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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

image1.jpg







 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

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