While the common environment representation in structure from motion is given by a sparse point cloud, the community has also investigated the use of lines to better enforce the inherent regularities in man-made surroundings. Following the potential of this idea, the present paper introduces a more flexible higher-order extension of points that provides a general model for structural edges in the environment, no matter if straight or curved. Our model relies on linked Bezier curves, the geometric intuition of which proves great benefits during parameter initialization and regularization. We present the first fully automatic pipeline that is able to generate spline-based representations without any human supervision. Besides a full graphical formulation of the problem, we introduce both geometric and photometric cues as well as higher-level concepts such overall curve visibility and viewing angle restrictions to automatically manage the correspondences in the graph. Results prove that curve-based structure from motion with splines is able to outperform state-of-the-art sparse feature-based methods, as well as to model curved edges in the environment.
Curve-based geometric incidence relations have since ever intrigued the structure-from-motion community. For example, rather than solving the relative pose problem from points correspondences @cite_1 @cite_33 , early works such as @cite_34 and lateron @cite_19 and @cite_22 looked into the possibility of using curves and surface tangents to solve the stereo calibration problem. However, the presented constraints for solving geometric computer vision problems are easily influenced by noise, and not practically useful. In order to improve the quality of curve-based structure from motion, further works therefore looked at special types of curves such as straight lines and cones, respectively @cite_9 @cite_2 .
@cite_22 @cite_33 @cite_9 @cite_1 @cite_19 @cite_2 @cite_34
2150416825 1936156518 2135064677 1925320057
Abstract The topological obstacles to the matching of smooth curves in stereo images are shown to occur at epipolar tangencies. Matching is possible when these tangencies satisfy certain projective constraints (the tangent lines form corresponding pencils) and metric contraints dependent on the camera geometry. Such points are good matching primitives, even when the image curves correspond to smooth surface profiles. An iterative scheme for improving camera calibration based on these results is derived, and performance demonstrated on real data. We propose a novel solution for computing the relative pose between two generalized cameras that includes reconciling the internal scale of the generalized cameras. This approach can be used to compute a similarity transformation between two coordinate systems, making it useful for loop closure in visual odometry and registering multiple structure from motion reconstructions together. In contrast to alternative similarity transformation methods, our approach uses 2D-2D image correspondences thus is not subject to the depth uncertainty that often arises with 3D points. We utilize a known vertical direction (which may be easily obtained from IMU data or vertical vanishing point detection) of the generalized cameras to solve the generalized relative pose and scale problem as an efficient Quadratic Eigenvalue Problem. To our knowledge, this is the first method for computing similarity transformations that does not require any 3D information. Our experiments on synthetic and real data demonstrate that this leads to improved performance compared to methods that use 3D-3D or 2D-3D correspondences, especially as the depth of the scene increases. Is the real problem in resolving correspondence using current stereo algorithms the lack of the "right" matching criterion? In studying the related task of reconstructing three-dimensional space curves from their projections in multiple views, we suggest that the problem is more basic: matching and reconstruction are coupled, and so reconstruction algorithms should exploit this rather than assuming that matching can be successfully performed before reconstruction. To realize this coupling, a generative model of curves is introduced which has two key components: (i) a prior distribution of general space curves and (ii) an image formation model which describes how 3D curves are projected onto the image plane. A novel aspect of the image formation model is that it uses an exact description of the gradient field of a piecewise constant image. Based on this forward model, a fully automatic algorithm for solving the inverse problem is developed for an arbitrary number of views. The resulting algorithm is robust to partial occlusion, deficiencies in image curve extraction and it does not rely on photometric information. The relative motion of the cameras is assumed to be given. Several experiments are carried out on various realistic scenarios. In particular, we focus on scenes where traditional correlation-based methods would fail. Common techniques in structure from motion do not explicitly handle foreground occlusions and disocclusions, leading to several trajectories of a single 3D point. Hence, different discontinued trajectories induce a set of (more inaccurate) 3D points instead of a single 3D point, so that it is highly desirable to enforce long continuous trajectories which automatically bridge occlusions after a re-identification step. The solution proposed in this paper is to connect features in the current image to trajectories which discontinued earlier during the tracking. This is done using a correspondence analysis which is designed for wide baselines and an outlier elimination strategy using the epipolar geometry. The reference to the 3D object points can be used as a new constraint in the bundle adjustment. The feature localization is done using the SIFT detector extended by a Gaussian approximation of the gradient image signal. This technique provides the robustness of SIFT coupled with increased localization accuracy. Our results show that the reconstruction can be drastically improved and the drift is reduced, especially in sequences with occlusions resulting from foreground objects. In scenarios with large occlusions, the new approach leads to reliable and accurate results while a standard reference method fails.