After calibration of camera $C,$ it was determined that the focal length $f$ was $6mm,$ the optic

center $c=[199,193{]}^{TT},$ with distortion modelled as a first order radial distortion $-0\mathrm{.}8863$

$m{m}^{-2}.$ We further assume the image plane coordinates to have the origin at the bottom left, $u$

pointing horizontal, $v$ pointing vertical. The pixels were determined to be square with side

lengths of $0\mathrm{.}001mm$ on the camera's image sensor$.$ The extrinsic parameters were as follows:

$p=\left[\begin{array}{cccc}0\mathrm{.}7547& 0\mathrm{.}0& 0\mathrm{.}6561& 7\mathrm{.}0\\ 0\mathrm{.}0& 1\mathrm{.}0& 0\mathrm{.}0& -6\mathrm{.}0\\ -0\mathrm{.}6561& 0\mathrm{.}0& 0\mathrm{.}7547& 84\mathrm{.}0\\ 0\mathrm{.}0& 0\mathrm{.}0& 0\mathrm{.}0& 1\mathrm{.}0\end{array}\right]$

Assume that Tsai calibration was performed, and that corner features of a calibration grid were

used for this calibration. If one of these corner features was projected from the calibration

plane $Z=0$ to be at pixel location $p=[6,292{]}^{TT}$ within the image, what is the expected $3$D

location of this corner within the scene $($assuming no calibration error$)?$

Select one:

a$.[-16\mathrm{.}86-3\mathrm{.}060\mathrm{.}0{]}^{TT}$

b$.[-15\mathrm{.}36,12\mathrm{.}140\mathrm{.}0{]}^{TT}$

c$.[-13\mathrm{.}064\mathrm{.}540\mathrm{.}0{]}^{TT}$

d$.[-18\mathrm{.}166\mathrm{.}540\mathrm{.}0{]}^{TT}$

e$.{\left[\begin{array}{ccc}-14\mathrm{.}36& 13\mathrm{.}54& 0\mathrm{.}0\end{array}\right]}^{TT}$