来自基本矩阵的 3D 对应关系 [英] 3D Correspondences from fundamental matrix

问题描述

在 MATLAB 中，我计算了 基本矩阵(两个图像)使用标准化的八点算法.由此我需要三角化 3D 空间中的相应图像点.据我了解，要做到这一点，我需要图像相机的旋转和平移.当然，最简单的方法是先校准相机然后拍摄图像，但是这对我的应用程序来说太狭窄了，因为它需要这个额外的步骤.

In MATLAB I have calculated the Fundamental matrix (of two images) using the normalized Eight point algorithm. From that I need to triangulate the corresponding image points in 3D space. From what I understand, to do this I would need the rotation and translation of the image's cameras. The easiest way of course would be calibrate the cameras first then take the images, but this is too constricting for my application as it would require this extra step.

所以剩下的就是自动(自)相机校准.我看到提到 捆绑调整，但是在 邀请 3D 视觉 似乎需要初始平移和旋转，这让我觉得需要校准相机或我的理解不足.

So that leaves me with auto (self) camera calibration. I see mention of bundle adjustment, however in An Invitation to 3D Vision it seems it requires an initial translation and rotation, which makes me think that a calibrated camera is needed or my understanding is falling short.

所以我的问题是如何自动提取旋转/平移，以便将图像点重新投影/三角剖分到 3D 空间中.任何 MATLAB 代码或伪代码都会很棒.

So my question is how can I automatically extract the rotation/translation so I can reprojected/triangulate the image points into 3D space. Any MATLAB code or pseudocode would be fantastic.

推荐答案

您可以使用基本矩阵来恢复相机矩阵并从图像中对 3D 点进行三角测量.但是，您必须知道，您将获得的重建将是投影重建，而不是欧几里得重建.如果您的目标是测量原始场景中的投影不变量(例如交叉比率、线交叉点等)，这将很有用，但它不足以测量角度和距离(您必须为此校准相机).

You can use the fundamental matrix to recover the camera matrices and triangulate the 3D points from their images. However, you must be aware that the reconstruction you will obtain will be a projective reconstruction and not a Euclidean one. This is useful if your goal is to measure projective invariants in the original scene such as the cross ratio, line intersections, etc. but it won't be enough to measure angles and distances (you will have to calibrate the cameras for that).

如果您可以访问 Hartley 和 Zisserman 的教科书，您可以检查第 9.5.3 节，您将在其中找到从基本矩阵到允许您计算投影重建的一对相机矩阵所需的内容(我相信相同的内容出现在 Yi Ma 的书的第 6.4 节中).由于本书算法的源代码可在线获取，您可以想检查函数 vgg_P_from_F、vgg_X_from_xP​​_lin 和 vgg_X_from_xP​​_nonlin.

If you have access to Hartley and Zisserman's textbook, you can check section 9.5.3 where you will find what you need to go from the fundamental matrix to a pair of camera matrices that will allow you to compute a projective reconstruction (I believe the same content appears in section 6.4 of Yi Ma's book). Since the source code for the book's algorithms is available online, you may want to check the functions vgg_P_from_F, vgg_X_from_xP_lin, and vgg_X_from_xP_nonlin.

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