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Vision-based Registration for AR. Presented by Diem Vu Nov 20, 2003. Markerless Tracking using Planar Structure in the Scene . G. Simon, A.W. Fitzgibbon and A. Zisserman, 2000. Calibration-Free Augmented Reality . K.N Kutulakos and J.R. Vallino , 1998. Planar-surface tracking. - PowerPoint PPT Presentation
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Vision-based Registration for AR
Presented by Diem VuNov 20, 2003
Markerless Tracking using Planar Structure in the Scene. G. Simon, A.W. Fitzgibbon and A. Zisserman, 2000.
Calibration-Free Augmented Reality. K.N Kutulakos and J.R. Vallino, 1998.
Planar-surface tracking.Camera position can be recovered from
planar homography.Planar structure is common in almost all
scenarios.
y
x
z
Hw
World to image homography
jiH
Image to image homography
World to image homographyConsider our tracking plane is the plane
Z=0
y
x
z
Hw
1H
1w YX
yx
Projection matrix
trrr 321KP
trrrr 2121 KP
Projection matrix
1yx
10YX
y
x
z
P
10
K1
2
YX
yx
trrr 31
trrrr 2121 KP
Projection matrix
1yx
10YX
y
x
z
P
1K
1YX
yx
trr 21
If K and Hw are known, then r1, r2 and t can be recovered, thus P.
Question: How to compute Hw?Direct.Indirect.
trr 21KHw
Direct measurement of Hw
Select 4 points {xk} on a rectangle in the scene.
Compute H which maps the unit square to {xk}.
(0,0)
(0,1) (1,1)
((1,0))
Direct measurement of Hw
Select 4 points {xk} on a rectangle in the scene.
Compute H which maps the unit square to {xk}.
s,1)(1,diagH H w
trr 21 s HK -1
s,1)(1,diagK H trr 21
Compute Hw=Hdiag(1,1/s,1)
(0,0)
(0,s) (1,s)
((1,0))
Indirect measurement of Hw
iwH
jiH
? H jw
y
x
z
Indirect measurement of Hw
iwH
jiH
iw
ji
jw HHH
y
x
z
Algorithm summaryCompute (direct measure).For each frame i, compute frame to frame
homography (RANSAC)Compute by:
0wH
1-iw
i1-i
iw HHH
i1-iH
iwH
Other …Using only 2 points in direct method ??Matching the frame i with frame 0 in order
to reduce error.Estimate intrinsic parameters K Hand-off mechanism.
Possible problems?Homography is only up-to-scale?Plain surface (no texture) or moving
objects in the foreground ?Depth order, occlusion ?Speed ?
Affine virtual object representation
Represent virtual objects so that their projection can be computed as a linear combination of the projection of the fiducial points.
Project a point from its affine coordinates
Compute affine coordinates from projection along two viewing
direction
Algorithm Setup the affine basis
Algorithm Setup the affine basis Locate the object in 2 frames.
Algorithm Setup the affine basis Locate the object in 2 frames. Compute the affine coordinates
for each point.
Algorithm Setup the affine basis Locate the object in 2 frames. Compute the affine coordinates
for each point. Compute projection of the object
and render the object in each frame.
Camera viewing direction and are the first and second row of
2x3.The camera viewing direction expressed in
the coordinate frame of the affine basis points: =
Depth order
w is the z-value of point p (x,y,z).
AdvantagesNo need any metric information.Able to use with the existing hardware to
accelerate graphics operations.Can be used to improve tracking.
LimitationAffine constraints.Lost of metric information.