sorry for my late reply, but work sometime is time consuming
well...you said it "The ICC profile converts the image color data firstly to XYZ or L*a*b*", so from where and to where?
so basically to my understanding and according to the resources (that I am trying to collect for now), when creating an ICC profile you are encoding your photo's colors in one of your chosen color spaces that is preferably must be wide enough (e.g. ProPhoto). Then there is a transformation happening when you want to print/display your photo and this transformation is carried out in one of the PCS (Profile Connection Space) e.g. CIELAB, CIEXYZ. hence the shrinkage or some loss/inaccuracies during this process of remapping colors (the inaccuracies severity depend of course on how your workflow handle that, clearest example here is moving from display RGB to printer CMYK).
well quite much, I mean there is no possibility of displaying raw data/numbers after all - it will be just a mess of gray intensities- hence you need to define them inside some boundaries where Red, Green and Blue have pre-defined values --> again that is why you process/any raw engine or studio studio processes your raw data usually in a wide gamut color space (e.g. ProPhoto) which has ,as you mentioned, some (quite much) values outside the defined xyY triangle and even outside the boundaries of the defined visible colors!!Remember that raw data has no gamut and some values can be well outside of the CIE xyY triangle.
sorry but I am not quite sure based on what you are claiming that converting from ICC profile's color space through XYZ to your monitor sRGB causes not much of clippings?Of course the mapping is from the ICC PCS (say XYZ) to the monitor's color space (say sRGB) but that itself does not cause "too much cut-off's and missing information". Therefore your statement 3 is incorrect.
I beg to differ, clearest example I can provide is:
imagine if you have your ICC profile encoded in Adobe RGB color space and you assign it to a photo, then the photo needs to be displayed on a standard monitor with sRGB color gamut (smaller gamut than Adobe)...then necessarily a transformation and remapping for the colors will happen from Adobe RGB --> sRGB and clearly sRGB gamut is limited compared to Adobe RGB hence the loss in information or inaccuracies.
I don't think a discussion about color space and color accuracy can avoid the use of the word "gamut" it is the building block of what we are talking about, right?Please try to avoid bringing "gamut" into the discussion
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please feel free to correct any misunderstanding from my side
best,
Tarek