On computing exact visual hulls of solids bounded by smooth surfaces

This paper presents a method for computing the visual hull that is based on two novel representations: the rim mesh, which describes the connectivity of contour generators on the object surface; and the visual hull mesh, which describes the exact structure of the surface of the solid formed by intersecting a finite number of visual cones. We describe the topological features of these meshes and show how they can be identified in the image using epipolar constraints. These constraints are used to derive an image-based practical reconstruction algorithm that works with weakly calibrated cameras. Experiments on synthetic and real data validate the proposed approach.

[1]  Ramesh Raskar,et al.  Image-based visual hulls , 2000, SIGGRAPH.

[2]  Richard Szeliski,et al.  Rapid octree construction from image sequences , 1993 .

[3]  Bruce G. Baumgart,et al.  Geometric modeling for computer vision. , 1974 .

[4]  Julie Dorsey,et al.  Reconstructing 3D Tree Models from Instrumented Photographs , 2001, IEEE Computer Graphics and Applications.

[5]  David Nistér,et al.  Reconstruction from Uncalibrated Sequences with a Hierarchy of Trifocal Tensors , 2000, ECCV.

[6]  J J Koenderink,et al.  What Does the Occluding Contour Tell Us about Solid Shape? , 1984, Perception.

[7]  Amnon Shashua,et al.  Novel view synthesis in tensor space , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[8]  Luc Van Gool,et al.  Stratified Self-Calibration with the Modulus Constraint , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

[9]  Andrew Zisserman,et al.  Surface Reconstruction from Multiple Views Using Apparent Contours and Surface Texture , 2000, Confluence of Computer Vision and Computer Graphics.

[10]  Roberto Cipolla,et al.  Motion from the frontier of curved surfaces , 1995, Proceedings of IEEE International Conference on Computer Vision.

[11]  Peter F. Sturm,et al.  Critical motion sequences for monocular self-calibration and uncalibrated Euclidean reconstruction , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[12]  John Porrill,et al.  Curve matching and stereo calibration , 1991, Image Vis. Comput..

[13]  Roberto Cipolla,et al.  The visual motion of curves and surfaces , 1998, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[14]  Olivier D. Faugeras,et al.  Using Extremal Boundaries for 3-D Object Modeling , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[15]  Olivier D. Faugeras,et al.  What can two images tell us about a third one? , 1994, ECCV.

[16]  Matthias Zwicker,et al.  Ieee Transactions on Visualization and Computer Graphics Ewa Splatting , 2002 .

[17]  Reinhard Koch,et al.  Self-calibration and metric reconstruction in spite of varying and unknown internal camera parameters , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[18]  M. Docarmo.  Differential geometry of curves and surfaces , 1976 .

[19]  Jean Ponce,et al.  Automatic model construction, pose estimation, and object recognition from photographs using triangular splines , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[20]  Jean Ponce,et al.  Automatic Model Construction and Pose Estimation From Photographs Using Triangular Splines , 1998, IEEE Trans. Pattern Anal. Mach. Intell..

[21]  Peter J. Giblin,et al.  Epipolar curves on surfaces , 1995, Image Vis. Comput..

[22]  Zicheng Liu,et al.  Model-based bundle adjustment with application to face modeling , 2001, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001.

[23]  H. Piaggio.  Differential Geometry of Curves and Surfaces , 1952, Nature.

[24]  Roberto Cipolla,et al.  Camera Self-Calibration from Unknown Planar Structures Enforcing the Multiview Constraints between Collineations , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[25]  Marie-Odile Berger,et al.  3D Surface Reconstruction Using Occluding Contours , 1995, International Journal of Computer Vision.

[26]  A. Laurentini,et al.  The Visual Hull Concept for Silhouette-Based Image Understanding , 1994, IEEE Trans. Pattern Anal. Mach. Intell..