04/13/10. Stereo and Projective Structure from Motion. Computer Vision CS 543 / ECE 549 University of Illinois Derek Hoiem. Many slides adapted from Lana Lazebnik, Silvio Saverese, Steve Seitz. This class. Recap of epipolar geometry Recovering structure
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04/13/10
Stereo and Projective Structure from Motion
Computer Vision
CS 543 / ECE 549
University of Illinois
Derek Hoiem
Many slides adapted from Lana Lazebnik, Silvio Saverese, Steve Seitz
Assume we have matched points x x’ with outliers
Homography (No Translation)
Fundamental Matrix (Translation)
Assume we have matched points x x’ with outliers
Homography (No Translation)
Fundamental Matrix (Translation)
Assume we have matched points x x’ with outliers
Homography (No Translation)
Fundamental Matrix (Translation)
Correspondence Relation
Normalize image coordinates
RANSAC with 8 points
Enforce by SVD
De-normalize:
function P = vgg_P_from_F(F)
[U,S,V] = svd(F);
e = U(:,3);
P = [-vgg_contreps(e)*F e];
See HZ p. 255-256
X
x
x'
Further reading: HZ p. 312-313
Given P, P’, x, x’
Pros and Cons
Code: http://www.robots.ox.ac.uk/~vgg/hzbook/code/vgg_multiview/vgg_X_from_xP_lin.m
Further reading: HZ p. 318
Xj
x1j
x3j
x2j
P1
P3
P2
Slides from Lana Lazebnik
points
cameras
points
cameras
points
cameras
Xj
P1Xj
x3j
x1j
P3Xj
P2Xj
x2j
P1
P3
P2
Photo synth
Noah Snavely, Steven M. Seitz, Richard Szeliski, "Photo tourism: Exploring photo collections in 3D," SIGGRAPH 2006
http://photosynth.net/
Building Rome in a Day: Agarwal et al. 2009
image 1
image 2
Dense depth map
Many of these slides adapted from Steve Seitz and Lana Lazebnik
Epipolar constraint:
R = I t = (T, 0, 0)
x
x’
t
The y-coordinates of corresponding points are the same!
X
z
x
x’
f
f
BaselineB
O
O’
Disparity is inversely proportional to depth!
Left
Right
scanline
Matching cost
disparity
Left
Right
scanline
SSD
Left
Right
scanline
Norm. corr
W = 3
W = 20
Occlusions, repetition
Textureless surfaces
Non-Lambertian surfaces, specularities
Data
Window-based matching
Ground truth
Ordering constraint doesn’t hold
I2
D
I1
W1(i)
W2(i+D(i))
D(i)
Ground truth
Graph cuts