18 accepted papers
Rotation averaging is a key subproblem in applications of computer vision and robotics. Many methods for solving this problem exist, and there are also several theoretical results analyzing difficulty and optimality. However, one aspect that most of these have in common is a focus on the isotropic s…
Clustering multiple motions from observed point trajectories is a fundamental task in understanding dynamic scenes. Most motion models require multiple tracks to estimate their parameters hence identifying clusters when multiple motions are observed is a very challenging task. This is even aggravate…
In this paper we tackle the problem of learning Structure-from-Motion (SfM) through the use of graph attention networks. SfM is a classic computer vision problem that is solved though iterative minimization of reprojection errors referred to as Bundle Adjustment (BA) starting from a good initializat…
One of the classical multi-view geometry problems is the so called P3P problem, where the absolute pose of a calibrated camera is determined from three 2D-to-3D correspondences. Since these solvers form a critical component of many vision systems (e.g. in localization and Structure-from-Motion), the…
Bundle adjustment is a key component in practically all available Structure from Motion systems. While it is crucial for achieving accurate reconstruction, convergence to the right solution hinges on good initialization. The recently introduced factorization-based pOSE methods formulate a surrogate…
In this paper we study structure from motion problems for 1D radial cameras. Under this model the projection of a 3D point is a line in the image plane going through the principal point, which makes the model invariant to radial distortion and changes in focal length. It can therefore effectively be…
Low rank inducing penalties have been proven to successfully uncover fundamental structures considered in computer vision and machine learning; however, such methods generally lead to non-convex optimization problems. Since the resulting objective is non-convex one often resorts to using standard sp…
Factorization methods are frequently used for structure from motion problems (SfM). In the presence of noise they are able to jointly estimate camera matrices and scene points in overdetermined settings, without the need for accurate initial solutions. While the early formulations were restricted to…
In this paper we study the convex envelopes of a new class of functions. Using this approach, we are able to unify two important classes of regularizers from unbiased non-convex formulations and weighted nuclear norm penalties. This opens up for possibilities of combining the best of both worlds, an…
Fitting a matrix of a given rank to data in a least squares sense can be done very effectively using 2nd order methods such as Levenberg-Marquardt by explicitly optimizing over a bilinear parameterization of the matrix. In contrast, when applying more general singular value penalties, such as weight…
In this paper we present a study of global optimality conditions for Point Set Registration (PSR) with missing data. PSR is the problem of aligning multiple point clouds with an unknown target point cloud. Since non-linear rotation constraints are present the problem is inherently non-convex and typ…
In this paper we explore the role of duality principles within the problem of rotation averaging, a fundamental task in a wide range of computer vision applications. In its conventional form, rotation averaging is stated as a minimization over multiple rotation constraints. As these constraints are…
Traditional matrix factorization methods approximate high dimensional data with a low dimensional subspace. This imposes constraints on the matrix elements which allow for estimation of missing entries. A lower rank provides stronger constraints and makes estimation of the missing entries less ambig…
This paper considers the problem of recovering either a low rank matrix or a sparse vector from observations of linear combinations of the vector or matrix elements. Recent methods replace the non-convex regularization with l1 or nuclear norm relaxations. It is well known that this approach recovers…
In computer vision, many problems can be formulated as finding a low rank approximation of a given measurement matrix. Ideally, if all elements of the measurement matrix are available, this is easily solved in the L2-norm using factorization. However, in practice this is rarely the case. Lately, thi…
Previous work on estimating the epipolar geometry of two views relies on being able to reliably match feature points based on appearance. In this paper, we go one step further and show that it is feasible to compute both the epipolar geometry and the correspondences at the same time based on geometr…
Outliers pose a problem in all real structure from motion systems. Due to the use of automatic matching methods one has to expect that a (sometimes very large) portion of the detected correspondences can be incorrect. In this paper we propose a method that estimates the relative translation between…
Many standard optimization methods for segmentation and reconstruction compute ML model estimates for appearance or geometry of segments, e.g. Zhu-Yuille 1996, Torr 1998, Chan-Vese 2001, GrabCut 2004, Delong et al. 2012. We observe that the standard likelihood term in these formulations correspond…