Camera Calibration

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The tree(3D) ←→ Camera(2D)

 

The tree : The point we're seeing with our eyes, 3D point which has world coordinate

Camera : When we take the tree, it transforms to 2D

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When we take the picture of the tree, the camera influenced by the Camera intrinsic parameters-lens, the distance between the lens and the image sensor, the angle between the lens and the image sensor, etc.

 

Therefore, when finding the position where the 3D points are projected on the image or, conversely, restoring the 3D coordinates from the image coordinates, these internal factors must be removed to ensure accurate calculation.

 

And the process of finding the parameter values of these internal factors is called camera calibration.

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\begin{equation}A[R\mid t]{\begin{bmatrix}X\\Y\\Z\\1\end{bmatrix}}\end{equation}

 

- X,Y,Z : 3D coordinates in the world
- [R|t] : extrinsic parameter(Rotation matrix, Translation matrix)-related to the outer space, such as the height of the camera, the orientation(fan, tilt)
- A : intrinsic camera matrix-Internal parameters of the camera itself, such as the focal length, aspect ratio, and center point of the camera

- A[R|t] : camera matrix(projection matrix)

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• Camera intrinsic parameters

 

Focal length, Principal point, Skew coefficient.

 

$\left[\begin{array}{ccc}{\mathrm{f}}_{\mathrm{x}}& \mathrm{s}\mathrm{k}\mathrm{e}{\mathrm{w}}_{\mathrm{c}}{\mathrm{f}}_{\mathrm{x}}& {\mathrm{c}}_{\mathrm{x}}\\ 0& {\mathrm{f}}_{\mathrm{y}}& {\mathrm{c}}_{\mathrm{y}}\\ 0& 0& 1\end{array}\right]$

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• Focal length

 

Pinhole Camera Model

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Pinhole Model

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Distance between lens center and image sensor in pixels.

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• Principal point

 

Lens center point.

 

In the ideal case, Cx = width/2, Cy = height/2

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Ideally, the main point (=lens center point) matches the image center point, but there are cases where it does not match due to various issues arising from the camera manufacturing process.

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• Skew coefficient

 

Inclined degree of y-axis.

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• Camera extrinsic parameters

 

Rotation, Translation

3D←→2D

 

These are not camera specific parameters, so they depend on where and in what direction the camera is installed and how the world coordinate system is defined.

 

https://intuitive-robotics.tistory.com/110

https://velog.io/@noogoolgga/Camera-model

https://darkpgmr.tistory.com/107