How to calculate Rotation and Translation matrices from homography?

Question

I have already done the comparison of 2 images of same scene which are taken by one camera with different view angles(say left and right) using SURF in emgu

Answer 1

To figure out camera motion (exact rotation and translation up to a scaling factor) you need

• Calculate fundamental matrix F, for example, using eight-point algorithm
• Calculate Essential matrix E = A’FA, where A is intrinsic camera matrix
• Decompose E which is by definition Tx * R via SVD into E=ULV’

• Create a special 3x3 matrix

      0 -1  0   
  W = 1  0  0      
      0  0  1  
  

that helps to run decomposition:

R = UW^-1V^T, Tx = ULWU^T, where

      0  -tx  ty
Tx =  tz  0   -tx
     -ty  tx   0 

• Since E can have an arbitrary sign and W can be replace by Winv we have 4 distinct solution and have to select the one which produces most points in front of the camera.