Hi again - Unfortunately, I didn't see your most recent post before I began to construct the tutorial below, so it is not exactly what you want, but it will give you the idea of how to proceed. Specifically, when I constructed this tutorial, I thought you wanted the average color of the "A3 sample tooth" to match the color in the rectangle, so I based everything on that. Now, I see that it should match an 11x11 sample from the middle of the tooth. I think that after this tutorial, it should be clear how to match any color you want, not just the average like I did. Anyway, let me begin.
First, I placed a copy of the "A3 sample tooth" on its own layer and used the blur/average tool to flood that area with a solid, uniform color that is the average color of the entire sample tooth. I then placed a color sampler on the rectangle, and a second color sampler on the "averaged sample tooth":
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(Note: double click on these in-line small previews to see the full resolution version of each of the screen shots.)
Next, I used the RGB values of the "averaged A3 sample tooth" as the input values that I typed into each channel of a curves adjustment layer, for the output values, I used the RGB values of the rectangular area. The following screen shot shows me adjusting the blue channel.
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The next screen shot shows that my modifications of the curves had the desired effects. Look at the "after" RGB values of the 2nd color sampler. Notice that they are now exactly equal to the RGB values of the rectangular area.
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Finally, I turned off the "averaged A3 sample tooth" so that we could see the real "A3 sample tooth", but now, with the curves layer that we just generated being applied.
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The very last image is a GIF animation that shows the effect of the curves adjustment layer that we constructed being turned on and off.
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HTH,
Tom
PS - The "after" version looks a bit too bright to me. If I had seen your most recent post, where you described that the target color was an 11x11 sample from the middle of the tooth, and not the average of the whole tooth, I suspect we would have a much better match.