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Abstract : |
implicit systems, exterior differential systems, differential algebraic equations The "visual motion estimation " problem concerns the estimation of the motion of an object viewed under projection. This paper addresses the feasibility of such a problem. We will show that the model which defines the visual motion estimation problem for feature points in the Euclidean 3D space lacks both linear and local (weak) observability. The locally observable manifold is covered with three levels of Lie differentiations. It is possible, indeed, to reduce the set of indistinguishable states by imposing metric constraints on the state-space. We analyze a model for visual motion estimation in terms of identification of an exterior differential system, whose parameters live on a topological manifold, called the essential manifold, which explicitly encodes the forementioned metric constraints. We show that rigid motion is globally observable/identifiable under perspective projection with zero level of Lie differentiation under some general position conditions. Such conditions hold when the path of the viewer and the visible objects cannot be embedded in a quadric surface of IR, |
