找到4个非共面点的2D-3D对应 [英] Find 2D-3D correspondence of 4 non-coplanar points

问题描述

我有一个有4个非共面特征点的三维物体。它们的空间布置是已知的，即，存在对象坐标系，并且我知道这四个特征点相对于该坐标系的3D坐标。

I have a 3-dimensional object with 4 non-coplanar feature points. Their spatial arrangement is known, i.e., there is an "object" coordinate system and I know the 3D coordinates of these 4 feature points with respect to this coordinate system.

来自这个物体的2D投影图像（例如，来自任意视角的照片），我可以定位这4个特征点的2D坐标，但不知道哪些坐标属于哪个特征点。

In a 2D projection image (e.g., a photograph from an arbitrary perspective) of this very object, I can locate the 2D coordinates of these 4 feature points but without knowing which coordinates belong to which feature point.

换句话说：我有4个不同的2D坐标 a ， b ， c strong>其中我知道它们分别属于4个特征点 A ， B ， C 和 D 。每个特征点具有ID​​，其仅仅是从1到4的数字。如何能够找到2D投影坐标和相应的3D特征点之间的对应关系，即，如何确定每个投影到哪个特征点属于？

In other words: I have 4 distinct 2D coordinates a, b, c, and d of which I know that they each belong to exactly one of the 4 feature points A, B, C, and D. Each of the feature points has an ID, which is simply a number from 1 to 4. How can I find the correspondence between 2D projection coordinates and the respective 3D feature points, i.e, how can I determine to which feature point each of the projections belongs?

推荐答案

我认为你的问题没有解决方案。想象一下你拍一张正四面体的照片。现在旋转它120°你得到相同的图片，但点是不同的。所以你需要更多的信息。

I think that there is not a solution to your problem. Imagine you take a picture of regular tetrahedra. Now rotate it by 120° you get the same picture but the points are different. So you need more info.

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