Efficiently Determining Silhouette Consistency

Volume intersection is a frequently used technique to solve the Shape-From-Silhouette problem, which constructs a 3D object estimate from a set of silhouettes taken with calibrated cameras. It is natural to develop an efficient algorithm to determine the consistency of a set of silhouettes before performing time-consuming reconstruction, so that inaccurate silhouettes can be omitted. In this paper we first present a fast algorithm to determine the consistency of three silhouettes from known (but arbitrary) viewing directions, assuming the projection is scaled orthographic. The temporal complexity of the algorithm is linear in the number of points of the silhouette boundaries. We further prove that a set of more than three convex silhouettes are consistent if and only if any three of them are consistent. Another possible application of our approach is to determine the miscalibrated cameras in a large camera system. A consistent subset of cameras can be determined on the fly and miscalibrated cameras can also be recalibrated at a coarse scale. Real and synthesized data are used to demonstrate our results.

[1]  J. Eckhoff.  Helly, Radon, and Carathéodory Type Theorems , 1993 .

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

[3]  L. Davis,et al.  Background and foreground modeling using nonparametric kernel density estimation for visual surveillance , 2002, Proc. IEEE.

[4]  W. Eric L. Grimson,et al.  Adaptive background mixture models for real-time tracking , 1999, Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149).

[5]  BakerSimon,et al.  Shape-From-Silhouette Across Time Part II , 2005 .

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

[7]  David A. Forsyth,et al.  Recognizing algebraic surfaces from their outlines , 1993, Vision.

[8]  David W. Jacobs,et al.  Judging Whether Multiple Silhouettes Can Come from the Same Object , 2001, IWVF.

[9]  Takeo Kanade,et al.  Shape-From-Silhouette Across Time Part I: Theory and Algorithms , 2005, International Journal of Computer Vision.

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

[11]  N. Otsu.  A threshold selection method from gray level histograms , 1979 .

[12]  Andrea Bottino,et al.  Introducing a New Problem: Shape-from-Silhouette when the Relative Positions of the Viewpoints is Unknown , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[13]  Roberto Cipolla,et al.  Silhouette Coherence for Camera Calibration under Circular Motion , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[14]  Richard Szeliski,et al.  Robust Shape Recovery from Occluding Contours Using a Linear Smoother , 1993, Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

[15]  Andrew Blake,et al.  Surface shape from the deformation of apparent contours , 1992, International Journal of Computer Vision.

[16]  Fumiaki Tomita,et al.  Plane-based calibration algorithm for multi-camera systems via factorization of homography matrices , 2003, Proceedings Ninth IEEE International Conference on Computer Vision.

[17]  Nina Amenta,et al.  Helly theorems and generalized linear programming , 1993, SCG '93.

[18]  Rama Chellappa,et al.  Segmentation and Probabilistic Registration of Articulated Body Models , 2006, 18th International Conference on Pattern Recognition (ICPR'06).

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

[20]  David J. Kriegman,et al.  Structure and Motion from Images of Smooth Textureless Objects , 2004, ECCV.

[21]  Rama Chellappa,et al.  Identification of humans using gait , 2004, IEEE Transactions on Image Processing.

[22]  Takeo Kanade,et al.  Shape-From-Silhouette Across Time Part II: Applications to Human Modeling and Markerless Motion Tracking , 2005, International Journal of Computer Vision.

[23]  Roberto Cipolla,et al.  Generalised Epipolar Constraints , 1996, ECCV.