2016/04/27 by Ricardo Fabbri, Benjamin B. Kimia, Benjamin Kimia · 19 citations
Computer Science · Engineering · Mathematics · #3D Shape Modeling and Analysis #Advanced Vision and Imaging #Camera resectioning #Curvature #Differential (mechanical device) #Differential geometry #Digital Image Processing Techniques #Epipolar geometry #Fundamental matrix (linear differential equation) #Image rectification #Motion field #Point cloud #Projective geometry #acm:53A04 #acm:53A17 #acm:53A20 #cs.CG #cs.CV #cs.GR #math.DG #msc:53A04 #msc:53A17 #msc:53A20
paper · pdf · doi:10.1007/s11263-016-0912-7
published in International Journal of Computer Vision 120(3), 324-346 (Springer Science+Business Media) · International Journal of Computer Vision Final Accepted version. International Journal of Computer Vision, 2016. The final publication is available at Springer via http://dx.doi.org/10.1007/s11263-016-0912-7
arxiv created 2016/04/27 · arxiv updated 2016/04/29 · openalex publication_date 2016/05/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
The field of multiple view geometry has seen tremendous progress in reconstruction and calibration due to methods for extracting reliable point features and key developments in projective geometry. Point features, however, are not available in certain applications and result in unstructured point cloud reconstructions. General image curves provide a complementary feature when keypoints are scarce, and result in 3D curve geometry, but face challenges not addressed by the usual projective geometry of points and algebraic curves. We address these challenges by laying the theoretical foundations of a framework based on the differential geometry of general curves, including stationary curves, occluding contours, and non-rigid curves, aiming at stereo correspondence, camera estimation (including calibration, pose, and multiview epipolar geometry), and 3D reconstruction given measured image curves. By gathering previous results into a cohesive theory, novel results were made possible, yielding three contributions. First we derive the differential geometry of an image curve (tangent, curvature, curvature derivative) from that of the underlying space curve (tangent, curvature, curvature derivative, torsion). Second, we derive the differential geometry of a space curve from that of two corresponding image curves. Third, the differential motion of an image curve is derived from camera motion and the differential geometry and motion of the space curve. The availability of such a theory enables novel curve-based multiview reconstruction and camera estimation systems to augment existing point-based approaches. This theory has been used to reconstruct a "3D curve sketch", to determine camera pose from local curve geometry, and tracking; other developments are underway.