Projection Error: Explanation and Causes

Introduction

When running a correlation in Vic-3D, one of the values given for each image is the Projection error. This article will explain how the projection error is calculated and what can cause a high projection error.

Based on the calibration, we can take a given point in the Camera 1 image and predict a line along which it must lie in the Camera 2 image. This constraint is called the epipolar constraint^*, and the line is called the epipolar line. If we find the point away from this line, the distance away is called the projection error; this distance is reported in terms of pixels.

Expected Values

With a good test setup, projection error should be low - approximately on the same order as the calibration score, or typically in the 0.02-0.05 range. Slightly higher errors are generally not an indication of a problem although errors of approximately 0.1 or above may indicate issues.

Troubleshooting

If the error is significant, it means that we either made an incorrect match, or that we made a good match, but that our epipolar line is not where we expected it. Here are some possible causes: 

• The most common cause: the calibration has been bumped or disturbed. Any adjustments to the lens or camera position can disturb the rig enough to raise the projection error; for high magnification setups, slight disturbances can create high errors - even something like a Firewire cable pulling on a camera. To avoid this, make sure to tighten all adjustment points securely, and, if necessary, tie cables to the crossbar to relieve any strain. Also, do not change focus, aperture, or zoom settings after calibration.
• Sometimes just a few bad points have a very high error, which drive the average error up into the red. In this case the bad points should be visible as noise in the result. Try enabling the projection error threshold in the Threshold tab of the Run dialog.
• Heat waves rising from a hot specimen or light source can cause projection errors. Be sure to position the light so that it is not below the optical path from the camera to the specimen; if necessary, use a fan to blow hot air away from the specimen and optical path.
• If exposure times are too long during a dynamic test, motion blur can result and cause projection errors. If the errors are low before the motion starts, then become high, suspect motion blur, and reduce exposure times if necessary. Ideally, your selected exposure time will keep motions below approximately 0.01 pixel during the exposure.
• More uncommonly, a poor calibration model can be the culprit of a high projection error.  If an undersized grid was used, not enough calibration images were taken, or not enough grid tilt was present in the calibration images, then it's possible that not enough data was obtained to build an accurate model.  In this case, it's possible that you can get a low calibration score because the sampling of data was so small.  As a rule of thumb, calibration grids should fill at least 80% of the field of view, take at least 15 image pairs, and include some images that have as much grid tilt as possible while still remaining in focus.

For cases where the calibration has been bumped or disturbed, it may be possible to correct the calibration without recalibrating. This will only work if the camera orientations - but not the focus or aperture - have been disturbed. Otherwise, it may be necessary to fully recalibrate. Note that it is just as valid to calibrate after a test as before, as long as the cameras do not experience any motion between the test and the calibration, regardless of order. 

^*For more information on epipolar geometry, reference the Wikipedia article.