Mapping between image pixel and spherical surface

Hi there,

my name is Apostolos and I am quite new with computer vision and image
processing...

My question sounds simple but so far I have not found the right answer. I would
really appreciate any trial to help me on that!

Problem description:

Given the f (focal length) of a camera , thegeometric size of the detector of
the camera and a pixel image which was taken with that camera , I want to find
the mapping between pixels coordinates /values (RGB) and the coordinate system
x,y,z on the surface of the lens of the camera. The type of projection is
assumed to be "central perspective projection".

Assumptions:
i) the coordinate system is x,y,z which considers the projection of the image
onto the surface of the lens shall be of spherical shape (so that the image is
projected on a sphere.)

ii) The lens are of "thin" type.
iii) Homogeneous coordinates shall be used.

I would like to do this in Matlab and so far I have looked at all bilt in
functions there. I would really appreciate any kind of help.
If it is not possible to give a integrated answer there are two things that I
would like to know in general:

i) What can be found using the focal length and the geometrical size of the
detector in relation with the mapping.
ii) What is the type of transformation I am looking for?

Thank you very much for your time!

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