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.
Modern structure from motion (SfM) remains dependent on point features to recover camera positions, meaning that reconstruction is severely hampered in low-texture environments, for example scanning a plain coffee cup on an uncluttered table. We show how 3D curves can be used to refine camera position estimation in challenging low-texture scenes. In contrast to previous work, we allow the curves to be partially observed in all images, meaning that for the first time, curve-based SfM can be demonstrated in realistic scenes. The algorithm is based on bundle adjustment, so needs an initial estimate, but even a poor estimate from a few point correspondences can be substantially improved by including curves, suggesting that this method would benefit many existing systems. In this paper, we extend the notion of affine shape, introduced by Sparr, from finite point sets to curves. The extension makes it possible to reconstruct 3D-curves up to projective transformations, from a number of their 2D-projections. We also extend the bundle adjustment technique from point features to curves. The first step of the curve reconstruction algorithm is based on affine shape. It is independent of choice of coordinates, is robust, does not rely on any preselected parameters and works for an arbitrary number of images. In particular this means that, except for a small set of curves (e.g. a moving line), a solution is given to the aperture problem of finding point correspondences between curves. The second step takes advantage of any knowledge of measurement errors in the images. This is possible by extending the bundle adjustment technique to curves. Finally, experiments are performed on both synthetic and real data to show the performance and applicability of the algorithm. 3D morphable models are low-dimensional parameterizations of 3D object classes which provide a powerful means of associating 3D geometry to 2D images. However, morphable models are currently generated from 3D scans, so for general object classes such as animals they are economically and practically infeasible. We show that, given a small amount of user interaction (little more than that required to build a conventional morphable model), there is enough information in a collection of 2D pictures of certain object classes to generate a full 3D morphable model, even in the absence of surface texture. The key restriction is that the object class should not be strongly articulated, and that a very rough rigid model should be provided as an initial estimate of the “mean shape.” The model representation is a linear combination of subdivision surfaces, which we fit to image silhouettes and any identifiable key points using a novel combined continuous-discrete optimization strategy. Results are demonstrated on several natural object classes, and show that models of rather high quality can be obtained from this limited information. Interest point-based multiview 3D reconstruction and calibration methods have been very successful in select applications but are not applicable when an abundance of feature points are not available. They also lead to an unorganized point cloud reconstruction where the geometry of the scene is not explicit. The multiview stereo methods on the other hand yield dense surface geometry but require a highly controlled or calibrated setting. We propose and develop a novel framework for 3D reconstruction and calibration based on image curve content, whose output is a 3D curve sketch, an unorganized set of 3D curve fragments. This approach, which is meant to augment the previous approaches, results in a reconstruction of geometric curve structure which can serve as a scaffold on which surface patches can be potentially reconstructed. It is intented for the setting where a number of images are available with coarsely calibrated cameras. The approach operates in two stages. A reliable partial 3D curve sketch is first reconstructed and this is used to refine the cameras to yield a more complete 3D curve sketch in a second stage. A key advantage of this approach is the ability to integrate information across a large number of views. The results have been evaluated on a few datasets.