The Geometry and Matching of Curves in Multiple Views

In this paper there are two innovations. First, the geometry of imaged curves is developed in two and three views. A set of results are given for both conics and non-algebraic curves. It is shown that the homography between the images induced by the plane of the curve can be computed from two views given only the epipolar geometry, and that the trifocal tensor can be used to transfer a conic or the curvature from two views to a third. The second innovation is an algorithm for automatically matching individual curves between images. The algorithm uses both photometric information and the multiple view geometric results. For image pairs the homography facilitates the computation of a neighbourhood cross-correlation based matching score for putative curve correspondences. For image triplets cross-correlation matching scores are used in conjunction with curve transfer based on the trifocal geometry to disambiguate matches. Algorithms are developed for both short and wide baselines. The algorithms are robust to deficiencies in the curve segment extraction and partial occlusion. Experimental results are given for image pairs and triplets, for varying motions between views, and for different scene types. The method is applicable to curve matching in stereo and trinocular rigs, and as a starting point for curve matching through monocular image sequences.

[1]  F. Bookstein.  Fitting conic sections to scattered data , 1979 .

[2]  J P Frisby,et al.  PMF: A Stereo Correspondence Algorithm Using a Disparity Gradient Limit , 1985, Perception.

[3]  Michael Brady,et al.  Stereo Matching Of Curves By Least Deformation , 1989, Proceedings. IEEE/RSJ International Workshop on Intelligent Robots and Systems '. (IROS '89) 'The Autonomous Mobile Robots and Its Applications.

[4]  Andrew Blake,et al.  Robust Estimation of Surface Curvature from Deformation of Apparent Contours , 1990, ECCV.

[5]  Régis Vaillant.  Using Occluding Contours for 3D Object Modeling , 1990, ECCV.

[6]  Olivier D. Faugeras,et al.  Curve-based stereo: figural continuity and curvature , 1991, Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[7]  R. Nevatia,et al.  Use of monocular groupings and occlusion analysis in a hierarchical stereo system , 1991, Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[8]  B. Benhabib,et al.  3D-pose estimation from a quadratic-curved feature in two perspective views , 1992, [1992] Proceedings. 11th IAPR International Conference on Pattern Recognition.

[9]  Andrew Zisserman,et al.  Geometric invariance in computer vision , 1992 .

[10]  Andrew Zisserman,et al.  A Case Against Epipolar Geometry , 1993, Applications of Invariance in Computer Vision.

[11]  Thierry Viéville,et al.  Canonic Representations for the Geometries of Multiple Projective Views , 1994, ECCV.

[12]  Amnon Shashua,et al.  Trilinearity in Visual Recognition by Alignment , 1994, ECCV.

[13]  Richard I. Hartley,et al.  A linear method for reconstruction from lines and points , 1995, Proceedings of IEEE International Conference on Computer Vision.

[14]  Jan J. Gerbrands,et al.  Method for matching general stereo planar curves , 1995, Image Vis. Comput..

[15]  Rachid Deriche,et al.  A Robust Technique for Matching two Uncalibrated Images Through the Recovery of the Unknown Epipolar Geometry , 1995, Artif. Intell..

[16]  Gérard G. Medioni,et al.  Segmented shape descriptions from 3-view stereo , 1995, Proceedings of IEEE International Conference on Computer Vision.

[17]  Long Quan,et al.  Conic Reconstruction and Correspondence From Two Views , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[18]  Paul A. Beardsley,et al.  3D Model Acquisition from Extended Image Sequences , 1996, ECCV.

[19]  Andrew Zisserman,et al.  Robust parameterization and computation of the trifocal tensor , 1997, Image Vis. Comput..

[20]  Cordelia Schmid,et al.  Automatic line matching across views , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[21]  Andrew Zisserman,et al.  Quadric Surface Reconstruction from Dual-Space Geometry. , 1998, ICCV 1998.

[22]  Andrew Zisserman,et al.  Quadric reconstruction from dual-space geometry , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).