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

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

GSLAM: Initialization-robust Monocular Visual SLAM via Global Structure-from-Motion

Many monocular visual SLAM algorithms are derived from incremental structure-from-motion (SfM) methods. This work proposes a novel monocular SLAM method which integrates recent advances made in global SfM. In particular, we present two main contributions to visual SLAM. First, we solve the visual odometry problem by a novel rank-1 matrix factorization technique which is more robust to the errors in map initialization. Second, we adopt a recent global SfM method for the pose-graph optimization, which leads to a multi-stage linear formulation and enables L1 optimization for better robustness to false loops. The combination of these two approaches generates more robust reconstruction and is significantly faster (4X) than recent state-of-the-art SLAM systems. We also present a new dataset recorded with ground truth camera motion in a Vicon motion capture room, and compare our method to prior systems on it and established benchmark datasets.Comment: 3DV 2017 Project Page: https://frobelbest.github.io/gsla

Adaptive Relaxed ADMM: Convergence Theory and Practical Implementation

Many modern computer vision and machine learning applications rely on solving difficult optimization problems that involve non-differentiable objective functions and constraints. The alternating direction method of multipliers (ADMM) is a widely used approach to solve such problems. Relaxed ADMM is a generalization of ADMM that often achieves better performance, but its efficiency depends strongly on algorithm parameters that must be chosen by an expert user. We propose an adaptive method that automatically tunes the key algorithm parameters to achieve optimal performance without user oversight. Inspired by recent work on adaptivity, the proposed adaptive relaxed ADMM (ARADMM) is derived by assuming a Barzilai-Borwein style linear gradient. A detailed convergence analysis of ARADMM is provided, and numerical results on several applications demonstrate fast practical convergence.Comment: CVPR 201