关于相机坐标中通过原点的线
我有一个关于相机坐标中的线的问题。
假设一个点的像素/屏幕坐标是(u,v)。以及相机坐标 (u,v) 的（相对于相机的坐标系）为 (p,q,r)，其中 (u,v) 给定和一个 L 线穿过点 (0,0,0) [原点相机位置] 和 (p,q,r)，其中 r 是 给予。是否可以找到(p,q)？
我知道一条直线的参数方程是：
(xa, yb, zc)= t(x_0, y_0, z_0)
但我只知道(a,b,c) code> 是 (0,0,0) 和 z_0 是 r。谁能告诉我是否可以找到 (p,q) 的值？我可以以某种方式使用 (u,v) 吗？
I have a question regarding a line in camera coordinate.
Suppose the pixel/screen coordinate of a point is (u,v). And the camera coordinate
(coordinate system relative to camera) of (u,v) is (p,q,r) where (u,v) is given and a
line L goes through the point (0,0,0) [origin camera location] and (p,q,r) where r is
given. Is it possible to find (p,q)?
I know that the parametric equation of a line is:
(x-a, y-b, z-c)= t(x_0, y_0, z_0)
But I know only (a,b,c) which is (0,0,0) and z_0 which is r. Can anyone kindly tell me if it is possible to find
the value of (p,q)? Can I use (u,v) in some way?
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评论（1）
除非您了解有关
(u, v)之类的内容的更多信息，否则这是不可能的。这样想吧。假设您声称您可以仅根据(u, v)和r计算出来。现在，如果我重新标记你的像素会怎么样？像素不必表示任何特定距离，因此如果我说 (125, 100) 是 (250, 200)，那也是有道理的。假设我只是将较高分辨率的芯片换成较低分辨率的芯片。要实际恢复
(p, q)，您必须知道像素对应的物理距离。您还必须知道相机模型中的针孔在像素参考系中是否为 (0,0) 等。It's not possible until you have more information about what something like
(u, v)represents. Think of it this way. Suppose you claimed you could figure it out just based on(u, v)andr. Now, what if I just relabeled your pixels? A pixel doesn't have to represent any specific distance, so if I said (125, 100) was (250, 200) instead, that would make sense too. Suppose I just swap in a higher resolution chip for a lower resolution chip.To actually recover
(p, q), you'd have to know what physical distance a pixel corresponds to. You'd also have to know whether the pinhole in your camera model is (0,0) in your pixel reference frame, etc.