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I was amazed when I found that Mathematica gives True for the following code (on 32 bit Windows XP with Mathematica 8.0.1):

Rasterize[Graphics[{RGBColor[0, 0, 0], Disk[]}]] === 
 Rasterize[Graphics[{RGBColor[0, 0, 1/257], Disk[]}]]

What is the minimal difference in RGB color values which Mathematica renders and exports as different colors? Is it machine-dependent?

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Alexey Popkov
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3 Answers3

4

I believe this behaviour is machine dependent, but I do not know how exactly it depends on the OS. On my machine, it evaluates to True only when the denominator is 511.

n = 257; 
While[(Rasterize[Graphics[{RGBColor[0, 0, 0], Disk[]}]] === 
    Rasterize[Graphics[{RGBColor[0, 0, 1/n], Disk[]}]]) != True, 
 n++]; 
Print@n

Out[1]=511

There is a difference between the two images for n<511

p1 = ImageData@Rasterize[Graphics[{RGBColor[0, 0, 0], Disk[]}]];
p2 = ImageData@Rasterize[Graphics[{RGBColor[0, 0, 1/257], Disk[]}]];
ArrayPlot[p1 - p2]

enter image description here

This difference is constant all the way through n=510 and is equal to 1/255. 

Max[p2 - p1] === N[1/255]
Out[1]=True
abcd
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  • It is also interesting to compare a set of rectangles of different colors as they are shown on-screen (by taking a screenshot with the `PrtSc` key). Probably the results will be the same as with `Rasterize` - just for the check. For example: `Graphics[{RGBColor[0,0,#],Rectangle[]},ImageSize->40]&/@{0,1/256,1/257,1/510,1/511}`. Please post the screenshot saved in PNG format. On my machine only the second rectangle has RGB value {0,0,1} - others have {0,0,0}. – Alexey Popkov Oct 16 '11 at 08:44
  • @AlexeyPopkov Here's what I get: http://i.stack.imgur.com/mCCoc.png It's interesting how you get `{0,0,1}`... – abcd Oct 16 '11 at 14:00
  • In your screenshot rectangles have RGB value {0,0,0} for the first and the last rectangles but for others it has RGB value {0,0,1}. I get it with Adobe Photoshop CS4. It is as expected from your answer. Thank you. – Alexey Popkov Oct 16 '11 at 14:06
  • @AlexeyPopkov Oh, you mean RGB value of `{0,0,1/255}`. That is correct, and is what I mentioned in the answer. I was very surprised when you said `{0,0,1}`, because that's `Blue` (I understand now that you were giving the 8-bit value)... – abcd Oct 16 '11 at 14:24
3

Looks like Rasterize rounds each pixel's R G B channels to the closest 8bit value (to the closest 1/256).

image = Image[{{{0, 0, .2/256}, {0, 0, .7/256}, {0, 0, 1.2/256}, {0, 
     0, 1.7/256}}}, ImageSize -> 4]
ImageData@image
Rasterize@image
ImageData@Rasterize@image

enter image description here

So the minimal difference, rasterizing into different colors should be around 0.000000000000000000000000000...

Nakilon
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1

Guilty party here is Rasterize, which chops off color precision. Get help on ImageType[] to see that Mathematica actually recognizes other bit depths, but Rasterize[] vandalizes anything beyond Byte.

Gregory Klopper
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