Epipolar constraint from 2D affine lines, and its application in face image rendering

This paper has two parts. In the first part of the paper, we note the property that under the para perspective camera projection model of a camera, the set of 2D images produced by a 3D point can be optimally represented by two lines in the affine space (α - β space). The slope of these two lines are same, and we observe that this constraint is exactly the same as the epipolar line constraint. Using this constraint, the equation of the epipolar line can be derived. In the second part of the paper, we use the 'same slope' property of the lines in the α - β space to derive the affine structure of the human face. The input to the algorithm is not limited to an image sequence of a human head under rigid motion. It can be snapshots of the human face taken by the same or different cameras, over different periods of time. Since the depth variation of the human face is not very large, we use the para perspective camera projection model. Using this property, we reformulate the (human) face structure reconstruction problem in terms of the much familiar multiple baseline stereo matching problem. Apart from the face modeling aspect, we also show how we use the results for reprojecting human faces in identification tasks.