Motion Estimation on the Essential Manifold

Abstract

We introduce a novel perspective for viewing the “ego-motion reconstruction” problem as the estimation of the state of a dynamical system having an implicit measurement constraint and unknown inputs. Such a system happens to be “linear”, but it is defined on a space (the “Essential Manifold”) which is not a linear (vector) space. We propose two recursive schemes for performing the estimation task: the first consists in “flattening the space” and solving a nonlinear estimation problem on the flat (euclidean) space. The second consists in viewing the system as embedded in a larger euclidean space, and solving at each step a linear estimation problem on a linear space, followed by a “projection” onto the Essential Manifold. Both schemes output motion estimates together with the joint second order statistics of the estimation error, which can be used by any “structure from motion” module which incorporates motion error [18, 22] in order to estimate 3D scene structure. Experiments are presented with real and synthetic image sequences.