonstrated in synthetic experiments where feature uncertainties are exactly known. Pre-estimating the features uncertainties in real experiments is, though, not easy. In this paper we model feature uncertainty as 2D Gaussian distributions representing the sensitivity of the 2D feature detectors to different camera viewpoints. When using these noise models with our PnP formulation we still obtain promising pose estimation results that outperform the most recent approaches.This work has been partially funded by Spanish government under projects DPI2011-27510, IPT-2012-0630-020000, IPT-2011-1015-430000 and CICYT grant TIN2012-39203; by the EU project ARCAS FP7-ICT-2011-28761; and by the ERA-Net Chistera project ViSen PCIN-2013-047.Peer Reviewe