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I posted this question on signal processing stack exchange but no bites.

Normally intrinsic parameters are estimated using a pattern of a known size but unknown location. I don't understand how intrinsic parameters can be estimated from this alone since changing the focal length and changing the distance to the pattern result in an equivalent projected image. How do you address this unknown scale issue?

I looked at the paper Matlab cities in their camera calibration code but this wasn't directly addressed.

FourierFlux
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  • If you calibrate the camera, normally the focal length remains fixed. For a given fixed configuration you get the intrinsic camera matrix (and distortion coefficients). – decadenza Mar 19 '22 at 23:08

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A pinhole camera is not the same as a orthographic one. Changing the focal length is not equivalent to changing the distance of the target from the camera, when the (planar) target is not parallel to the image plane. The perspective foreshortening changes.

Francesco Callari
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  • The pinhole camera model keeps proportions, changing the focal length should just result in the image becoming smaller/larger? Issues with occlusion would come up but you should be able to reproduce the same image? – FourierFlux Mar 18 '22 at 21:50
  • Looking at this more it appears you are right based upon a qualitative comparison: https://thelenslounge.com/what-is-focal-length/. But I have not seen a formula derived, depth of multiple objects must lose some proportionality as focus/position is altered simultaneously with respect to a parallel plane. – FourierFlux Mar 20 '22 at 19:36