Direct computation of qualitative 3D shape and motion invariants

The author shows that the sign of the normal curvature in a given direction at a given point in the image can be computed from a simple difference of slopes of line-segments in one image. Using this result, local surface patches can be classified as convex, concave, parabolic (cylindrical), hyperbolic (saddle point) or planar. At the same time the translational component of the optical flow is obtained, from which the focus of expansion can be computed. In addition, the axes of principal curvature and the axes of zero curvature are obtained.<<ETX>>

[1]  H. C. Longuet-Higgins,et al.  A computer algorithm for reconstructing a scene from two projections , 1981, Nature.

[2]  Randal C. Nelson,et al.  Qualitative detection of motion by a moving observer , 1991, Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[3]  Jan J. Koenderink,et al.  Local structure of movement parallax of the plane , 1976 .

[4]  H. C. Longuet-Higgins,et al.  The interpretation of a moving retinal image , 1980, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[5]  Isaac Weiss,et al.  Projective invariants of shapes , 1988, Proceedings CVPR '88: The Computer Society Conference on Computer Vision and Pattern Recognition.

[6]  Jake K. Aggarwal,et al.  Curvature-based representation of objects from range data , 1986, Image Vis. Comput..

[7]  Daphna Weinshall,et al.  Direct computation of 3-D shape and motion invariants , 1989, Annual Meeting Optical Society of America.

[8]  Ramesh C. Jain,et al.  Invariant surface characteristics for 3D object recognition in range images , 1985, Comput. Vis. Graph. Image Process..

[9]  Thomas S. Huang,et al.  Uniqueness and Estimation of Three-Dimensional Motion Parameters of Rigid Objects with Curved Surfaces , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[10]  A.L Yuille,et al.  Zero crossings on lines of curvature , 1989, Comput. Vis. Graph. Image Process..

[11]  Tomaso Poggio,et al.  Computational vision and regularization theory , 1985, Nature.

[12]  S Ullman,et al.  Maximizing Rigidity: The Incremental Recovery of 3-D Structure from Rigid and Nonrigid Motion , 1984, Perception.

[13]  Berthold K. P. Horn,et al.  Determining Optical Flow , 1981, Other Conferences.

[14]  Andrea J. van Doorn,et al.  Invariant Properties of the Motion Parallax Field due to the Movement of Rigid Bodies Relative to an Observer , 1975 .