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
motion from time=0 to time=1, as seen through A
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
time = 0
B
time = 1
camera views related by fundamental matrix F
time = 1
time = 0
A B
camera views still related by same fundamental matrix F
A
time = 0
B
time = 1
A B
each object W has its own fundamental matrix FW
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
Environment Map Morphing
time=0.0
time=0.4
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
Interpolating Augmented Views
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
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
DONE
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
time=0.0
time=0.4
time=1.0
Analogous to View Morphing
View Morphing
Environment Map 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
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”
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
Environment Map Morphing
• (STEP 3) project environment map onto
“image cylinder” (a.k.a “pipe”)
this is the cylinder y2 + z2 = 1
• (STEP 4) interpolate conjugate points
and morph
cylinder y2 + z2 = 1
TBA x
B
after applying TBA
A and B
=
A
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
Preconditions/Output
Appearance of Straight-line
Motion
Orthographic Projection
physically correct
straight-line motion
constant-velocity motion
A
B
TBA x
B
=
A
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