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.
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.  From the Publisher: A basic problem in computer vision is to understand the structure of a real world scene given several images of it. Recent major developments in the theory and practice of scene reconstruction are described in detail in a unified framework. The book covers the geometric principles and how to represent objects algebraically so they can be computed and applied. The authors provide comprehensive background material and explain how to apply the methods and implement the algorithms directly. Analytical reconstruction of 3D curves from their stereo images is an important issue in computer vision. We present an optimization framework for such a problem based on a nonuniform rational B-spline (NURBS) curve model that converts reconstruction of a 3D curve into reconstruction of control points and weights of a NURBS representation of the curve, accordingly bypassing the error-prone point-to-point correspondence matching. Perspective invariance of NURBS curves and constraints deduced on stereo NURBS curves are employed to formulate the 3D curve reconstruction problem into a constrained nonlinear optimization. A parallel rectification technique is then adopted to simplify the constraints, and the Levenberg–Marquardt algorithm is applied to search for the optimal solution of the simplified problem. The results from our experiments show that the proposed framework works stably in the presence of different data samplings, randomly posed noise, and partial loss of data and is potentially suitable for real scenes. We present a system that can reconstruct 3D geometry from large, unorganized collections of photographs such as those found by searching for a given city (e.g., Rome) on Internet photo-sharing sites. Our system is built on a set of new, distributed computer vision algorithms for image matching and 3D reconstruction, designed to maximize parallelism at each stage of the pipeline and to scale gracefully with both the size of the problem and the amount of available computation. Our experimental results demonstrate that it is now possible to reconstruct city-scale image collections with more than a hundred thousand images in less than a day. Motivated by a Bayesian vision of the 3D multi-view reconstruction from images problem, we propose a dense 3D reconstruction technique that jointly refines the shape and the camera parameters of a scene by minimizing the photometric reprojection error between a generated model and the observed images, hence considering all pixels in the original images. The minimization is performed using a gradient descent scheme coherent with the shape representation (here a triangular mesh), where we derive evolution equations in order to optimize both the shape and the camera parameters. This can be used at a last refinement step in 3D reconstruction pipelines and helps improving the 3D reconstruction's quality by estimating the 3D shape and camera calibration more accurately. Examples are shown for multi-view stereo where the texture is also jointly optimized and improved, but could be used for any generative approaches dealing with multi-view reconstruction settings (ie depth map fusion, multi-view photometric stereo). This paper introduces a novel method for feature-based 3D reconstruction using multiple calibrated 2D views. We use a probabilistic formulation of the problem in the 3D, reconstructed space that allows using features that cannot be matched one-to-one, or which cannot be precisely located, such as points along edges. The reconstructed scene, modelled as a probability distribution in the 3D space, is defined as the intersection of all reconstructions compatible with each available view. We introduce a method based on importance sampling to retrieve individual samples from that distribution, as well as an iterative method to identify contiguous regions of high density. This allows the reconstruction of continuous 3D curves compatible with all the given input views, without establishing specific correspondences and without relying on connectivity in the input images, while accounting for uncertainty in the input observations, due e.g. to noisy images and poorly calibrated cameras. The technical formulation is attractive in its flexibility and genericity. The implemented system, evaluated on several very different publicly-available datasets, shows results competitive with existing methods, effectively dealing with arbitrary numbers of views, wide baselines and imprecise camera calibrations. We address the problem of camera motion and 3D structure reconstruction from line correspondences across multiple views, from initialization to final bundle adjustment. One of the main difficulties when dealing with line features is their algebraic representation. First, we consider the triangulation problem. Based on Plucker coordinates to represent the 3D lines, we propose a maximum likelihood algorithm, relying on linearizing the Plucker constraint and on a Plucker correction procedure, computing the closest Plucker coordinates to a given 6-vector. Second, we consider the bundle adjustment problem, which is essentially a nonlinear optimization process on camera motion and 3D line parameters. Previous overparameterizations of 3D lines induce gauge freedoms and or internal consistency constraints. We propose the orthonormal representation, which allows handy nonlinear optimization of 3D lines using the minimum four parameters with an unconstrained optimization engine. We compare our algorithms to existing ones on simulated and real data. Results show that our triangulation algorithm outperforms standard linear and bias-corrected quasi-linear algorithms, and that bundle adjustment using our orthonormal representation yields results similar to the standard maximum likelihood trifocal tensor algorithm, while being usable for any number of views. We present a novel method for recovering the 3D-line structure of a scene from multiple widely separated views. Traditional optimization-based approaches to line-based structure from motion minimize the error between measured line segments and the projections of corresponding 3D lines. In such a case, 3D lines can be optimized using a minimum of 4 parameters. We show that this number of parameters can be further reduced by introducing additional constraints on the orientations of lines in a 3D scene. In our approach, 2D-lines are automatically detected in images with the assistance of an EM-based vanishing point estimation method which assumes the existence of edges along mutally orthogonal vanishing directions. Each detected line is automatically labeled with the orientation (e.g. vertical, horizontal) of the 3D line which generated the measurement, and it is this additional knowledge that we use to reduce the number of degrees of freedom of 3D lines during optimization. We present 3D reconstruction results for urban scenes based on manually established feature correspondences across images.