Invariant tracking for planar rigid body dynamics

Hamiltonian dynamics of planar affinely-rigid body

The general formulation of the mechanics of an affinely-rigid body in n dimensions was presented in [1, 2, 3]. Obviously, it is the special case n = 3 that is directly physically applicable, if a proper potential model is chosen. For realistic potentials, the three-dimensional problem is very difficult. The reason is that the group SO(3, IR) (and generally SO(n, IR) for n > 2) is semisimple and...

Rigid Motion Constraints for Tracking Planar Objects

Typical tracking algorithms exploit temporal coherence, in the sense of expecting only small object motions. Even without exact knowledge of the scene, additional spatial coherence can be exploited by expecting only a rigid 3d motion. Feature tracking will benefit from knowing about this rigidity of the scene, especially if individual features cannot be tracked by themselves due to occlusions o...

Dynamics and Controllability of a Planar Rigid Body with aThruster

In this paper we discuss the dynamics of a planar rigid body with a thruster. We identify the position and orientation of the planar rigid body with an element of the Lie group SE(2). The invariance of the kinetic energy Lagrangian and the forcing term (thrust) under the SE(2) action of translations and rotations is used to obtain a set of Poisson-reduced equations on T SE(2)=SE(2) which is iso...

Title : Rigid body dynamics

High performance rigid body tracking

Many potential applications of computer vision require a 3D tracking system which can cope with very unpredictable, rapid motions of the camera while operating at frame rate. This cannot be achieved using previously available techniques. Robustness in tracking is achieved by combining different systems in a non trivial way. This allows trackers to be designed in such a way that they are not gen...