Computer Graphics
Input:3D Image
Output:2D image
Computer Vision
Input:2D Image
Output:3D Image
= to understand 3D world by some 2Dimages
(scene geometry, object color, illumination etc.)
Inverse Problem
Human can recognize image by
example:disparity(視差)
->the apparent movin distance of a point between two images
Such as stereo vision
In stereo...
generally, all camera parameters(intrinsic, position, pose) are known.
Camera Model (How an image is generated)
perspective projection
f:Focal length:distance between camera center and image plane
z:distance between cameracener and optycal axis
Global to Local
Global coordinate system(P_G)
↓(R,T)
Camera coordinate system(P):Local
P = R^t(P_G-T)
=(R^t - R^tT)P_G'
P_G'=(P 1)^t
Pinhole Camera
P=(X, Y, Z) と Q=(sX, sY, sZ)は同じ点に投影される
are projected the same point int he image plane.
→(X/Z, Y/Z, 1)=(x, y, 1)
However CCD; an actual picture is not equal to an Image plane
Image plane: an ideal image!!!
CCD has u,v,u0,v0,θ parameters.
early camera θnot= 90deg.
u = k_u*x - k_u*cotθ*y + u0
v = k_v*y/sinθ + v0
A:Intrinsic Parameter(3x3)
(R^t-R^tT):Extrinsic parameter(3x4)
k(u v 1)^t = A(R^t-R^tT)(X_G Y_G Z_G 1)^t
If the same point X_G is obsered from 2known cameras,
it is possible to calculate X_G!!
[Reason]
k1u1 = P1X_G
k2u2 = P2X_G
Unknown variables:5
Constant:6
Camera Ccalibration
= to estimate of the camera parameters(intrinsic and extrinsic)
3D use cube which has marker
2D Z.Zhang('00) PAMI uses a checker board
1D use a stick wich marker and tilt it
Lens Distortion
Method:
Parametric Method
Assumption: a distortion obeys a formula
Solution: estimate parameters in the formula
Non-parametric Method
Prepare: checker board
Solution: maek a look-up table between
the checker board and the distorted image.
Estimate 3D position
In order to estimate the X_G point, it has to be observed from several known cameras.
Can we identify the samepoint u1,u2,,,,uN?
We need search....
How to Search
With 2 2Dimage, we want to search teh corresponding point from the right image!
However, 2D search is consuming and inefficient.
Finding Correspondence
Use Epipoler Geometry
Epipoler plane: a plane consisted of camera1, camera2 and 3D point.
Camera2 can know epipoler line of camera 1
vector p1: orientation from camera1 to object(calculated from u1,v1)
vector t: from camera1 to camera2
http://www.eb.waseda.ac.jp/murata/junichi.mimura/knowledgh.html
http://tessy.org/wiki/index.php?%A5%A8%A5%D4%A5%DD%A1%BC%A5%E9%C0%FE%A4%CE%B7%D7%BB%BB
Epipoler line : au2 + bv2 + c = 0
camera2 image only has to search on the Epipoler line.
☆Efficient search!!!
→E matrix and F matrix
p1 E p2 = 0
E matrix DOF=5, Defined in 3D
_u1^t F _u2^t = 0
F matrix DOF 8, Defined in 2D
F = A1^t t x R A2^-1
Advantage of usin F matrix
Easy to find correspondence(1D search)
(Without F matrix, we have to search whole area:2D search)
Rectification(Search Technique)
Generally, epipoler lines are laid obliquely
If all correspoonding epipoler line are aligned.
Very effective to calculate the correspondence.
http://ci.nii.ac.jp/naid/110006164770/en
Disparity Map & Depth Estimation
Window(or Block) Matching
Only search in similar window or box.
SAD(sam of absolute difference)
Σ|I1(u,v)-I2(u+d),v)|
SSD(sum o f squared difference)
Σ|I1(u,v)0I2(u+d,v)^2|
NCC(normalized cross correlation)
Cov(I1(u,v),I2(u+d,v))/Sqrt(Var(I1(u,v))*Var(I2(u+d,v)))
Surface Approach
Multi-View Matching (Can get high accuracy)
Index of Similarity (use SSAD SSSD SNCC which has Z depth)
Multi-View Stereo
Next
State-of-the-Art Algorhithm
Visual Hull
Real-time Stereo
Active Stereo
出席あります
PR
