Thanks a lot, Ronald.

I really used the wrong word. The method proposed in the article has nothing in common with lossy compression and is more like histogram enhancement, despite it is hard to distinguish any changes in the image by simple observation. But I still cannot understand how the algorithm was derived.

Well, if you're just worried about the constants, simply scale the pixel values by 1/256 and use floating-point math. This only needs to be done for the calculation of W(I), since the watershed transformation should not care about the pixel value range.

A better approach, of course, is to simply change the constants on the W(I) function. Simply replace I with I/256 everywhere in the formula. So, the first range becomes 0 < I/256 < 88 and the first piece of the function becomes 20-12 I/(88*256). After you've done that for all 3 pieces, multiply W(I) by 256. That should give you the correct function. Plot the old W(I) over the range [0,255] and the new one over [0,65536] to verify that your change is correct.

Sorry, no problem about current implementation. I ask about intensities re-assignation in part 3.3. I cannot understand where any of the constants (7,12,20,0.002, etc.) come from. There are no references concerning the part.

Thanks, Alireza,

But can it be that we should partition the 16bit range for more than three parts used for 8bit? I know the Weber law formulation, but can't understand the implementation logic.

Actually, I don't know where the author got that from either; it seems they also spelled it wrong (It should be Weber not Webber). Perhaps it would be best to email the authors about it.

That was the first one I did when read the article two weeks ago)