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Register a new userA New Rank Constraint on Multi-view Fundamental Matrices, and its Application to Camera Location Recovery
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Added by
Soumyadip Sengupta
Publication date
2017
fields
Informatics Engineering
and research's language is
English
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Accurate estimation of camera matrices is an important step in structure from motion algorithms. In this paper we introduce a novel rank constraint on collections of fundamental matrices in multi-view settings. We show that in general, with the selection of proper scale factors, a matrix formed by stacking fundamental matrices between pairs of images has rank 6. Moreover, this matrix forms the symmetric part of a rank 3 matrix whose factors relate directly to the corresponding camera matrices. We use this new characterization to produce better estimations of fundamental matrices by optimizing an L1-cost function using Iterative Re-weighted Least Squares and Alternate Direction Method of Multiplier. We further show that this procedure can improve the recovery of camera locations, particularly in multi-view settings in which fewer images are available.
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Global methods to Structure from Motion have gained popularity in recent years. A significant drawback of global methods is their sensitivity to collinear camera settings. In this paper, we introduce an analysis and algorithms for averaging bifocal tensors (essential or fundamental matrices) when either subsets or all of the camera centers are collinear. We provide a complete spectral characterization of bifocal tensors in collinear scenarios and further propose two averaging algorithms. The first algorithm uses rank constrained minimization to recover camera matrices in fully collinear settings. The second algorithm enriches the set of possibly mixed collinear and non-collinear cameras with additional, virtual cameras, which are placed in general position, enabling the application of existing averaging methods to the enriched set of bifocal tensors. Our algorithms are shown to achieve state of the art results on various benchmarks that include autonomous car datasets and unordered image collections in both calibrated and unclibrated settings.
Low-rank Multi-view Subspace Learning (LMvSL) has shown great potential in cross-view classification in recent years. Despite their empirical success, existing LMvSL based methods are incapable of well handling view discrepancy and discriminancy simultaneously, which thus leads to the performance degradation when there is a large discrepancy among multi-view data. To circumvent this drawback, motivated by the block-diagonal representation learning, we propose Structured Low-rank Matrix Recovery (SLMR), a unique method of effectively removing view discrepancy and improving discriminancy through the recovery of structured low-rank matrix. Furthermore, recent low-rank modeling provides a satisfactory solution to address data contaminated by predefined assumptions of noise distribution, such as Gaussian or Laplacian distribution. However, these models are not practical since complicated noise in practice may violate those assumptions and the distribution is generally unknown in advance. To alleviate such limitation, modal regression is elegantly incorporated into the framework of SLMR (term it MR-SLMR). Different from previous LMvSL based methods, our MR-SLMR can handle any zero-mode noise variable that contains a wide range of noise, such as Gaussian noise, random noise and outliers. The alternating direction method of multipliers (ADMM) framework and half-quadratic theory are used to efficiently optimize MR-SLMR. Experimental results on four public databases demonstrate the superiority of MR-SLMR and its robustness to complicated noise.
Multi-view point cloud registration is a hot topic in the communities of multimedia technology and artificial intelligence (AI). In this paper, we propose a framework to reconstruct the 3D models by the multi-view point cloud registration algorithm with adaptive convergence threshold, and subsequently apply it to 3D model retrieval. The iterative closest point (ICP) algorithm is implemented combining with the motion average algorithm for the registration of multi-view point clouds. After the registration process, we design applications for 3D model retrieval. The geometric saliency map is computed based on the vertex curvature. The test facial triangle is then generated based on the saliency map, which is applied to compare with the standard facial triangle. The face and non-face models are then discriminated. The experiments and comparisons prove the effectiveness of the proposed framework.
In this paper, the problem of matrix rank minimization under affine constraints is addressed. The state-of-the-art algorithms can recover matrices with a rank much less than what is sufficient for the uniqueness of the solution of this optimization problem. We propose an algorithm based on a smooth approximation of the rank function, which practically improves recovery limits on the rank of the solution. This approximation leads to a non-convex program; thus, to avoid getting trapped in local solutions, we use the following scheme. Initially, a rough approximation of the rank function subject to the affine constraints is optimized. As the algorithm proceeds, finer approximations of the rank are optimized and the solver is initialized with the solution of the previous approximation until reaching the desired accuracy. On the theoretical side, benefiting from the spherical section property, we will show that the sequence of the solutions of the approximating function converges to the minimum rank solution. On the experimental side, it will be shown that the proposed algorithm, termed SRF standing for Smoothed Rank Function, can recover matrices which are unique solutions of the rank minimization problem and yet not recoverable by nuclear norm minimization. Furthermore, it will be demonstrated that, in completing partially observed matrices, the accuracy of SRF is considerably and consistently better than some famous algorithms when the number of revealed entries is close to the minimum number of parameters that uniquely represent a low-rank matrix.
Indoor localization is a fundamental problem in location-based applications. Current approaches to this problem typically rely on Radio Frequency technology, which requires not only supporting infrastructures but human efforts to measure and calibrate the signal. Moreover, data collection for all locations is indispensable in existing methods, which in turn hinders their large-scale deployment. In this paper, we propose a novel neural network based architecture Graph Location Networks (GLN) to perform infrastructure-free, multi-view image based indoor localization. GLN makes location predictions based on robust location representations extracted from images through message-passing networks. Furthermore, we introduce a novel zero-shot indoor localization setting and tackle it by extending the proposed GLN to a dedicated zero-shot version, which exploits a novel mechanism Map2Vec to train location-aware embeddings and make predictions on novel unseen locations. Our extensive experiments show that the proposed approach outperforms state-of-the-art methods in the standard setting, and achieves promising accuracy even in the zero-shot setting where data for half of the locations are not available. The source code and datasets are publicly available at https://github.com/coldmanck/zero-shot-indoor-localization-release.
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