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The tvecs and rvecs seem to be intermediate values used to calculate the camera matrix and distortion coefficients. There's one tvec and rvec returned for each corner of your chessboard. I'm not sure what use they are after the calibration is done.

As for your bonus question, the answer is no, but it's possible to convert the u, v into azimuth (90-(u-cx)/width*fovx) and inclination (90-(v-cy)/height*fovy) angles. If you have some way to determine the distance from the camera to the point, then you have the real-world spherical coordinate with the camera as the origin.

From above, width, height are the screen dimensions in pixels, and fovx, fovy are the camera field of view angles (first two values returned from cv2.calibrationMatrixValues()).