Projection Error: Explanation and Causes 关于投影误差的解释与说明

Posted by Micah Simonsen, Last modified by Micah Simonsen on 13 October 2016 01:05 PM

引言 Introduction

在Vic-3D中进行相关运算时，为每幅图像提供的数值中有一项是"投影误差"。本文将阐述投影误差的计算方法以及导致高投影误差的可能原因。

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.

根据校准结果，我们可以获取摄像机1图像中的某个特定点，并预测其在摄像机2图像中必须位于的一条线。此约束条件称为极线约束*，该直线则称为极线。如果我们在该极线之外发现了该点，其偏离的距离即称为投影误差；此距离以像素为单位进行报告。

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.

预期值 Expected Values

在良好的测试设置下，投影误差应保持较低水平——其数量级大约与校准分数相同，通常在0.02至0.05像素范围内。略高的误差通常不代表存在问题，但若误差达到约0.1像素或以上，则可能表明存在异常。

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.

问题排查 Troubleshooting

若投影误差显著，这意味着我们要么进行了错误的匹配，要么匹配正确但极线位置与预期不符。以下是一些可能的原因：

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:

最常见原因： 校准状态受到撞击或干扰。对镜头或摄像机位置的任何调整都可能足以干扰设备架设，从而导致投影误差升高。对于高放大倍率的设置，轻微的干扰即可产生高误差——即使是像火线电缆拉扯摄像机这样的小事。为避免此情况，请确保牢固拧紧所有调整点，并在必要时将电缆绑到横杆上以消除应力。此外，校准后请勿更改焦距、光圈或变焦设置。

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.

坏点影响： 有时仅少数坏点具有极高误差，从而将平均误差拉高至异常范围。此时，这些坏点应在结果中表现为噪声。可以尝试在"运行"对话框的"阈值"选项卡中启用投影误差阈值功能进行筛选。

Sometime 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.

热扰动影响： 从高温试件或光源上升的热气流可能导致投影误差。务必确保光源位置不处于摄像机到试件的光路下方；如有必要，可使用风扇将热空气从试件和光路旁吹散。

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.

动态测试中的运动模糊： 若在动态测试中曝光时间过长，可能导致运动模糊并引发投影误差。如果在运动开始前误差较低，运动开始后变高，则应怀疑是运动模糊所致，并在必要时缩短曝光时间。理想情况下，所选的曝光时间应使曝光期间的运动保持在约0.01像素以下。

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.

校准模型不佳： 相对少见的情况是，较差的校准模型可能是高投影误差的根源。如果使用了尺寸过小的标定板、采集的校准图像数量不足、或者校准图像中标定板的倾斜度不够，则可能因获取的数据不足而无法建立精确模型。此时，由于数据采样过少，您可能会得到一个较低的校准分数。根据经验，标定板应至少占据视场的80%，至少采集15对图像，并且应包含一些在保持对焦的前提下尽可能具有最大标定板倾斜度的图像。

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.

特殊情况处理

对于校准状态已受撞击或干扰的情况，有时可能无需重新校准即可进行校正。但这仅适用于摄像机方位（而非焦距或光圈）受到干扰的情形。否则，可能需要进行完整的重新校准。请注意，只要摄像机在测试和校准之间（无论先后顺序）未经历任何移动，在测试后进行校准与测试前进行校准同样有效。

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.