Motion and Depth from Optical Flow

Abstract

Passive navigation of mobile robots is one of the challenging goals of machine vision. This note demonstrates the use of optical flow, which encodes the visual information in a sequence of time varying images [1], for the recovery of motion and the understanding of the three dimensional structure of the viewed scene. By using a modified version of an algorithm, which has recently been proposed to compute optical flow, it is possible to obtain dense and accurate estimates of the true ID motion field. Then these estimates are used to recover the angular velocity of the viewed rigid objects. Finally it is shown that, when the camera translation is known, a coarse depth map of the scene can be extracted from the optical flow of real time varying images. The navigation of a robot in any environment requires the knowledge of the motion of the robot relative to the environment, the three dimensional structure of the scene and the motion parameters of the object moving in the scene. These informations can be obtained by using active sensors and/or by passive vision, provided by cameras mounted on the robot. In this note it is shown how passive vision can be used to recover depth when the camera on the robot is translating and angular velocity when the camera looks at rotating objects. The proposed technique first computes the optical from a sequence of time varying images by using a modification of the algorithm recently proposed [2,3]. The angular velocity can be obtained by exploiting mathematical properties of the 2D motion field [5]. Depth is obtained from the computed optical flow, using an equation already proposed by many authors (Horn 1987 , Tommasi personal communication).