A compact formula for the derivative of a 3-D rotation in exponential coordinates

We present a compact formula for the derivative of a 3-D rotation matrix with respect to its exponential coordinates. A geometric interpretation of the resulting expression is provided, as well as its agreement with other less-compact but better-known formulas. To the best of our knowledge, this simpler formula does not appear anywhere in the literature. We hope by providing this more compact expression to alleviate the common pressure to reluctantly resort to alternative representations in various computational applications simply as a means to avoid the complexity of differential analysis in exponential coordinates.Comment: 6 page

A Novel Method for the Absolute Pose Problem with Pairwise Constraints

Absolute pose estimation is a fundamental problem in computer vision, and it is a typical parameter estimation problem, meaning that efforts to solve it will always suffer from outlier-contaminated data. Conventionally, for a fixed dimensionality d and the number of measurements N, a robust estimation problem cannot be solved faster than O(N^d). Furthermore, it is almost impossible to remove d from the exponent of the runtime of a globally optimal algorithm. However, absolute pose estimation is a geometric parameter estimation problem, and thus has special constraints. In this paper, we consider pairwise constraints and propose a globally optimal algorithm for solving the absolute pose estimation problem. The proposed algorithm has a linear complexity in the number of correspondences at a given outlier ratio. Concretely, we first decouple the rotation and the translation subproblems by utilizing the pairwise constraints, and then we solve the rotation subproblem using the branch-and-bound algorithm. Lastly, we estimate the translation based on the known rotation by using another branch-and-bound algorithm. The advantages of our method are demonstrated via thorough testing on both synthetic and real-world dataComment: 10 pages, 7figure

A Compact Formula for the Derivative of a 3-D Rotation in Exponential Coordinates

We present a compact formula for the derivative of a 3-D rotation matrix with respect to its exponential coordinates. A geometric interpretation of the resulting expression is provided, as well as its agreement with other less-compact but better-known formulas. To the best of our knowledge, this simpler formula does not appear anywhere in the literature. We hope by providing this more compact expression to alleviate the common pressure to reluctantly resort to alternative representations in various computational applications simply as a means to avoid the complexity of differential analysis in exponential coordinates

Sparse learning approach to the problem of robust estimation of camera locations

International audienceIn this paper, we propose a new approach--inspired by the recent advances in the theory of sparse learning-- to the problem of estimating camera locations when the internal parameters and the orientations of the cameras are known. Our estimator is defined as a Bayesian maximum a posteriori with multivariate Laplace prior on the vector describing the outliers. This leads to an estimator in which the fidelity to the data is measured by the L∞-norm while the regularization is done by the L1 -norm. Building on the papers [11, 15, 16, 14, 21, 22, 24, 18, 23] for L∞ -norm minimization in multiview geometry and, on the other hand, on the papers [8, 4, 7, 2, 1, 3] for sparse recovery in statistical framework, we propose a two-step procedure which, at the first step, identifies and removes the outliers and, at the second step, estimates the unknown parameters by minimizing the L∞ cost function. Both steps are fairly fast: the outlierremoval is done by solving one linear program (LP), while the final estimation is performed by a sequence of LPs. An important difference compared to many existing algorithms is that for our estimator it is not necessary to specify neither the number nor the proportion of the outliers

KSS-ICP: Point Cloud Registration based on Kendall Shape Space

Point cloud registration is a popular topic which has been widely used in 3D model reconstruction, location, and retrieval. In this paper, we propose a new registration method, KSS-ICP, to address the rigid registration task in Kendall shape space (KSS) with Iterative Closest Point (ICP). The KSS is a quotient space that removes influences of translations, scales, and rotations for shape feature-based analysis. Such influences can be concluded as the similarity transformations that do not change the shape feature. The point cloud representation in KSS is invariant to similarity transformations. We utilize such property to design the KSS-ICP for point cloud registration. To tackle the difficulty to achieve the KSS representation in general, the proposed KSS-ICP formulates a practical solution that does not require complex feature analysis, data training, and optimization. With a simple implementation, KSS-ICP achieves more accurate registration from point clouds. It is robust to similarity transformation, non-uniform density, noise, and defective parts. Experiments show that KSS-ICP has better performance than the state of the art.Comment: 13 pages, 20 figure

Robustness and Accuracy of Feature-Based Single Image 2-D–3-D Registration Without Correspondences for Image-Guided Intervention

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Towards Robust Visual Localization in Challenging Conditions

Visual localization is a fundamental problem in computer vision, with a multitude of applications in robotics, augmented reality and structure-from-motion. The basic problem is to, based on one or more images, figure out the position and orientation of the camera which captured these images relative to some model of the environment. Current visual localization approaches typically work well when the images to be localized are captured under similar conditions compared to those captured during mapping. However, when the environment exhibits large changes in visual appearance, due to e.g. variations in weather, seasons, day-night or viewpoint, the traditional pipelines break down. The reason is that the local image features used are based on low-level pixel-intensity information, which is not invariant to these transformations: when the environment changes, this will cause a different set of keypoints to be detected, and their descriptors will be different, making the long-term visual localization problem a challenging one. In this thesis, five papers are included, which present work towards solving the problem of long-term visual localization. Two of the articles present ideas for how semantic information may be included to aid in the localization process: one approach relies only on the semantic information for visual localization, and the other shows how the semantics can be used to detect outlier feature correspondences. The third paper considers how the output from a monocular depth-estimation network can be utilized to extract features that are less sensitive to viewpoint changes. The fourth article is a benchmark paper, where we present three new benchmark datasets aimed at evaluating localization algorithms in the context of long-term visual localization. Lastly, the fifth article considers how to perform convolutions on spherical imagery, which in the future might be applied to learning local image features for the localization problem

Long-Term Visual Localization Revisited

Visual localization enables autonomous vehicles to navigate in their surroundings and augmented reality applications to link virtual to real worlds. Practical visual localization approaches need to be robust to a wide variety of viewing conditions, including day-night changes, as well as weather and seasonal variations, while providing highly accurate six degree-of-freedom (6DOF) camera pose estimates. In this paper, we extend three publicly available datasets containing images captured under a wide variety of viewing conditions, but lacking camera pose information, with ground truth pose information, making evaluation of the impact of various factors on 6DOF camera pose estimation accuracy possible. We also discuss the performance of state-of-the-art localization approaches on these datasets. Additionally, we release around half of the poses for all conditions, and keep the remaining half private as a test set, in the hopes that this will stimulate research on long-term visual localization, learned local image features, and related research areas. Our datasets are available at visuallocalization.net, where we are also hosting a benchmarking server for automatic evaluation of results on the test set. The presented state-of-the-art results are to a large degree based on submissions to our server

Long-Term Visual Localization Revisited

Visual localization enables autonomous vehicles to navigate in their surroundings and augmented reality applications to link virtual to real worlds. Practical visual localization approaches need to be robust to a wide variety of viewing conditions, including day-night changes, as well as weather and seasonal variations, while providing highly accurate six degree-of-freedom (6DOF) camera pose estimates. In this paper, we extend three publicly available datasets containing images captured under a wide variety of viewing conditions, but lacking camera pose information, with ground truth pose information, making evaluation of the impact of various factors on 6DOF camera pose estimation accuracy possible. We also discuss the performance of state-of-the-art localization approaches on these datasets. Additionally, we release around half of the poses for all conditions, and keep the remaining half private as a test set, in the hopes that this will stimulate research on long-term visual localization, learned local image features, and related research areas. Our datasets are available at visuallocalization.net, where we are also hosting a benchmarking server for automatic evaluation of results on the test set. The presented state-of-the-art results are to a large degree based on submissions to our server