Initial Closed-Form Solution to Mapping from Unknown Planar Motion of an Omni-directional Vision Sensor

Abstract

This paper proposes a novel method to construct a stationary environment map and estimate the ego-motion of a sensor system from unknown planar motion by using an omni-directional vision sensor. Most environments where sensor moves to obtain maps are limited to two-dimensional space. However, conventional ”Structure from Motion (SFM)” algorithms cannot be applied to planar motion and one-dimensional measurements because they use the epipolar geometry. We propose an algorithm that can be applied to two-dimensional space. Since the number of parameters to be estimated is reduced, computational advantages can be obtained for large map reconstruction. Proposed algorithm exploits the azimuths of features which are obtained from an omni-directional vision sensor and gives robust results against the noise of image information by taking advantage of large field of view. A relation between observed azimuth and motion parameters of a vision sensor are constrained by a nonlinear equation. The proposed method obtains closed form solutions to all the motion parameters and an environment map through a two-step procedure. These estimation results can be used as a good initial seed for the incremental reconstruction of a large map.