skip to main content


Search for: All records

Award ID contains: 1910530

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. Abstract—We present a method for solving two minimal problems for relative camera pose estimation from three views, which are based on three view correspondences of (i) three points and one line and the novel case of (ii) three points and two lines through two of the points. These problems are too difficult to be efficiently solved by the state of the art Gro ̈bner basis methods. Our method is based on a new efficient homotopy continuation (HC) solver framework MINUS, which dramatically speeds up previous HC solving by specializing HC methods to generic cases of our problems. We characterize their number of solutions and show with simulated experiments that our solvers are numerically robust and stable under image noise, a key contribution given the borderline intractable degree of nonlinearity of trinocular constraints. We show in real experiments that (i) SIFT feature location and orientation provide good enough point-and-line correspondences for three-view reconstruction and (ii) that we can solve difficult cases with too few or too noisy tentative matches, where the state of the art structure from motion initialization fails. 
    more » « less
  2. Abstract. Similaritysearchisafundamentalbuildingblockforinformation retrieval on a variety of datasets. The notion of a neighbor is often based on binary considerations, such as the k nearest neighbors. However, considering that data is often organized as a manifold with low intrinsic dimension, the notion of a neighbor must recognize higher-order relationship, to capture neighbors in all directions. Proximity graphs such as the Relative Neighbor Graphs (RNG), use trinary relationships which capture the notion of direc- tion and have been successfully used in a number of applications. However, the current algorithms for computing the RNG, despite widespread use, are approximate and not scalable. This paper proposes a novel type of graph, the Generalized Relative Neighborhood Graph (GRNG) for use in a pivot layer that then guides the efficient and exact construction of the RNG of a set of exemplars. It also shows how to extend this to a multi-layer hier- archy which significantly improves over the state-of-the-art methods which can only construct an approximate RNG. 
    more » « less
  3. This paper presents the Brown Pedestrian Odometry Dataset (BPOD) for benchmarking visual odometry algo- rithms on data from head-mounted sensors. This dataset was captured with stereo and RGB streams from RealSense cameras with rolling and global shutters in 12 diverse in- door and outdoor locations on Brown University’s cam- pus. Its associated ground-truth trajectories were gener- ated from third-person videos that documented the recorded pedestrians’ positions relative to stick-on markers placed along their paths. We evaluate the performance of canoni- cal approaches representative of direct, feature-based, and learning-based visual odometry methods on BPOD. Our finding is that current methods which are successful on other benchmarks fail on BPOD. The failure modes cor- respond in part to rapid pedestrian rotation, erratic body movements, etc. We hope this dataset will play a significant role in the identification of these failure modes and in the design, development, and evaluation of pedestrian odome- try algorithms. 
    more » « less
  4. The Homotopy Continuation (HC) method is known as a prevailing and robust approach for solving numerically complicated polyno- mial systems with guarantees of a global solution. In recent years we are witnessing tremendous advances in the theoretical and al- gorithmic foundations of HC. Furthermore, there are very efficient implementations of several variants of HC that solve large polyno- mial systems that we could not even imagine some years ago. The success of HC has motivated approaching even larger problems or gaining real-time performance. We propose to accelerate the HC computation significantly through a parallel implementation of path tracker in both straight line coefficient HC and parameter HC on a Graphical Processing Unit (GPU). The implementation involves computing independent tracks to convergence simulta- neously, as well as a parallel linear system solver and a parallel evaluation of Jacobian matrices and vectors. We evaluate the per- formance of our implementation using both popular benchmarking polynomial systems as well as polynomial systems of computer vi- sion applications. The experiments demonstrate that our GPU-HC provides as high as 28× and 20× faster than the multi-core Julia in polynomial benchmark problems and polynomial systems for computer vision applications, respectively. Code is made publicly available in https://rb.gy/cvcwgq. 
    more » « less
  5. Relative pose estimation using the 5-point or 7-point Random Sample Consensus (RANSAC) algorithms can fail even when no outliers are present and there are enough inliers to support a hypothesis. These cases arise due to numerical instability of the 5- and 7-point minimal problems. This paper characterizes these instabilities, both in terms of minimal world scene configurations that lead to infinite condition number in epipolar estimation, and also in terms of the related minimal image feature pair correspondence configurations. The instability is studied in the context of a novel framework for analyzing the conditioning of minimal problems in multiview geometry, based on Riemannian manifolds. Experiments with synthetic and real-world data reveal that RANSAC does not only serve to filter out outliers, but RANSAC also selects for well-conditioned image data, sufficiently separated from the ill-posed locus that our theory predicts. These findings suggest that, in future work, one could try to accelerate and increase the success of RANSAC by testing only well-conditioned image data. 
    more » « less
  6. Systems of polynomial equations arise frequently in computer vision, especially in multiview geometry problems. Traditional methods for solving these systems typically aim to eliminate variables to reach a univariate polynomial, e.g., a tenth-order polynomial for 5-point pose estimation, using clever manipulations, or more generally using Grobner basis, resultants, and elimination templates, leading to successful algorithms for multiview geometry and other problems. However, these methods do not work when the problem is complex and when they do, they face efficiency and stability issues. Homotopy Continuation (HC) can solve more complex problems without the stability issues, and with guarantees of a global solution, but they are known to be slow. In this paper we show that HC can be parallelized on a GPU, showing significant speedups up to 56 times on polynomial benchmarks. We also show that GPU-HC can be generically applied to a range of computer vision problems, including 4-view triangulation and trifocal pose estimation with unknown focal length, which cannot be solved with elimination template but they can be efficiently solved with HC. GPU-HC opens the door to easy formulation and solution of a range of computer vision problems. 
    more » « less