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 constant-velocity motion (because motion vectors aligned) (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

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

A time = 0 B time = 1

A B each object  has its own fundamental matrix F 

denoted T AB once known, view interpolations portray “constant velocity” motion potential for model building Camera-to-camera transformation

Finding T AB 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 static “table, walls, and floor” object gets broken into two pieces improves sense of object rigidity

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  has its own fundamental matrix F 

Environment Map Morphing view morphing for environment maps time=0.0 time=0.4 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 View MorphingEnvironment Map Morphing

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

z = 1 “image plane” y 2 + z 2 = 1 “image cylinder”

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 that is, make T BA = a b c

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 y 2 + z 2 = 1

cylinder y 2 + z 2 = 1

A and B after applying T BA A B = T BA x

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 AB

B = T BA x A

A and B t = 1 t = 0 B took this view A took this view after applying T BA

physically correct straight-line motion constant-velocity motion AB