Consensus maximization has proven to be a useful tool for robust estimation. While randomized methods like RANSAC are fast, they do not guarantee global optimality and fail to manage large amounts of outliers. On the other hand, global methods are commonly slow because they do not exploit the structure of the problem at hand. In this paper, we show that the solution space can be reduced by introducing Linear Matrix Inequality (LMI) constraints. This leads to significant speed ups of the optimization time even for large amounts of outliers, while maintaining global optimality. We study several cases in which the objective variables have a special structure, such as rotation, scaled-rotation, and essential matrices, which are posed as LMI constraints. This is very useful in several standard computer vision problems, such as estimating Similarity Transformations, Absolute Poses, and Relative Poses, for which we obtain compelling results on both synthetic and real datasets. With up to 90 percent outlier rate, where RANSAC often fails, our constrained approach is consistently faster than the non-constrained one - while finding the same global solution.

Metric learning has proved very successful. However, human annotations are necessary. In this paper, we propose an unsupervised method, dubbed Metric Imitation (MI), where metrics over cheap features (target features, TFs) are learned by imitating the standard metrics over more sophisticated, off-the-shelf features (source features, SFs) by transferring view-independent property manifold structures. In particular, MI consists of: 1) quantifying the properties of source metrics as manifold geometry, 2) transferring the manifold from source domain to target domain, and 3) learning a mapping of TFs so that the manifold is approximated as well as possible in the mapped feature domain. MI is useful in at least two scenarios where: 1) TFs are more efficient computationally and in terms of memory than SFs; and 2) SFs contain privileged information, but are not available during testing. For the former, MI is evaluated on image clustering, category-based image retrieval, and instance-based object retrieval, with three SFs and three TFs. For the latter, MI is tested on the task of example-based image super-resolution, where high-resolution patches are taken as SFs and low-resolution patches as TFs. Experiments show that MI is able to provide good metrics while avoiding expensive data labeling efforts and that it achieves state-of-the-art performance for image super-resolution. In addition, manifold transfer is an interesting direction of transfer learning.

We present a novel vanishing point (VP) detection and tracking algorithm for calibrated monocular image sequences. Previous VP detection and tracking methods usually assume known camera poses for all frames or detect and track separately. We advance the state-of-the-art by combining VP extraction on a Gaussian sphere with recent advances in multi-target tracking on probabilistic occupancy fields. The solution is obtained by solving a Linear Program (LP). This enables the joint detection and tracking of multiple VPs over sequences. Unlike existing works we do not need known camera poses, and at the same time avoid detecting and tracking in separate steps. We also propose an extension to enforce VP orthogonality. We augment an existing video dataset consisting of 48 monocular videos with multiple annotated VPs in 14448 frames for evaluation. Although the method is designed for unknown camera poses, it is also helpful in scenarios with known poses, since a multi-frame approach in VP detection helps to regularize in frames with weak VP line support.