A common operation on camera matrices is to use RQ factorization to obtain the camera calibration matrix given a 3*4 projection matrix. The simple example below shows how to do this using the scipy.linalg module. Assuming the camera is modeled as P = K [R | t], the goal is to recover K and R by factoring the first 3*3 part of P.
The scipy.linalg module actually contains RQ factorization although this is not always clear from the documentation (here is a page that shows it though). To use this version, import rq like this:
Alternatively, you can use the more common QR factorization and with some modifications write your own RQ function.
RQ factorization is not unique. The sign of the diagonal elements can vary. In computer vision we need them to be positive to correspond to focal length and other positive parameters. To get a consistent result with positive diagonal you can apply a transform that changes the sign. Try this on a camera matrix like this:
The scipy.linalg module actually contains RQ factorization although this is not always clear from the documentation (here is a page that shows it though). To use this version, import rq like this:
from scipy.linalg import rq
Alternatively, you can use the more common QR factorization and with some modifications write your own RQ function.
from scipy.linalg import qr
def rq(A):
Q,R = qr(flipud(A).T)
R = flipud(R.T)
Q = Q.T
return R[:,::-1],Q[::-1,:]
RQ factorization is not unique. The sign of the diagonal elements can vary. In computer vision we need them to be positive to correspond to focal length and other positive parameters. To get a consistent result with positive diagonal you can apply a transform that changes the sign. Try this on a camera matrix like this:
# factor first 3*3 part of P
K,R = rq(P[:,:3])
# make diagonal of K positive
T = diag(sign(diag(K)))
K = dot(K,T)
R = dot(T,R) #T is its own inverse