为什么相机固有矩阵中的焦距具有二维？ [英] Why does the focal length in the camera intrinsics matrix have two dimensions?

问题描述

在针孔相机模型中，只有一个焦距介于主点和

In the pinhole camera model there is only one focal length which is between the principal point and the camera center.

但是，在计算完相机的固有参数后，矩阵包含

However, after calculating the camera's intrinsic parameters, the matrix contains

(fx,  0,  offsetx,  0,
 0,  fy,  offsety,  0,
 0,   0,  1,        0)

这是因为图像传感器的像素在x和y上不是正方形吗？

Is this because the pixels of the image sensor are not square in x and y?

谢谢

推荐答案

总之：是的。为了建立可以描述具有矩形像素的相机的数学模型，您必须引入两个单独的焦距。我将引用经常被推荐的 学习OpenCV （第373页）涵盖了该部分的内容，如果您希望了解更多背景知识，我建议您获取它：

In short: yes. In order to make a mathematical model that can describe a camera with rectangular pixels, you have to introduce two separate focal lengths. I'll quote from the often recommended "Learning OpenCV" (p. 373) which covers that section pretty well and which I recommend getting if you would like more background on this:

焦距fx（例如）实际上是镜头的
物理焦距与单个
成像器元件的尺寸sx的乘积（这应该是有道理的因为sx的像素单位是每毫米
，而F的单位是毫米，这意味着fx
是必需的像素单位）。 [...]重要的是要牢记
，但是，不能通过任何
相机校准过程直接测量sx和sy，也不能直接测量物理焦距F
可测量的。在不实际拆卸相机并直接测量
组件的情况下，仅可以导出fx = F * sx和fy = F * sy
的组合。

The focal length fx (for example) is actually the product of the physical focal length of the lens and the size sx of the individual imager elements (this should make sense because sx has units of pixels per millimeter while F has units of millimeters, which means that fx is in the required units of pixels). [...] It is important to keep in mind, though, that sx and sy cannot be measured directly via any camera calibration process, and neither is the physical focal length F directly measurable. Only the combinations fx = F*sx and fy = F*sy can be derived without actually dismantling the camera and measuring its components directly.

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