%0 Conference Paper %B Computer Vision and Pattern Recognition, 1993. Proceedings CVPR '93., 1993 IEEE Computer Society Conference on %D 1993 %T 2D images of 3-D oriented points %A Jacobs, David W. %K 2D %K 3-D %K database %K derivation; %K image %K images; %K indexing; %K linear %K model %K nonrigid %K oriented %K points; %K processing; %K recovery; %K structure-form-motion %K structure-from-motion %K transformation; %X A number of vision problems have been shown to become simpler when one models projection from 3-D to 2-D as a nonrigid linear transformation. These results have been largely restricted to models and scenes that consist only of 3-D points. It is shown that, with this projection model, several vision tasks become fundamentally more complex in the somewhat more complicated domain of oriented points. More space is required for indexing models in a database, more images are required to derive structure from motion, and new views of an object cannot be synthesized linearly from old views %B Computer Vision and Pattern Recognition, 1993. Proceedings CVPR '93., 1993 IEEE Computer Society Conference on %P 226 - 232 %8 1993/06// %G eng %R 10.1109/CVPR.1993.340985 %0 Conference Paper %B Workshop on Visual Motion, 1989.,Proceedings %D 1989 %T Optimal motion estimation %A Spetsakis, M. E %A Aloimonos, J. %K 3D motion interpretation %K Automation %K Computer vision %K computerised pattern recognition %K computerised picture processing %K constraint minimization %K dynamic imagery %K Educational institutions %K feature correspondences %K Gaussian noise %K Image motion analysis %K Laboratories %K maximum-likelihood-principle %K Minimization methods %K Motion analysis %K Motion estimation %K motion parameters %K moving object %K multiple frames %K nonlinear constraint %K Optical computing %K optimal motion estimation %K parameter estimation %K quadratic minimization %K quadratic programming %K redundancy %K rigidity assumption %K robotics applications %K structure-from-motion %K successive images %K two-frame %X The problem of using feature correspondences to recover the structure and 3D motion of a moving object from its successive images is analyzed. They formulate the problem as a quadratic minimization problem with a nonlinear constraint. Then they derive the condition for the solution to be optimal under the assumption of Gaussian noise in the input, in the maximum-likelihood-principle sense. The authors present two efficient ways to approximate it and discuss some inherent limitations of the structure-from-motion problem when two frames are used that should be taken into account in robotics applications that involve dynamic imagery. Finally, it is shown that some of the difficulties inherent in the two-frame approach disappear when redundancy in the data is introduced. This is concluded from experiments using a structure-from-motion algorithm that is based on multiple frames and uses only the rigidity assumption %B Workshop on Visual Motion, 1989.,Proceedings %I IEEE %P 229 - 237 %8 1989/03/20/22 %@ 0-8186-1903-1 %G eng %R 10.1109/WVM.1989.47114