An SVD-Based Projection Method for Interpolation on \u3cem\u3eSE\u3c/em\u3e(3)

This paper develops a method for generating smooth trajectories for a moving rigid body with specified boundary conditions. Our method involves two key steps: 1) the generation of optimal trajectories in GA+(n), a subgroup of the affine group in IRn and 2) the projection of the trajectories onto SE(3), the Lie group of rigid body displacements. The overall procedure is invariant with respect to both the local coordinates on the manifold and the choice of the inertial frame. The benefits of the method are threefold. First, it is possible to apply any of the variety of well-known efficient techniques to generate optimal curves on GA+(n). Second, the method yields approximations to optimal solutions for general choices of Riemannian metrics on SE(3). Third, from a computational point of view, the method we propose is less expensive than traditional methods

An SVD-Based Projection Method for Interpolation on \u3ci\u3eSE\u3c/i\u3e(3)

This paper develops a method for generating smooth trajectories for a moving rigid body with specified boundary conditions. Our method involves two key steps: 1) the generation of optimal trajectories in GA+(n), a subgroup of the affine group in Rn and 2) the projection of the trajectories onto SE(3), the Lie group of rigid body displacements. The overall procedure is invariant with respect to both the local coordinates on the manifold and the choice of the inertial frame. The benefits of the method are threefold. First, it is possible to apply any of the variety of well-known efficient techniques to generate optimal curves on GA+(n). Second, the method yields approximations to optimal solutions for general choices of Riemannian metrics on SE(3). Third, from a computational point of view, the method we propose is less expensive than traditional methods

Probabilistc and sequential computation of optical flow using temporal coherence

Caption title. "Revised version of LIDS-P-2122."Includes bibliographical references (p. 23-26).Supported by the Office on Naval Research. N00014-91-J-1004 N00014-91-J-1120 (Random Field in Oceanography ARI) Supported by the National Sceice Foundation. MIP-9195281 Supported by the Army Research Office. DAAL03-86-K-0171Toshio M. Chin, William C. Karl, Alan S. Willsky