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Solving Visibility with Epipolar Geometry. Tien-Tsin Wong. Chinese University of Hong Kong. View Interpolation. Given the reference images. Synthesize the (desired) image in between. Tien-Tsin Wong (Nov. 1999). Visibility. View Interpolation (2). Two sub-problems:
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Solving Visibility with Epipolar Geometry Tien-Tsin Wong Chinese University of Hong Kong
View Interpolation • Given the reference images • Synthesize the (desired) image in between Tien-Tsin Wong (Nov. 1999)
Visibility View Interpolation (2) • Two sub-problems: • Where should pixels be moved to? • Depth • Correspondences • or optical flows Tien-Tsin Wong (Nov. 1999)
Visibility • Traditional solution: depth-buffering • Depths may not be available (especially in real image) • Can we solve the visibility without depth? • Epipolar geometry Tien-Tsin Wong (Nov. 1999)
Epipolar Geometry • Consider another pixel i2 • p2 will occlude p1 only when p1, p2 & e are coplanar, colinear and p2 is in between • Configuration of two cameras Reference image Desired image Reference camera Desired camera Tien-Tsin Wong (Nov. 1999)
positive epipole Epipolar Geometry (2) • Only pixels on the same epipolar line may occlude each other • Although we don’t know where are p1 & p2, their projection on the epipolar line determines the visibility (e.g. i1 will never occludes i2) • If we always draw i1 before i2, the correct visibility is ensured without knowing the depth information • To identify pixels potentially occlude each other, the epipolar plane is intersected with the reference image to give the epipolar line Epipolar plane Tien-Tsin Wong (Nov. 1999)
Pattern of Drawing Order • By intersecting the epipolar planes with the reference image, a pattern of drawing order can be obtained Tien-Tsin Wong (Nov. 1999)
Pattern of Drawing Order • A diverging pattern is formed if the direction of the epipolar ray reverses. Tien-Tsin Wong (Nov. 1999)
Pixel-based Drawing Order • In fact, there are only three kinds of patterns Tien-Tsin Wong (Nov. 1999)
Results Reference image Desired image • To illustrate the ordering, the triangle should be drawn earlier is shaded in darker color. • Foreground surface should be brighter Tien-Tsin Wong (Nov. 1999)
The End Tien-Tsin Wong (Nov. 1999)