1. Dynamic View Morphing
performs view interpolation of dynamic scenes

2. Expanded Theory orthography
methods for finding camera-to-camera transformation
virtual camera not restricted to line connecting original cameras
“weak rectification” is sufficient for physical correctness
appearance of straight-line motion without camera-to-camera transformation

3. A B A A
motion from time=0 to time=1, as seen through A

4. For Orthographic ProjectionB
physically correct A B
straight-line motion
(because motion vectors aligned) A B
constant-velocity motion
(because motion vectors identical)

5. For Perspective Projection
IF first make image planes parallel to:
motion of object, and
each other
THEN orthographic results apply
condition above is “weak rectification”

6. A
time = 0 B
time = 1
camera views related by fundamental matrix F

7. time = 1
time = 0 A B
camera views still related by same fundamental matrix F

8. A
time = 0 B
time = 1

9. A B
each object W has its own fundamental matrix FW

10. Camera-to-camera transformation
denoted TAB
once known, view interpolations portray “constant velocity” motion
potential for model building A B T

11. Finding TAB
can be determined from fundamental matrices for two distinct objects
can be determined from four conjugate directions
can be approximated from two conjugate directions

12. A B
each object W has its own fundamental matrix FW

13. Environment Map
“environment map” or “panoramic mosaic” or “plenoptic function”: all the light that reaches a given point in space at an instant in time

14. Environment Map Morphing
view morphing for environment maps A
time=0.0
???
time=0.4 B
time=1.0

15. Environment Map Morphing
(STEP 1) find fundamental matrix
(STEP 2) “strongly rectify” the views
that is, make TBA =
a b c
0 1 0
0 0 1
then notice that, for any point in space, camera A and
camera B will give the same y and z coordinates

16. Environment Map Morphing
(STEP 3) project environment map onto “image cylinder” (a.k.a “pipe”)
(STEP 4) interpolate conjugate points and morph
this is the cylinder y2 + z2 = 1

17. z = 1 “image plane”
y2 + z2 = 1 “image cylinder”

18. Interpolating Augmented ViewsB

19. Benefits placing synthetic object over real object segmentation
point correspondences
camera-to-camera transformation
added realism: moving parts, shadows, transparency, don’t morph synthetic object
can also use real object views instead of a synthetic object

20. Benefits automation scenario visualization
by matching edges, computer can place model automatically
all previous benefits become automated
scenario visualization
combine synthetic objects with real scenes to create new scenarios

21. cylinder y2 + z2 = 1

22. B A =
TBA x
after applying TBA
A and B

23. Outline layering; static scenes, improvement orthography
generalization of math for view morphing
making objects appear to follow line
Tab and how to find

24. Layering

25. Underlying Mathematics
“weak” rectification: image planes parallel
virtual movement not restricted to line

26. Orthography long-distance photography
no prewarps needed! (physical correctness)
straight-line motion by aligning directions

27. Preconditions/Output

28. Appearance of Straight-line Motion

30. Orthographic Projection
physically correct
straight-line motion
constant-velocity motion A B

32. B x = A
TBA A B T A B T A B A A B

33. t = 1 t = 0 B took this view A took this view A and B
after applying TBA
A and B

34. [

35. A B
physically correct
straight-line motion
constant-velocity motion