Projective Shape Analysis for Noncalibrated Pinhole Camera Views . To the Memory of

In this paper nonparametric statistical technology is derived for estimating with confidence a 3D configuration of points from noncalibrated camera views of such a configuration. This is applied to pattern recognition of a spatial scene, from multiple views, in absence of occlusions. keywordsscene reconstruction, pinhole camera views, image analysis, projective shape data analysis AMS subject classificationPrimary 62G35 Secondary 62H35 ∗Research supported by National Science Foundation Grant IIS-0307998 †Research supported by National Science Foundation Grant DMS-0652353

[1]  S. Shankar Sastry,et al.  An Invitation to 3-D Vision , 2004 .

[2]  M. J. Prentice.  A distribution-free method of interval estimation for unsigned directional data , 1984 .

[3]  N. L. Johnson,et al.  Multivariate Analysis , 1958, Nature.

[4]  Olivier D. Faugeras,et al.  What can be seen in three dimensions with an uncalibrated stereo rig , 1992, ECCV.

[5]  D. Kendall.  SHAPE MANIFOLDS, PROCRUSTEAN METRICS, AND COMPLEX PROJECTIVE SPACES , 1984 .

[6]  K. Mardia,et al.  Projective Shape Analysis , 1999 .

[7]  F. Bookstein,et al.  Morphometric Tools for Landmark Data: Geometry and Biology , 1999 .

[8]  Stefano Soatto,et al.  3-D Shape Estimation and Image Restoration - Exploiting Defocus and Motion Blur , 2006 .

[9]  M. Fréchet.  Les éléments aléatoires de nature quelconque dans un espace distancié , 1948 .

[10]  R. Bhattacharya,et al.  LARGE SAMPLE THEORY OF INTRINSIC AND EXTRINSIC SAMPLE MEANS ON MANIFOLDS—II , 2003 .

[11]  C. Goodall.  Procrustes methods in the statistical analysis of shape , 1991 .

[12]  V. Patrangenaru,et al.  NEW LARGE SAMPLE AND BOOTSTRAP METHODS ON SHAPE SPACES IN HIGH LEVEL ANALYSIS OF NATURAL IMAGES , 2001 .

[13]  Nicholas I. Fisher,et al.  Improved pivotal methods for constructing confidence regions with directional data , 1996 .

[14]  Richard I. Hartley,et al.  In defence of the 8-point algorithm , 1995, Proceedings of IEEE International Conference on Computer Vision.

[15]  Anuj Srivastava,et al.  Interpolations with elasticae in Euclidean spaces , 2004 .

[16]  T. K. Carne,et al.  Shape and Shape Theory , 1999 .

[17]  William H. Press,et al.  Numerical recipes in C , 2002 .

[18]  K. Mardia,et al.  Matching problems for unlabelled configurations , 2003 .

[19]  Yoshiaki Shirai,et al.  Three-Dimensional Computer Vision , 1987, Symbolic Computation.

[20]  R. Bhattacharya,et al.  Nonparametic estimation of location and dispersion on Riemannian manifolds , 2002 .

[21]  Rajiv Gupta,et al.  Stereo from uncalibrated cameras , 1992, Proceedings 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[22]  K. Mardia,et al.  Affine shape analysis and image analysis , 2003 .