1. Solving Visibility with Epipolar Geometry Tien-Tsin Wong Chinese University of Hong Kong

2. View Interpolation zGiven the reference images zSynthesize the (desired) image in between Tien-Tsin Wong (Nov. 1999)

3. View Interpolation (2) zTwo sub-problems: yWhere should pixels be moved to? yVisibility Depth Correspondences or optical flows Tien-Tsin Wong (Nov. 1999)

4. Visibility zTraditional solution: depth-buffering zDepths may not be available (especially in real image) zCan we solve the visibility without depth? zEpipolar geometry Tien-Tsin Wong (Nov. 1999)

5. Epipolar Geometry zConfiguration of two cameras Reference camera Desired camera  Consider another pixel i 2  p 2 will occlude p 1 only when p 1, p 2 & e are coplanar, colinear and p 2 is in between Reference image Desired image Tien-Tsin Wong (Nov. 1999)

6. zTo identify pixels potentially occlude each other, the epipolar plane is intersected with the reference image to give the epipolar line zOnly pixels on the same epipolar line may occlude each other  Although we don’t know where are p 1 & p 2, their projection on the epipolar line determines the visibility (e.g. i 1 will never occludes i 2 )  If we always draw i 1 before i 2, the correct visibility is ensured without knowing the depth information Epipolar Geometry (2) Epipolar plane positive epipole Tien-Tsin Wong (Nov. 1999)

7. Pattern of Drawing Order zBy intersecting the epipolar planes with the reference image, a pattern of drawing order can be obtained Tien-Tsin Wong (Nov. 1999)

8. Pattern of Drawing Order zA diverging pattern is formed if the direction of the epipolar ray reverses. Tien-Tsin Wong (Nov. 1999)

9. Pixel-based Drawing Order zIn fact, there are only three kinds of patterns Tien-Tsin Wong (Nov. 1999)

10. Results zTo illustrate the ordering, the triangle should be drawn earlier is shaded in darker color. Reference image Desired image zForeground surface should be brighter Tien-Tsin Wong (Nov. 1999)

11. The End Tien-Tsin Wong (Nov. 1999)