> Probably the best approach to the problem would be to implement an algorithm which allows to generate pixel positions in the original image along the Line without using the FrontEnd

I think [`ImageTransformation`](http://reference.wolfram.com/language/ref/ImageTransformation.html) doest just that. Using your definitions:

    r = Min[id]/2;
    dir = N@AngleVector[α];
    (*modify step distance so we step at least 1 pixel in x or y \
    direction*)
    dir = dir/Max[Abs[dir]];
    profile = 
      First@ImageData@
        ImageTransformation[img, 
         center + #[[1]] dir + {1, 0} &, {Round[r], 1}, DataRange -> Full,
          PlotRange -> {{0, r - 1}, {0, 1}}, Resampling -> "Nearest"];
    
    ListLinePlot[{profile, radialProfile}, PlotRange -> All]

[![enter image description here][1]][1]


  [1]: https://i.sstatic.net/re6ow.png