如何计算基于相机的相对姿态测量的协方差? [英] How can I compute the covariance of a camera-based relative pose measurement?

问题描述

我正在尝试通过通常的功能对应方式，使用它们捕获的图像来计算两个摄像机之间的相对姿态.我使用这些特征匹配来计算基本矩阵，然后进行分解，从而导致两个视图之间的旋转和平移.我目前在OpenCV中使用 findEssentialMat 和 recoverPose 函数来实现此目的.一旦我计算出相对姿势:

I am trying to compute the relative pose between two cameras using their captured images through the usual way of feature correspondences. I use these feature matches to compute the essential matrix, decomposing which results in the rotation and translation between both the views. I am currently using findEssentialMat and recoverPose functions in OpenCV to achieve this. Once I compute this relative pose:

1. 如何找到此测量的不确定性?我是否应该尝试(使用对极误差)细化基本矩阵本身，从而导致基本矩阵的协方差，并且是否有可能从中找到姿态协方差?还是有其他方法可以直接找到此姿势的不确定性?

1. How can I find the uncertainty of this measurement? Should I try to refine the essential matrix itself (using the epipolar error), which results in the essential matrix's covariance and is it possible to find the pose covariance from this? Or is there another way to find the uncertainty in this pose directly?

这里还存在另一个问题:在我从摄像机C1计算摄像机C2(称为P2)的相对姿态时，摄像机C1(例如P1)的姿态将具有其自己的协方差.这对P2有何影响?

There is also another issue in play here: While I am computing the relative pose of camera C2 (call it P2) from camera C1, the pose of camera C1 (say P1) would have its own covariance. How does this affect P2?

推荐答案

1)您应该直接通过束调整来调整姿态估计，并在最佳状态下计算成本函数的Hessian，其逆函数将产生您寻求的协方差.某些BA软件包(例如Ceres)具有API来简化此操作.

1) You should refine your pose estimation directly through bundle adjustment, and compute the Hessian of the cost function at the optimum, whose inverse will yield the covariance you seek. Some BA packages (e.g. Ceres) have APIs to facilitate that.

2)不相关.缺少绝对参考，您只能期望估计相对姿势的不确定性.换句话说，如果您只测量两个摄像机之间的相对运动，则您还可以假设一个摄像机是确定的，并将运动不确定性完全归因于另一个摄像机的姿势.

2) Irrelevant. Lacking an absolute reference, all you can hope for is an estimation of the uncertainty on the relative pose. Putting it in another way, if all you have is measurements of relative motion between two cameras, you may as well assume that one is certain and attribute the motion uncertainty entirely to the pose of the other.

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