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Dynamic View Morphing

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- performs view interpolation of dynamic scenes

- 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

A

A

B

A

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

A

A

A

B

B

B

physically correct

straight-line motion

(because motion vectors aligned)

constant-velocity motion

(because motion vectors identical)

- IF first make image planes parallel to:
- motion of object, and
- each other

- THEN orthographic results apply
- condition above is “weak rectification”

A

B

time = 0

time = 1

camera views related by fundamental matrix F

A

B

time = 1

time = 0

camera views still related by same fundamental matrix F

A

B

time = 0

time = 1

A

B

each object W has its own fundamental matrix FW

T

B

B

A

A

- denoted TAB
- once known, view interpolations portray “constant velocity” motion
- potential for model building

- can be determined from fundamental matrices for two distinct objects
- can be determined from four conjugate directions
- can be approximated from two conjugate directions

- improves sense of object rigidity

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

A

time=0.0

???

time=0.4

B

time=1.0

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

- 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

A

A

B

- 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

- 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

- greatly improves sense of object solidity

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

A

B

each object W has its own fundamental matrix FW

- view morphing for environment maps

A

time=0.0

???

time=0.4

B

time=1.0

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

View Morphing

Environment Map 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

z = 1 “image plane”

y2 + z2 = 1 “image cylinder”

a b c

0 1 0

0 0 1

that is, make TBA =

- (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

- (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

cylinder y2 + z2 = 1

A

B

=

TBA

x

after applying TBA

A and B

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

- “weak” rectification: image planes parallel
- virtual movement not restricted to line

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

physically correct

straight-line motion

constant-velocity motion

A

B

T

B

B

A

A

T

B

B

A

B

A

A

=

x

TBA

A

B

A

A

B

t = 1

t = 0

B took this view

A took this view

after applying TBA

A and B

[

[

A

B

physically correct

straight-line motion

constant-velocity motion