Usual Structure-from-Motion (SfM) techniques require at least trifocal overlaps to calibrate cameras and reconstruct a scene. We consider here scenarios of reduced image sets with little overlap, possibly as low as two images at most seeing the same part of the scene. We propose a new method, based on line coplanarity hypotheses, for estimating the relative scale of two independent bifocal calibrations sharing a camera, without the need of any trifocal information or Manhattan-world assumption. We use it to compute SfM in a chain of up-to-scale relative motions. For accuracy, we however also make use of trifocal information for line and or point features, when present, relaxing usual trifocal constraints. For robustness to wrong assumptions and mismatches, we embed all constraints in a parameterless RANSAC-like approach. Experiments show that we can calibrate datasets that previously could not, and that this wider applicability does not come at the cost of inaccuracy.
@cite_9: This paper presents a new linear method for reconstructing simultaneously 3D features (points, lines and planes) and cameras from many perspective views by solving a single linear system. It assumes that a real or virtual reference plane is visible in all views. We call it the Direct Reference Plane (DRP) method. It is well known that the projection relationship between uncalibrated cameras and 3D features is nonlinear in the absence of a reference plane. With a known reference plane, points and cameras have a linear relationship, as shown by Rother and Carlsson (2001). The main contribution of this paper is that lines and cameras, as well as, planes and cameras also have a linear relationship. Consequently, all 3D features and all cameras can be reconstructed simultaneously from a single linear system, which handles missing image measurements naturally. A further contribution is an extensive experimental comparison, using real data, of different reference plane and nonreference plane reconstruction methods. For difficult reference plane scenarios, with point or line features, the DRP method is superior to all compared methods. Finally, an extensive list of reference plane scenarios is presented, which shows the wide applicability of the DRP method.
@cite_6: This paper presents a new framework for solving geometric structure and motion problems based on the Linfin-norm. Instead of using the common sum-of-squares cost function, that is, the L2-norm, the model-fitting errors are measured using the Linfin-norm. Unlike traditional methods based on L2, our framework allows for the efficient computation of global estimates. We show that a variety of structure and motion problems, for example, triangulation, camera resectioning, and homography estimation, can be recast as quasi-convex optimization problems within this framework. These problems can be efficiently solved using second-order cone programming (SOCP), which is a standard technique in convex optimization. The methods have been implemented in Matlab and the resulting toolbox has been made publicly available. The algorithms have been validated on real data in different settings on problems with small and large dimensions and with excellent performance.
@cite_49: We present several methods for the estimation of relative pose between planes and cameras, based on projections of sets of coplanar features in images. While such methods exist for simple cases, especially one plane seen in one or several views, the aim of this paper is to propose solutions for multi-plane multi-view situations, possibly with little overlap. We propose a factorization-based method for the general case of n planes seen in m views. A mechanism for computing missing data, i.e. when one or several of the planes are not visible in one or several of the images, is described. Experimental results for real images are shown.
@cite_31: Traditional structure from motion is hard in indoor environments with only a few detectable point features. These environments, however, have other useful characteristics: they often contain severable visible lines, and their layout typically conforms to a Manhattan world geometry. We introduce a new algorithm to cluster visible lines in a Manhattan world, seen from two different viewpoints, into coplanar bundles. This algorithm is based on the notion of “characteristic line”, which is an invariant of a set of parallel coplanar lines. Finding coplanar sets of lines becomes a problem of clustering characteristic lines, which can be accomplished using a modified mean shift procedure. The algorithm is computationally light and produces good results in real world situations.
@cite_16: We introduce a new approach to structure and motion recovery directly from one or more large planes in the scene. When such a plane exists, we demonstrate how to automatically detect and track it robustly and consistently over a long video sequence, and how to efficiently self-calibrate the camera using the homographies induced by this plane. We build a complete structure from motion system which does not use any additional off-the-plane information about the scene, and show its advantage over conventional systems in handling two important issues which often occur in real world videos, namely, the plane degeneracy and the dynamic foreground problems. Experimental results on a variety of real video sequences verify the effectiveness and efficiency of our system.
@cite_12: This paper is about multi-view modeling of a rigid scene. We merge the traditional approaches of reconstructing image-extractable features and of modeling via user-provided geometry. We use features to obtain a first guess for structure and motion, fit geometric primitives, correct the structure so that reconstructed features lie exactly on geometric primitives and optimize both structure and motion in a bundle adjustment manner while enforcing the underlying constraints. We specialize this general scheme to the point features and the plane geometric primitives. The underlying geometric relationships are described by multi-coplanarity constraints. We propose a minimal parameterization of the structure enforcing these constraints and use it to devise the corresponding maximum likelihood estimator. The recovered primitives are then textured from the input images. The result is an accurate and photorealistic model. Experimental results using simulated data confirm that the accuracy of the model using the constrained methods is of clearly superior quality compared to that of traditional methods and that our approach performs better than existing ones, for various scene configurations. In addition, we observe that the method still performs better in a number of configurations when the observed surfaces are not exactly planar. We also validate our method using real images.
Our approach for relating the scale of two bifocal calibrations is based on coplanar line pairs. To our knowledge, coplanar lines have been used for pose estimation, but only in a two-view context and with a Manhattan-world assumption, to identify planar structures @cite_31 . A related topic is plane-based SfM, but it has mostly been studied assuming prior knowledge (user-given) about the scene planes @cite_49 @cite_12 or in tracking scenarios with videos @cite_16 . In @cite_9 @cite_6 , a reference plane is used to estimate both the global translations and 3D points, but it must be visible in all images.