Information contained in the motion field of lines and the cooperation between motion and stereo

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Abstract
We investigate the relationships that exist between the three‐dimensional structure and kinematics of a line moving rigidly in space and the two‐dimensional structure and kinematics (motion field) of its image in one or two cameras. We establish the fundamental equations that relate its three‐dimensional motion to its observed image motion. We show how this motion field can be estimated from a line‐based token tracker. We then assume that stereo matches have been established between image segments and show how the estimation of the motion field in the two images can be used to compute part of the kinematic screw of the corresponding 3D line. The equations are linear and if several lines belong to the same object provide a very simple way to estimate the full kinematic screw of that object. Finally, we show how the motion field can constrain the stereo matches by establishing necessary conditions that must be satisfied by the motion field of segments which are images of lines belonging to the same object. Only part of this theory has been implemented yet. This part uses Kalman filtering. Several experimental results using synthetic and real data are presented.

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