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I'm planning a concept for calibrating a robot model. For this purpose I want to use computer vision approaches. Since I'm not that experienced in that field I have some basic questions on the accuracy of NON STEREO approaches like the famous Aruco markers aruco marker description.

Using a simple pin hole camera model where $x_{img} = \frac{f_x}{z_C} x_C $ where $C$ denotes the cameras coordinate frame.

I know the size of a pixel of my camera ( $\Delta x_{img}\approx10\mathrm{\mu m}$) and the focal length ($f_x\approx664\mathrm{m}$). Somehow I'm having problems to estimate the accuracy I can expect. Especially in the depth ($z_C$) direction.

My fist approach was to use the distance between two pixels in the image frame to calculate a distance in z-direction but i) this depends on the $x_C$ coordinate, and ii) this leads to unrealistic values $\Delta z_C \approx 6.64e7 x_C$.

Now I'm seeking for help.

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