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Dynamic View Morphing

Dynamic View Morphing. performs view interpolation of dynamic scenes. 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 realism

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Dynamic View Morphing

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  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 realism • appearance of straight-line motion without camera-to-camera transformation

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

  4. A A A B B B For Orthographic Projection physically correct straight-line motion (because motion vectors aligned) 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 B time = 0 time = 1 camera views related by fundamental matrix F

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

  8. A B time = 0 time = 1

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

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

  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. Layering Static Objects • improves sense of object rigidity static “table, walls, and floor” object gets broken into two pieces

  13. A time=0.0 ??? time=0.4 B time=1.0 Environment Map Morphing

  14. 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

  15. Environment Map Morphing • View morphing of entire environment maps • uncalibrated cameras • sparse correspondences • widely separated views • In particular, view morphing with • camera moving towards scene • object’s vanishing point in view

  16. A Interpolating Augmented Views A B

  17. 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

  18. Benefits • automation • 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

  19. DONE

  20. Layering Static Objects • greatly improves sense of object solidity static “table, walls, and floor” object gets broken into two pieces

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

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

  23. rectify image planes interpolate conjugate points use interpolated points to guide morphing algorithm rectify image cylinders interpolate conjugate points use interpolated points to guide morphing algorithm Analogous to View Morphing View Morphing Environment Map Morphing

  24. locate conjugate points view morphing environment map morphing rectify image planes rectify image cylinders interpolate conjugate points Morph* based on interpolated points *cylinder-based morph needed for environment maps

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

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

  27. 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

  28. cylinder y2 + z2 = 1

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

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

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

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

  33. Preconditions/Output

  34. Appearance of Straight-line Motion

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

  36. T B B A A T B B A B A A = x TBA A B A A B

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

  38. [ [

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

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