# Dynamic View Morphing - PowerPoint PPT Presentation

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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

• 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

• 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

### For Orthographic Projection

physically correct

straight-line motion

(because motion vectors aligned)

constant-velocity motion

(because motion vectors identical)

### 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”

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

### Camera-to-camera transformation

• denoted TAB

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

• potential for model building

### 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

• 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

• “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 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

A

A

B

### Benefits

• placing synthetic object over real object

• segmentation

• point correspondences

• camera-to-camera transformation

• can also use real object views instead of a synthetic object

### 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

### Layering Static Objects

• 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

### Environment Map Morphing

• 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

### Analogous to View Morphing

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 =

### 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 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

cylinder y2 + z2 = 1

A

B

=

TBA

x

after applying TBA

A and B

### 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

• “weak” rectification: image planes parallel

• virtual movement not restricted to line

### Orthography

• long-distance photography

• no prewarps needed! (physical correctness)

• straight-line motion by aligning directions

### Orthographic Projection

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