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

Point triangulation through polyhedron collapse using the l∞ norm

Multi-camera triangulation of feature points based on a minimisation of the overall l(2) reprojection error can get stuck in suboptimal local minima or require slow global optimisation. For this reason, researchers have proposed optimising the l(infinity) norm of the l(2) single view reprojection errors, which avoids the problem of local minima entirely. In this paper we present a novel method for l(infinity) triangulation that minimizes the l(infinity) norm of the l(infinity) reprojection errors: this apparently small difference leads to a much faster but equally accurate solution which is related to the MLE under the assumption of uniform noise. The proposed method adopts a new optimisation strategy based on solving simple quadratic equations. This stands in contrast with the fastest existing methods, which solve a sequence of more complex auxiliary Linear Programming or Second Order Cone Problems. The proposed algorithm performs well: for triangulation, it achieves the same accuracy as existing techniques while executing faster and being straightforward to implement

Robust and large-scale quasiconvex programming in structure-from-motion

Structure-from-Motion (SfM) is a cornerstone of computer vision. Briefly speaking, SfM is the task of simultaneously estimating the poses of the cameras behind a set of images of a scene, and the 3D coordinates of the points in the scene. Often, the optimisation problems that underpin SfM do not have closed-form solutions, and finding solutions via numerical schemes is necessary. An objective function, which measures the discrepancy of a geometric object (e.g., camera poses, rotations, 3D coordi- nates) with a set of image measurements, is to be minimised. Each image measurement gives rise to an error function. For example, the reprojection error, which measures the distance between an observed image point and the projection of a 3D point onto the image, is a commonly used error function. An influential optimisation paradigm in SfM is the ℓ₀₀ paradigm, where the objective function takes the form of the maximum of all individual error functions (e.g. individual reprojection errors of scene points). The benefit of the ℓ₀₀ paradigm is that the objective function of many SfM optimisation problems become quasiconvex, hence there is a unique minimum in the objective function. The task of formulating and minimising quasiconvex objective functions is called quasiconvex programming. Although tremendous progress in SfM techniques under the ℓ₀₀ paradigm has been made, there are still unsatisfactorily solved problems, specifically, problems associated with large-scale input data and outliers in the data. This thesis describes novel techniques to tackle these problems. A major weakness of the ℓ₀₀ paradigm is its susceptibility to outliers. This thesis improves the robustness of ℓ₀₀ solutions against outliers by employing the least median of squares (LMS) criterion, which amounts to minimising the median error. In the context of triangulation, this thesis proposes a locally convergent robust algorithm underpinned by a novel quasiconvex plane sweep technique. Imposing the LMS criterion achieves significant outlier tolerance, and, at the same time, some properties of quasiconvexity greatly simplify the process of solving the LMS problem. Approximation is a commonly used technique to tackle large-scale input data. This thesis introduces the coreset technique to quasiconvex programming problems. The coreset technique aims find a representative subset of the input data, such that solving the same problem on the subset yields a solution that is within known bound of the optimal solution on the complete input set. In particular, this thesis develops a coreset approximate algorithm to handle large-scale triangulation tasks. Another technique to handle large-scale input data is to break the optimisation into multiple smaller sub-problems. Such a decomposition usually speeds up the overall optimisation process, and alleviates the limitation on memory. This thesis develops a large-scale optimisation algorithm for the known rotation problem (KRot). The proposed method decomposes the original quasiconvex programming problem with potentially hundreds of thousands of parameters into multiple sub-problems with only three parameters each. An efficient solver based on a novel minimum enclosing ball technique is proposed to solve the sub-problems.Thesis (Ph.D.) (Research by Publication) -- University of Adelaide, School of Computer Science, 201

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

An adversarial optimization approach to efficient outlier removal

This paper proposes a novel adversarial optimization approach to efficient outlier removal in computer vision. We characterize the outlier removal problem as a game that involves two players of conflicting interests, namely, optimizer and outlier. Such an adversarial view not only brings new insights into various existing methods, but also gives rise to a general optimization framework that provably unifies them. Under the proposed framework, we develop a new outlier removal approach that is able to offer a much needed control over the trade-off between reliability and speed, which is otherwise not available in previous methods. The proposed approach is driven by a mixed-integer minmax (convex-concave) optimization process. Although a minmax problem is generally not amenable to efficient optimization, we show that for some commonly used vision objective functions, an equivalent Linear Program reformulation exists. We demonstrate our method on two representative multiview geometry problems. Experiments on real image data illustrate superior practical performance of our method over recent techniques.Jin Yu, Anders Eriksson, Tat-Jun Chin, David Suterhttp://www.iccv2011.org

New algorithmic developments in maximum consensus robust fitting

In many computer vision applications, the task of robustly estimating the set of parameters of a geometric model is a fundamental problem. Despite the longstanding research efforts on robust model fitting, there remains significant scope for investigation. For a large number of geometric estimation tasks in computer vision, maximum consensus is the most popular robust fitting criterion. This thesis makes several contributions in the algorithms for consensus maximization. Randomized hypothesize-and-verify algorithms are arguably the most widely used class of techniques for robust estimation thanks to their simplicity. Though efficient, these randomized heuristic methods do not guarantee finding good maximum consensus estimates. To improve the randomize algorithms, guided sampling approaches have been developed. These methods take advantage of additional domain information, such as descriptor matching scores, to guide the sampling process. Subsets of the data that are more likely to result in good estimates are prioritized for consideration. However, these guided sampling approaches are ineffective when good domain information is not available. This thesis tackles this shortcoming by proposing a new guided sampling algorithm, which is based on the class of LP-type problems and Monte Carlo Tree Search (MCTS). The proposed algorithm relies on a fundamental geometric arrangement of the data to guide the sampling process. Specifically, we take advantage of the underlying tree structure of the maximum consensus problem and apply MCTS to efficiently search the tree. Empirical results show that the new guided sampling strategy outperforms traditional randomized methods. Consensus maximization also plays a key role in robust point set registration. A special case is the registration of deformable shapes. If the surfaces have the same intrinsic shapes, their deformations can be described accurately by a conformal model. The uniformization theorem allows the shapes to be conformally mapped onto a canonical domain, wherein the shapes can be aligned using a M¨obius transformation. The problem of correspondence-free M¨obius alignment of two sets of noisy and partially overlapping point sets can be tackled as a maximum consensus problem. Solving for the M¨obius transformation can be approached by randomized voting-type methods which offers no guarantee of optimality. Local methods such as Iterative Closest Point can be applied, but with the assumption that a good initialization is given or these techniques may converge to a bad local minima. When a globally optimal solution is required, the literature has so far considered only brute-force search. This thesis contributes a new branch-and-bound algorithm that solves for the globally optimal M¨obius transformation much more efficiently. So far, the consensus maximization problems are approached mainly by randomized algorithms, which are efficient but offer no analytical convergence guarantee. On the other hand, there exist exact algorithms that can solve the problem up to global optimality. The global methods, however, are intractable in general due to the NP-hardness of the consensus maximization. To fill the gap between the two extremes, this thesis contributes two novel deterministic algorithms to approximately optimize the maximum consensus criterion. The first method is based on non-smooth penalization supported by a Frank-Wolfe-style optimization scheme, and another algorithm is based on Alternating Direction Method of Multipliers (ADMM). Both of the proposed methods are capable of handling the non-linear geometric residuals commonly used in computer vision. As will be demonstrated, our proposed methods consistently outperform other heuristics and approximate methods.Thesis (Ph.D.) (Research by Publication) -- University of Adelaide, School of Computer Science, 201

Keyframe-based monocular SLAM: design, survey, and future directions

Extensive research in the field of monocular SLAM for the past fifteen years has yielded workable systems that found their way into various applications in robotics and augmented reality. Although filter-based monocular SLAM systems were common at some time, the more efficient keyframe-based solutions are becoming the de facto methodology for building a monocular SLAM system. The objective of this paper is threefold: first, the paper serves as a guideline for people seeking to design their own monocular SLAM according to specific environmental constraints. Second, it presents a survey that covers the various keyframe-based monocular SLAM systems in the literature, detailing the components of their implementation, and critically assessing the specific strategies made in each proposed solution. Third, the paper provides insight into the direction of future research in this field, to address the major limitations still facing monocular SLAM; namely, in the issues of illumination changes, initialization, highly dynamic motion, poorly textured scenes, repetitive textures, map maintenance, and failure recovery