Linear Global Translation Estimation with Feature Tracks

This paper derives a novel linear position constraint for cameras seeing a common scene point, which leads to a direct linear method for global camera translation estimation. Unlike previous solutions, this method deals with collinear camera motion and weak image association at the same time. The final linear formulation does not involve the coordinates of scene points, which makes it efficient even for large scale data. We solve the linear equation based on $L_1$ norm, which makes our system more robust to outliers in essential matrices and feature correspondences. We experiment this method on both sequentially captured images and unordered Internet images. The experiments demonstrate its strength in robustness, accuracy, and efficiency.Comment: Changes: 1. Adopt BMVC2015 style; 2. Combine sections 3 and 5; 3. Move "Evaluation on synthetic data" out to supplementary file; 4. Divide subsection "Evaluation on general data" to subsections "Experiment on sequential data" and "Experiment on unordered Internet data"; 5. Change Fig. 1 and Fig.8; 6. Move Fig. 6 and Fig. 7 to supplementary file; 7 Change some symbols; 8. Correct some typo

ShapeFit and ShapeKick for Robust, Scalable Structure from Motion

We introduce a new method for location recovery from pair-wise directions that leverages an efficient convex program that comes with exact recovery guarantees, even in the presence of adversarial outliers. When pairwise directions represent scaled relative positions between pairs of views (estimated for instance with epipolar geometry) our method can be used for location recovery, that is the determination of relative pose up to a single unknown scale. For this task, our method yields performance comparable to the state-of-the-art with an order of magnitude speed-up. Our proposed numerical framework is flexible in that it accommodates other approaches to location recovery and can be used to speed up other methods. These properties are demonstrated by extensively testing against state-of-the-art methods for location recovery on 13 large, irregular collections of images of real scenes in addition to simulated data with ground truth

LIFT: Learned Invariant Feature Transform

We introduce a novel Deep Network architecture that implements the full feature point handling pipeline, that is, detection, orientation estimation, and feature description. While previous works have successfully tackled each one of these problems individually, we show how to learn to do all three in a unified manner while preserving end-to-end differentiability. We then demonstrate that our Deep pipeline outperforms state-of-the-art methods on a number of benchmark datasets, without the need of retraining.Comment: Accepted to ECCV 2016 (spotlight

Deep Projective Rotation Estimation through Relative Supervision

Orientation estimation is the core to a variety of vision and robotics tasks such as camera and object pose estimation. Deep learning has offered a way to develop image-based orientation estimators; however, such estimators often require training on a large labeled dataset, which can be time-intensive to collect. In this work, we explore whether self-supervised learning from unlabeled data can be used to alleviate this issue. Specifically, we assume access to estimates of the relative orientation between neighboring poses, such that can be obtained via a local alignment method. While self-supervised learning has been used successfully for translational object keypoints, in this work, we show that naively applying relative supervision to the rotational group $SO(3)$ will often fail to converge due to the non-convexity of the rotational space. To tackle this challenge, we propose a new algorithm for self-supervised orientation estimation which utilizes Modified Rodrigues Parameters to stereographically project the closed manifold of $SO(3)$ to the open manifold of $\mathbb{R}^{3}$, allowing the optimization to be done in an open Euclidean space. We empirically validate the benefits of the proposed algorithm for rotational averaging problem in two settings: (1) direct optimization on rotation parameters, and (2) optimization of parameters of a convolutional neural network that predicts object orientations from images. In both settings, we demonstrate that our proposed algorithm is able to converge to a consistent relative orientation frame much faster than algorithms that purely operate in the $SO(3)$ space. Additional information can be found at https://sites.google.com/view/deep-projective-rotation/home .Comment: Conference on Robot Learning (CoRL), 2022. Supplementary material is available at https://sites.google.com/view/deep-projective-rotation/hom

Robust Camera Location Estimation by Convex Programming

$3$D structure recovery from a collection of $2$D images requires the estimation of the camera locations and orientations, i.e. the camera motion. For large, irregular collections of images, existing methods for the location estimation part, which can be formulated as the inverse problem of estimating $n$ locations $\mathbf{t}_1, \mathbf{t}_2, \ldots, \mathbf{t}_n$ in $\mathbb{R}^3$ from noisy measurements of a subset of the pairwise directions $\frac{\mathbf{t}_i - \mathbf{t}_j}{\|\mathbf{t}_i - \mathbf{t}_j\|}$, are sensitive to outliers in direction measurements. In this paper, we firstly provide a complete characterization of well-posed instances of the location estimation problem, by presenting its relation to the existing theory of parallel rigidity. For robust estimation of camera locations, we introduce a two-step approach, comprised of a pairwise direction estimation method robust to outliers in point correspondences between image pairs, and a convex program to maintain robustness to outlier directions. In the presence of partially corrupted measurements, we empirically demonstrate that our convex formulation can even recover the locations exactly. Lastly, we demonstrate the utility of our formulations through experiments on Internet photo collections.Comment: 10 pages, 6 figures, 3 table

Spectral Motion Synchronization in SE(3)

This paper addresses the problem of motion synchronization (or averaging) and describes a simple, closed-form solution based on a spectral decomposition, which does not consider rotation and translation separately but works straight in SE(3), the manifold of rigid motions. Besides its theoretical interest, being the first closed form solution in SE(3), experimental results show that it compares favourably with the state of the art both in terms of precision and speed