The Fundamental Matrix Song【经典：国外大牛把它的作用变成一首歌了】

The fundamental matrix 
Used in stereo geometry 
A matrix with nine entries 
It's square with size 3 by 3 
Has seven degrees of freedom 
It has a rank deficiency 
It's only of rank two 
Call the matrix F and you'll see...

Two points that correspond 
Column vectors called x and x-prime 
x-prime transpose times F times x 
Equals zero every time

The epipolar constraint 
Involves epipolar lines 
Postmultiplying F by x 
Results in vector l-prime 
It's the epipolar line 
In the other view passing through x-prime 
A three component vector 
Of homogeneous design

The left and right nullspaces of F 
Are the epipoles e-prime and e 
All of the epipolar lines 
Should pass through these

Here's a linear estimation example: 
Take a set of 8 point samples 
Construct a matrix, take the SVD 
And the elements of F are in the last column of V

If you try to estimate 
F with a coplanar set of points 
Your sample set will be degenerate 
And will not bring you joy

When doing the estimation 
If you don't perform rank deprivation 
Your epipolar lines 
And the epipoles will not coincide

But if your scene has three views 
The trifocal tensor is what you'd use 
Constraints from the third view act like glue 
That can't be determined from just two views

视频来自Youtube: http://www.youtube.com/watch?v=DgGV3l82NTk

附带RANSAC Song链接http://danielwedge.com/ransac/