Estimation of Three-dimensional Motion Information from Optical Flow Using Subspace Method

Abstract

Optical flow, a two-dimensional(2D) motion field on image plane, is essential for such tasks as the visual guidance of locomotion through the environment, the manipulation and recognition of objects. However, recovering three-dimensional(3D) motion information from optical flow, is a difficult problem because the relationship between the optical flow field and 3D motion parameters of the observer along with the depth of the environment, is nonlinear. In this paper, we propose a new method for estimating 3D motion information from optical flow. Considering an observer moving through a static environment, we intend to recover observer’s 3D motion parameters and environment’s relative depth map. Based on motion perspective, the estimation is carried out in three steps using three sets of equations derived from the nonlinear equation of motion perspective. First, direction of the translation components is recovered by searching a candidate over a discrete sampled space to minimize a residual function. Once the translation has been recovered, the rotation components of observer’s 3D motion can be resolved from the second set of equations by using least square optimization. Finally, the estimation of relative depth map of the environment is straightforward using the third set of equations, given the recovered 3D motion parameters.