From Multiview Image Curves to 3D Drawings

Reconstructing 3D scenes from multiple views has made impressive strides in recent years, chiefly by correlating isolated feature points, intensity patterns, or curvilinear structures. In the general setting - without controlled acquisition, abundant texture, curves and surfaces following specific models or limiting scene complexity - most methods produce unorganized point clouds, meshes, or voxel representations, with some exceptions producing unorganized clouds of 3D curve fragments. Ideally, many applications require structured representations of curves, surfaces and their spatial relationships. This paper presents a step in this direction by formulating an approach that combines 2D image curves into a collection of 3D curves, with topological connectivity between them represented as a 3D graph. This results in a 3D drawing, which is complementary to surface representations in the same sense as a 3D scaffold complements a tent taut over it. We evaluate our results against truth on synthetic and real datasets.Comment: Expanded ECCV 2016 version with tweaked figures and including an overview of the supplementary material available at multiview-3d-drawing.sourceforge.ne

Reconstruction of Curves in R³, using Factorization and Bundle Adjustment

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 2Dprojections. 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, is independent of choice of coordinates, robust, does not rely on any preselected parameters and works for an arbitrary number of images. In particular this means that 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

Reconstruction of curves in ℜ3, using factorization and bundle adjustment

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, is independent of choice of coordinates, robust, does not rely on any preselected parameters and works for an arbitrary number of images. In particular this means that 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

Cross-Calibration and Minimum Precision Standards for Dual-Energy X-Ray Absorptiometry: The 2005 ISCD Official Positions

The International Society for Clinical Densitometry (ISCD) Committee on Standards of Bone Measurement (CSBM) consists of experts in technical aspects of bone densitometry. The CSBM recently reviewed the scientific literature on cross-calibration and precision assessment. A report with recommendations was presented at the 2005 ISCD Position Development Conference (PDC). Based on a thorough review of the data by the ISCD Expert Panel during the conference, the ISCD adopted Official Positions with respect to (1) cross-calibration when changing or replacing hardware; (2) the approach to cross-calibration when an entire system is changed to one made by either the same or a different manufacturer; (3) when no cross-calibration study or bone mineral density (BMD) comparison is done between facilities; and (4) the minimum acceptable precision for an individual technologist. We present here the ISCD Official Positions on these topics that were established as a result of the 2005 PDC, together with the associated rationales and supportive evidence

High-Order Differential Geometry of Curves for Multiview Reconstruction and Matching

Abstract. The relationship between the orientation and curvature of projected curves and the orientation and curvature of the underlying space curve has been previously established. This has allowed a disambiguation of correspondences in two views and a transfer of these properties to a third view for confirmation. We propose that a higher-order intrinsic differential geometry attribute, namely, curvature derivative, is necessary to account for the range of variation of space curves and their projections. We derive relationships between curvature derivative in a projected view, and curvature derivative and torsion of the underlying space curve. Regardless of the point, tangent, and curvature, any pair of curvature derivatives are possible correspondences, but most would lead to very high torsion and curvature derivatives. We propose that the minimization of third order derivatives of the reconstruction, which combines torsion and curvature derivative of the space curve, regularizes the process of finding the correct correspondences.