The semantic reconstruction of a scene relies in part on the curvilinear structure inherent in images. The recovery of curvilinear structure is not only key to the representation of objects via ridges and other object curves but is also critical to the reconstruction from texture-poor images which lack a sufficient number of features. Prior methods advocate for the recovery of curve segments from images and reconstructing these into an organized collection of 3D curve segments often referred to as the 3D curve sketch, which serves as the basis for further reconstruction of curves and surfaces. Observing that the process of edge grouping can lead to fictitious curves or missing veridical groupings, this paper advocates for a reconstruction of curvilinear structure directly from image edges in the form of a 3D edge sketch. The multiview reconstruction of edges faces significant combinatorial challenges which are effectively addressed in this paper. We demonstrate through experiments that the 3D edge sketch recovers a vast majority of the curvilinear structure and is a reliable substrate from which 3D curves can be constructed.

We present a method for solving two minimal problems for relative camera pose estimation from three views, which are based on three view correspondences of (i) three points and one line and the novel case of (ii) three points and two lines through two of the points. These problems are too difficult to be efficiently solved by the state of the art Gröbner basis methods. Our method is based on a new efficient homotopy continuation (HC) solver framework MINUS, which dramatically speeds up previous HC solving by specializing hc methods to generic cases of our problems. We characterize their number of solutions and show with simulated experiments that our solvers are numerically robust and stable under image noise, a key contribution given the borderline intractable degree of nonlinearity of trinocular constraints. We show in real experiments that (i) sift feature location and orientation provide good enough point-and-line correspondences for three-view reconstruction and (ii) that we can solve difficult cases with too few or too noisy tentative matches, where the state of the art structure from motion initialization fails.

This paper considers and solves the problem of estimating camera pose given a pair of point-tangent correspondences between a 3D scene and a projected image. The problem arises when considering curve geometry as the basis of forming correspondences, computation of structure and calibration, which in its simplest form is a point augmented with the curve tangent. We show that while the resectioning problem is solved with a minimum of three points given the intrinsic parameters, when points are augmented with tangent information only two points are required, leading to substantial robustness and computational savings, e.g., as a minimal engine within ransac. In addition, algorithms are developed to find a practical solution shown to effectively recover camera pose using synthetic and real datasets. This technology is intended as a building block of curve-based structure from motion systems, allowing new views to be incrementally registered to a core set of views for which relative pose has been computed.

We present a method for solving two minimal problems for relative camera pose estimation from three views, which are based on three view correspondences of (i) three points and one line and (ii) three points and two lines through two of the points. These problems are too difficult to be efficiently solved by the state of the art Grobner basis methods. Our method is based on a new efficient homotopy continuation (HC) solver, which dramatically speeds up previous HC solving by specializing HC methods to generic cases of our problems. We show in simulated experiments that our solvers are numerically robust and stable under image noise. We show in real experiment that (i) SIFT features provide good enough point-and-line correspondences for three-view reconstruction and (ii) that we can solve difficult cases with too few or too noisy tentative matches where the state of the art structure from motion initialization fails.

The three-dimensional reconstruction of scenes from multiple views has made impressive strides in recent years, chiefly by methods correlating isolated feature points, intensities, or curvilinear structure. In the general setting, i.e., without requiring controlled acquisition, limited number of objects, abundant patterns on objects, or object curves to follow particular models, the majority of these methods produce unorganized point clouds, meshes, or voxel representations of the reconstructed scene, with some exceptions producing 3D drawings as networks of curves. Many applications, e.g., robotics, urban planning, industrial design, and hard surface modeling, however, require structured representations which make explicit 3D curves, surfaces, and their spatial relationships. Reconstructing surface representations can now be constrained by the 3D drawing acting like a scaffold to hang on the computed representations, leading to increased robustness and quality of reconstruction. This paper presents one way of completing such 3D drawings with surface reconstructions, by exploring occlusion reasoning through lofting algorithms.

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.

The Euclidean distance transform (EDT) is used in various methods in pattern recognition, computer vision, image analysis, physics, applied mathematics and robotics. Until now, several sequential EDT algorithms have been described in the literature, however they are time- and memory-consuming for images with large resolutions. Therefore, parallel implementations of the EDT are required specially for 3D images. This paper presents a parallel implementation based on domain decomposition of a well-known 3D Euclidean distance transform algorithm, and analyzes its performance on a cluster of workstations. The use of a data compression tool to reduce communication time is investigated and discussed. Among the obtained performance results, this work shows that data compression is an essential tool for clusters with low-bandwidth networks.