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I have a robotic arm 6-DOF and an Intel RealSense depth camera. I want to go from pixel values to 3D world coordinates, is it possible with eye-in-hand calibration? If yes can you guide me on how to perform this calibration? I have done some study on my own but have a lot of doubts.

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  • $\begingroup$ What do you mean by pixel values? $\endgroup$
    – Ralff
    Mar 26 at 8:31
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The steps are pretty easy to implement!

The Realsense provides you with the depth $d$ corresponding to the pixel $(u,v)$. Knowing from the forward kinematics of the robot arm the $4 \times 4$ homogeneous transformation $\mathbf{T}$ from the root reference frame to the 3D frame of the camera attached to the end-effector, the 3D coordinates of the point $\mathbf{p}$ projected in the pixel at hand are:

$$ \mathbf{p} = \mathbf{T} \cdot \left( \frac{d}{f} \cdot \left( u-\frac{w-1}{2} \right), \; \frac{d}{f} \cdot \left( v-\frac{h-1}{2} \right), \; d, \; 1 \right)', $$

where the resolution of the camera is $w \times h$ pixels, while $f$ is the camera focal length that you can retrieve from the Realsense API.

Clearly, $\mathbf{T}$ depends on the current configuration of the arm joints.

Bear in mind that the standard reference frame of the camera has the z-axis orthogonal to the image plane and pointing outward, the x-axis pointing rightward, and the y-axis pointing downward as specified by the pinhole camera model.

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