Recursive Motion Estimation on the Essential Manifold
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Abstract:
Visual motion estimation can be regarded as estimation of the state of a system of difference equations with unknown inputs defined on a manifold. Such a system happens to be "linear", but it is defined on a space (the so called "Essential manifold") which is not a linear (vector) space. In this paper we will introduce a novel perspective for viewing the motion estimation problem which results in three original schemes for solving it. The first consists in "flattening the space" and solving a nonlinear estimation problem on the flat (euclidean) space. The second approach consists in viewing the system as embedded in a larger euclidean space (the smallest of the embedding spaces), and solving at each step a linear estimation problem on a linear space, followed by a "projection " on the manifold (see fig. 5). A third "algebraic " formulation of motion estimation is inspired by the structure of the problem in local coordinates (flattened space), and consists in a double iteration for solving an "adaptive fixed-point " problem (see fig. 6). Each one of these three schemes outputs motion estimates together with the joint second
