Dynamic view morphing
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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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Dynamic view morphing

Dynamic View Morphing

  • performs view interpolation of dynamic scenes


Expanded theory

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


Dynamic view morphing

A

A

B

A

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


For orthographic projection

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)


For perspective projection

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”


Dynamic view morphing

A

B

time = 0

time = 1

camera views related by fundamental matrix F


Dynamic view morphing

A

B

time = 1

time = 0

camera views still related by same fundamental matrix F


Dynamic view morphing

A

B

time = 0

time = 1


Dynamic view morphing

A

B

each object W has its own fundamental matrix FW


Camera to camera transformation

T

B

B

A

A

Camera-to-camera transformation

  • denoted TAB

  • once known, view interpolations portray “constant velocity” motion

  • potential for model building


Finding t ab

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


Layering static objects

Layering Static Objects

  • improves sense of object rigidity

static “table, walls, and floor” object gets broken into two pieces


Environment map morphing

A

time=0.0

???

time=0.4

B

time=1.0

Environment Map Morphing


Environment map

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


Environment map morphing1

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


Interpolating augmented views

A

Interpolating Augmented Views

A

B


Benefits

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


Benefits1

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


Dynamic view morphing

DONE


Layering static objects1

Layering Static Objects

  • greatly improves sense of object solidity

static “table, walls, and floor” object gets broken into two pieces


Dynamic view morphing

A

B

each object W has its own fundamental matrix FW


Environment map morphing2

Environment Map Morphing

  • view morphing for environment maps

A

time=0.0

???

time=0.4

B

time=1.0


Analogous to view morphing

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


Dynamic view morphing

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


Dynamic view morphing

z = 1 “image plane”

y2 + z2 = 1 “image cylinder”


Environment map morphing3

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


Environment map morphing4

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


Dynamic view morphing

cylinder y2 + z2 = 1


Dynamic view morphing

A

B

=

TBA

x

after applying TBA

A and B


Outline

Outline

  • layering; static scenes, improvement

  • orthography

  • generalization of math for view morphing

  • making objects appear to follow line

  • Tab and how to find


Underlying mathematics

Underlying Mathematics

  • “weak” rectification: image planes parallel

  • virtual movement not restricted to line


Orthography

Orthography

  • long-distance photography

  • no prewarps needed! (physical correctness)

  • straight-line motion by aligning directions


Preconditions output

Preconditions/Output


Appearance of straight line motion

Appearance of Straight-line Motion


Orthographic projection

Orthographic Projection

physically correct

straight-line motion

constant-velocity motion

A

B


Dynamic view morphing

T

B

B

A

A

T

B

B

A

B

A

A

=

x

TBA

A

B

A

A

B


Dynamic view morphing

t = 1

t = 0

B took this view

A took this view

after applying TBA

A and B


Dynamic view morphing

[

[


Dynamic view morphing

A

B

physically correct

straight-line motion

constant-velocity motion


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