Assigning a profile is a process used to provide it's (hopefully correct) color space. Once done, that profile is embedded into the document.
Here's my very old analogy of why we need to assign profiles (and embed them):
Here’s a metaphor for a color space: suppose I supply a recipe for chocolate chip cookies but do not provide the unit for each ingredient in the recipe. The recipe provides each ingredient followed by a number. Without units you can’t make the cookies. The numbers alone are not enough information to describe how the cookies will be produced. Likewise, R78/G103/B23 or C23/M98/M123/K6 is not enough information to reproduce that color.
Going back to the chocolate chip cookie analogy, suppose a color model is a cookie recipe with only three ingredients. I give you this recipe, which simply calls for 1-flour, 8-butter and 2-chocolate chips. You don’t have enough information to make the cookies. However if I provide you the recipe with a specific scale—1 cup of flour, 8 tablespoons of butter, and 2 cups of chocolate chips—I’ve provided the necessary information, the scale, to make a dozen chocolate chip cookies. I can give you the cookie recipe in the metric scale such as liters and grams and you can still makes the same cookies even though the numbers are different. A color space is a color model that has a known reference and scale, in this case primaries (the ingredients, in this case RG and B) and scale (specific quantities of these ingredients).
Suppose I specify a color as R10/G130/B50 and specify a color reference by saying the color space is Adobe RGB (1998), which defines the scale of the RGB primaries; the color coordinates of this color space. The R10/G130/B50 set of numbers can now reproduce a color by anyone with the proper tools since the reference and scale have been defined. Different RGB color spaces use a different scale of red, green, and blue primaries. Adobe RGB (1998) and sRGB are different color spaces, however both are based on the RGB color model using RGB primaries. Although each color space uses the same three primary ingredients (R, G, and B), the specific colorimetric scale of each color space is different. The maximum of red, green, and blue are more saturated in the Adobe RGB (1998) color space than the sRGB color space. Even though R0/G255/B0 is the greenest green ingredient in both Adobe RGB (1998) and sRGB, knowing that the scale is different in both color spaces explains why this green value is more saturated in Adobe RGB (1998). This also illustrates how R0/G255/B0 alone can’t tell us what green.
An ICC profile simply defines this scale and gives the numbers a meaning allowing us to reproduce the color using something far more concrete than using the English word "Green" or a set of numbers which alone is far too ambiguous to produce a specific color appearance.
So R255 in Adobe RGB (1998) and R255 in sRGB share the same numbers but have a different scale. When you assign a color space to either number, you’re telling Photoshop the scale, it’s updating it’s preview and showing you this (correct or not, you’ve defined the scale so Photoshop believes you). The number hasn’t changed the color appearance has. Now you know why.
Thank you ...
Indeed, I would like to ask the difference between the "convert to profile" and "assign profile" options in the Edit menu ...
I thought that "convert to profile" is the tool for embeding and "assign profile" is the tool for assigning. So, I thought that there must be two different relationship between an image and a profile. But, it seems that it is not correct ... as you say, assigning a profile to an image is the same as embeding a profile to an image (I hope I understand you correctly)
It is ok now ))
I've read again your post today and some other articles on the net and it is clear for me now.
Thanks a lot Andrew ...
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A brief summary (but keep in mind entire books have been written on the subject of color management, so this is far from a complete description!):
One of the very basic principles of color management is that the RGB or CMYK values in the file don't actually mean anything by themselves, they are simply instructions. For example, if you send a color to a printer that is 100c 50m 25y 10k, you are instructing that printer to use 100% of its cyan colorant, 50% of its magenta, 25% of its yellow and 10% of its black. That's it; you're not describing a specific color, you're simply telling a device what to do. In the real world, most printers, monitors, scanners, digital cameras, etc. all behave at least somewhat differently, and sometimes dramatically differently, when it comes to their color capabilities, and will often display or print the same image with significant color differences.
Another example would be if you send an RGB image to a CMYK printer; the RGB values needs to be converted to CMYK, but how is this calculated? There is no one single CMYK formula for a given RGB color (or vice versa).
This is where color management and profiles come into play: they describe the capabilities of a device (a printer, a press, a monitor, a camera, etc.) and allow the software to make adjustments based on that description.
These adjustments fall into two categories:
ASSIGNING a profile retains the color numbers, but alters their appearance based on the profile. Try it for yourself: you can assign a wildly different profile that makes dramatic changes on-screen, but if you look in the Info panel the CMYK or RGB values have not changed at all.
CONVERTING to a profile modifies the numbers based on the profile to try to preserve the color appearance with the new profile. Convert an image from one profile to another; you should see very minor or perhaps no color shift at all, but the CMYK or RGB values have been altered, in some cases significantly.
Note that EMBEDDING a profile has nothing to do with either; it is simply a function of the Save command and whether or not you embed the profile when you save the file. If someone opens a file with an embedded profile they will know what color space you were working in; if they open a file without a profile their software will use whatever their default working color space is.
Hope this makes sense! As I mentioned at the top, this is a complex subject and this post is really just scratching the surface.
Thank you bpylant ... color is really a very complex subject, but I think that I'm starting to understand it with your great helps here.