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calib3d: fix reprojection error RMSE calculation in Python tutorial

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The tutorial code used cv.NORM_L2 (which takes a square root) and then
averaged those values. The correct RMSE formula should use NORM_L2SQR
to get squared errors, average them, and take the square root at the
end. Updated the explanatory text to match.

Fixes https://github.com/opencv/opencv/issues/28651
This commit is contained in:
Matt Van Horn
2026-03-13 10:00:23 -07:00
parent 00833f98d0
commit 5e4592440e
1 changed files with 5 additions and 5 deletions
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doc/py_tutorials/py_calib3d/py_calibration/py_calibration.markdown
+5 -5
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@@ -206,17 +206,17 @@ Re-projection Error
Re-projection error gives a good estimation of just how exact the found parameters are. The closer the re-projection error is to zero, the more accurate the parameters we found are. Given the intrinsic, distortion, rotation and translation matrices,
we must first transform the object point to image point using **cv.projectPoints()**. Then, we can calculate
the absolute norm between what we got with our transformation and the corner finding algorithm. To
find the average error, we calculate the arithmetical mean of the errors calculated for all the
calibration images.
the norm between what we got with our transformation and the corner finding algorithm. To find the
RMSE (root mean squared error), we average the squared errors over all points and images, then take
the square root.
@code{.py}
mean_error = 0
for i in range(len(objpoints)):
imgpoints2, _ = cv.projectPoints(objpoints[i], rvecs[i], tvecs[i], mtx, dist)
error = cv.norm(imgpoints[i], imgpoints2, cv.NORM_L2)/len(imgpoints2)
error = cv.norm(imgpoints[i], imgpoints2, cv.NORM_L2SQR) / len(imgpoints2)
mean_error += error
print( "total error: {}".format(mean_error/len(objpoints)) )
print( "total error: {}".format(np.sqrt(mean_error/len(objpoints))) )
@endcode
Exercises