3D基础矩阵的对应 [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。因此，我需要在3D空间中三角化对应的图像点。从我的理解，这样做我需要旋转和图像的相机的翻译。最简单的方法是先校准摄像机，然后拍摄图像，但这对我的应用程序来说过于收缩，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.

所以让我留下 auto（self）camera calibration 。我在套装调整。 google.com/books?id=jCsZ5rdwgqMC&lpg=PP1&ots=MjhMWP74VG&dq=an%20invitation%20to%203d%20vision&pg=PA167#v=onepage&q=&f=falserel =nofollow noreferrer>对3D视觉的邀请它似乎需要一个初始的翻译和旋转，这使我认为需要一个校准的相机或我的理解是短。

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/翻译，以便我可以将图像点重新投影/三角化到3D空间。

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对三维点进行三角测量从他们的图像。然而，你必须知道，你将获得的重建将是一个投影重建，而不是一个欧几里德重建。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，线交叉等，这将非常有用，但是它不足以测量角度和距离（您需要校准摄像机）。

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).

如果您有权访问 Hartley和Zisserman的教科书，你可以检查第9.5.3节，你会发现你需要从基本矩阵到一对相机矩阵，这将允许你计算一个投影重建（我相信相同的内容出现在易马的书的6.4节）。由于图书算法的源代码可在线，您可以可能需要检查函数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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