>>> import cv2, cvutils
>>> from numpy import array, round, ones, dot, linalg, absolute
>>> img = cv2.imread("../samples/val-dor-117-111.png")
>>> width = img.shape[1]
>>> height = img.shape[0]
>>> intrinsicCameraMatrix = array([[ 377.42,    0.  ,  639.12], [   0.  ,  378.43,  490.2 ], [   0.  ,    0.  ,    1.  ]])
>>> distortionCoefficients = array([-0.11759321, 0.0148536, 0.00030756, -0.00020578, -0.00091816])# distortionCoefficients = array([-0.11759321, 0., 0., 0., 0.])
>>> multiplicationFactor = 1.31
>>> [map1, map2], tmp = cvutils.computeUndistortMaps(width, height, multiplicationFactor, intrinsicCameraMatrix, distortionCoefficients)
>>> undistorted = cv2.remap(img, map1, map2, interpolation=cv2.INTER_LINEAR)
>>> (undistorted.shape == array([int(round(height*multiplicationFactor)), int(round(width*multiplicationFactor)), 3])).all()
True
>>> imgPoints = array([[[150.,170.],[220.,340.],[340.,440.],[401.,521.]]])
>>> newCameraMatrix = cv2.getDefaultNewCameraMatrix(intrinsicCameraMatrix, (int(round(width*multiplicationFactor)), int(round(height*multiplicationFactor))), True)
>>> undistortedPoints = cv2.undistortPoints(imgPoints, intrinsicCameraMatrix, distortionCoefficients, P = newCameraMatrix).reshape(-1, 2) # undistort and project as if seen by new camera
>>> invNewCameraMatrix = linalg.inv(newCameraMatrix)
>>> tmp = ones((imgPoints[0].shape[0], 3))
>>> tmp[:,:2] = undistortedPoints
>>> reducedPoints = dot(invNewCameraMatrix, tmp.T).T
>>> origPoints = cv2.projectPoints(reducedPoints, (0.,0.,0.), (0.,0.,0.), intrinsicCameraMatrix, distortionCoefficients)[0].reshape(-1,2)
>>> (round(origPoints[1:,:]) == imgPoints[0][1:,:]).all()
True
>>> (absolute(origPoints[0,:]-imgPoints[0][0,:])).max() < 6.
True
>>> reducedPoints2 = cvutils.newCameraProject(undistortedPoints.T, invNewCameraMatrix)
>>> (reducedPoints == reducedPoints).all()
True

>>> undistortedPoints2 = cv2.undistortPoints(imgPoints, intrinsicCameraMatrix, distortionCoefficients).reshape(-1, 2) # undistort and project as if seen by new camera
>>> undistortedPoints2 = cvutils.newCameraProject(undistortedPoints2.T, newCameraMatrix)
>>> (undistortedPoints == undistortedPoints2.T).all()
True

>>> undistortedPoints = cv2.undistortPoints(imgPoints, intrinsicCameraMatrix, distortionCoefficients).reshape(-1, 2) # undistort to ideal points
>>> origPoints = cvutils.worldToImageProject(undistortedPoints.T, intrinsicCameraMatrix, distortionCoefficients).T
>>> (round(origPoints[1:,:]) == imgPoints[0][1:,:]).all()
True
>>> (absolute(origPoints[0,:]-imgPoints[0][0,:])).max() < 6.
True

>>> undistortedPoints = cvutils.imageToWorldProject(imgPoints[0].T, intrinsicCameraMatrix, distortionCoefficients)
>>> origPoints = cvutils.worldToImageProject(undistortedPoints, intrinsicCameraMatrix, distortionCoefficients).T
>>> (round(origPoints[1:,:]) == imgPoints[0][1:,:]).all()
True
>>> (absolute(origPoints[0,:]-imgPoints[0][0,:])).max() < 6.
True