I am new on this forum, and glad to find it. I would like to know if anyone has found a suitable forumla to approximate a conversion from 8 bit gray shade values (0 - 255) to log denisty, e.g. 0.0 - 2.4, or 0 to 3.0? My math used to be pretty good, but with age, my mind doesn't work the way it used to. I realize the conversion will most likely be approximate. I have a densitometer, so this is more out of curiousity than anything... Thanks!
Brian
Well I don't have a formula but the conversion is about linear (of course) on a log/log plot as shown in a home made plot below. For that plot I used a Stouffer step wedge on a scanner then determined the 0 to 256 equivalent using a K density value on a Photoshop image of the scanner step wedge. Roundabout method but may be more or less OK for what you want.
STEPplot-1-WEDGE-D-vs-EPSON by hypolimnas, on Flickr
Nate Potter, Austin TX.
Nice graph, Nate.
One nitpicky comment...
As presented, your density range is 1 to 256, not 0 to 256.
- Leigh
If you believe you can, or you believe you can't... you're right.
Nate, that will help, and thanks for taking the time to do that. Only thing is, on GIMP in the "curves", the low density (blacker) values are lower numbers, and they increase as the image area increase in brightness. For example, Zone I looks to be about 28 or so, and Zone X would be 255. I can make what you've done work however. Thanks!Originally Posted by Nathan Potter
Well I don't have a formula but the conversion is about linear (of course) on a log/log plot as shown in a home made plot below. For that plot I used a Stouffer step wedge on a scanner then determined the 0 to 256 equivalent using a K density value on a Photoshop image of the scanner step wedge. Roundabout method but may be more or less OK for what you want.
STEPplot-1-WEDGE-D-vs-EPSON by hypolimnas, on Flickr
Nate Potter, Austin TX.
Brian
That's correct, and conforms to the actual values seen by the electronic components.
0 = solid black, 255 = solid white.
- Leigh
If you believe you can, or you believe you can't... you're right.
Brian,
The fact you have the question is enough to know that your math is pretty good.
I do not think the conversion itself is as linear as many members expressed. You approach show be logical first. How can you represent a range of densities maintaining the gray point at the center of the range?
I usually address the issue using normalization, which allows you to keep the gray point in the center of the scale, regardless of the range of densities.
The equation is quite simple, typical f(x)=a^x, with a <= 1.
If you center is 18% gray or approximately .745 density (D), then f(D)=MAX_VAL * (0.395)^D
For example, for 8 bits --> f(0.745)=255 *(0.395)^0.745 = 255 * 0.5006 = 127.5
I hope this help to answer your question.
There no generic conversion without assigning the 255 to some fixed density. What are you trying to accomplish?
Not sure what you mean.
You can assign any one binary value (output of the A/D) to any quantity received from the sensor.
The other 255 values are fixed ratios of 2 from that assigned value. No error or exception to that.
Of course that assumes the A/D is of decent quality with monotonic output, as most modern ones are.
- Leigh
If you believe you can, or you believe you can't... you're right.
The 255 is the "zero" density. How "zero" is defined depends on the hardware. Some scanners will do a pre-scan and set it via DACs. Others will have a little window off the scanning area to set it. In the case of film the zero should be the base + fog so I save a piece of the emulsion and place it in "zeroing" area.
Most table densitometers without light source have a way (typically a wheel) to "zero" the density.
Regarding the Epson or any other CCD based scanner, specially those using diffused light sources. They could give you an idea of the densities but sure will not replace a real densitometer.
There is no a priori relation between the two. That is an arbitrary assignment.
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