2006.09.17 10:39 "Re: [Tiff] is there alpha component presentin GrayscaleorPalettecolorimage", by Graeme Gill
By applying the arbitrary weight 1, you can effectively hide the fact that you're applying arbitrary weights, and that's what you seem to be doing.
Why do you think that's an arbitrary weight? Even the Alpha component can be related back to a visible L*a*b* distance, by the effect it has on the color, giving us the 4th dimension co-ordinate. If you wanted to do lots of work, you could even compute this by taking the color against a range of opaque backgrounds, and using some statistical extraction of the delta E (ie. median, largest etc.), that represents the visible result of the Alpha value.
In any case, there's nothing inherently wrong with arbitrary weights :- they're what you adjust to get an algorithm working in real world situations.
As to convertion to Lab, OK, I'm all for that. So now we do indeed have a 4D space. To make my point, let's encode L, a and b as their natural float value, and alpha as a float value ranging from 0 to 1. So, you're saying the difference between L*a*b*alpha (0,0,0,1) (which is non-transparent black) and (1,0,0,1) (which is non-transparent almost-black) is equal to the difference between (0,0,0,1) (again non-transparent black) and (0,0,0,0) (which is total transparency).
Hmm. Why would you do that? The notional range of L* is 0 to 100, and a* and b* are often taken to range from -128 to +128 (which is somewhat arbitrary, but that's the nature of the colorspace and the real world), so logically the Alpha should be scaled to be 0 to 100 (at least as a starting point). If, in the light of the result, fewer table values were to be given to variations in Alpha, then the scale could be lowered somewhat.
See, we apply weights (full transparent range is equally important as a difference of 1 in the L range). This is obvious if we pick very bad weights as we did here. So what are good weights? Full transparent range is equally important as a difference of 100 in the L range? Or is it twice as important as a difference of 100 in the L range? Why?
Do you expect everything to be handed to you on a plate? :-) Experiment and find out of course! - then write it up, and publish it in a suitable journal. That's what research is all about.