OpenCV: get perspective matrix from translation & rotation

Question

I\'m trying to verify my camera calibration, so I\'d like to rectify the calibration images. I expect that this will involve using a call to warpPerspective bu

Answer 1

This is a sketch of what I mean by "solving the system of equations" (in Python):

import cv2
import scipy  # I use scipy by habit; numpy would be fine too
#rvec= the rotation vector
#tvec = the translation *emphasized text*matrix
#A = the camera intrinsic

def unit_vector(v):
    return v/scipy.sqrt(scipy.sum(v*v))

(fx,fy)=(A[0,0], A[1,1])
Ainv=scipy.array( [ [1.0/fx, 0.0, -A[0,2]/fx],
                     [ 0.0,  1.0/fy, -A[1,2]/fy],
                     [ 0.0,    0.0,     1.0] ], dtype=scipy.float32 )
R=cv2.Rodrigues( rvec )
Rinv=scipy.transpose( R )

u=scipy.dot( Rinv, tvec ) # displacement between camera and world coordinate origin, in world coordinates


# corners of the image, for here hard coded
pixel_corners=[ scipy.array( c, dtype=scipy.float32 ) for c in [ (0+0.5,0+0.5,1), (0+0.5,640-0.5,1), (480-0.5,640-0.5,1), (480-0.5,0+0.5,1)] ]
scene_corners=[]
for c in pixel_corners:
    lhat=scipy.dot( Rinv, scipy.dot( Ainv, c) ) #direction of the ray that the corner images, in world coordinates
    s=u[2]/lhat[2]
    # now we have the case that (s*lhat-u)[2]==0,
    # i.e. s is how far along the line of sight that we need
    # to move to get to the Z==0 plane.
    g=s*lhat-u
    scene_corners.append( (g[0], g[1]) )

# now we have: 4 pixel_corners (image coordinates), and 4 corresponding scene_coordinates
# can call cv2.getPerspectiveTransform on them and so on..