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 prope rty that under the para perspective camera projection model of a camera, th e set of 2D images produced by a 3D point can be optimally represented by t wo lines in the affine space (alpha - beta space). The slope of these two l ines are same, and we observe that this constraint is exactly the same as t he epipolar line constraint. Using this constraint, the equation of the epi polar line can be derived. In the second part of the paper, we use the "sam e slope" property of the lines in the alpha - beta space to derive the affi ne structure of the human face. The input to the algorithm is not limited t o 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 p eriods of time. Since the depth variation of the human face is not very lar ge, we use the para perspective camera projection model. Using this propert y, we reformulate the (human) face structure reconstruction problem in term s of the much familiar multiple baseline stereo matching problem. Apart fro m the face modeling aspect. we also show how we use the results for reproje cting human faces in identification tasks.