How to display colored graphics object in the same color space?

Consider, I have a disk colored in "LAB" color space. When I convert the graphics into image object it is by default getting converted into "RGB" color space.

ImageColorSpace@Image[Graphics[{LABColor[0.4, 0.6, 0.8], Disk[]}]]

"RGB"

If I now convert it back to "LAB" color space,

ColorConvert[
 Image[Graphics[{LABColor[0.4, 0.6, 0.8], Disk[]}]], "LAB"]

The color value that I get is

{0.40047, 0.603491, 0.548764}

(* Sorry, this was a mistake on my part. Duely corrected after following the answer by Theelepel *)

How can I get the original color value in the "LAB" color space?

Updated question: If the original color value is not known and I am given only with the final Graphics object showing RGB color value, How can I retrieve the original LAB color value?

Updation 2: Following the answer of corey979 to this question, I can see

Table[data = 
  ImageData[
    ColorConvert[Graphics[{LABColor[0.4, 0.6, b], Disk[]}], 

     "LAB"]][[100, 100]];
 N@Rationalize[#, 1/255] &@data, {b, 0, 1, 0.1}]

{{0.4, 0.6, 0.}, {0.4, 0.6, 0.105263}, {0.4, 0.6, 0.2}, {0.4, 0.6, 0.3}, {0.4, 0.6, 0.407407}, {0.4, 0.6, 0.5}, {0.4, 0.6, 0.545455}, {0.4, 0.6, 0.545455}, {0.4, 0.6, 0.545455}, {0.4, 0.6, 0.545455}, {0.4, 0.6, 0.545455}}

Clearly, up to 0.5 for the value of b this works fine except for 0.1 and 0.4. However, from 0.6 onwards the b value remains fixed at 0.545455.

(1) Is it not possible to resolve this issue? (2) Can there be any way in the Graphics option to prevent it from automatic conversion to RGB?

Comments

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