Apple Aperture Digital Photography Fundamentals - Manual (Page 44)

44 Chapter 3 Understanding Resolution
Learning About the Relationship Between Floating Point
and Bit Depth
When you make multiple adjustments to a digital image, the adjustments are
mathematically calculated to create the result. Just as with analog-to-digital
conversions, there can be quantization errors when adjustments are calculated. For
example, consider the following calculation: 3 ÷ 2 = 1.5. Note that for the answer to be
accurate, a decimal point had to be added for an extra level of precision. However, if
the bit depth of your pixels does not allow this level of precision, the answer would
have to be rounded to either 2 or 1. In either direction, this causes a quantization error.
This is particularly noticeable when you try to return to the original value. Without the
precision of floating point, you’re left with 1 x 2 = 2 or 2 x 2 = 4. Neither calculation is
capable of returning the original value of 3. As you can see, this can become
problematic when adjustments require a series of calculations and each subsequent
value is inaccurate. Since a large number of calculations are required to perform
complicated adjustments to an image, it is important that the adjustments are
calculated at a significantly higher resolution than the input or output resolution in
order to ensure the final rounded numbers are more accurate.
In the example below, a green channel of a 24-bit pixel (with 8 bits per color channel)
is capable of displaying 256 shades of green. If an adjustment is made calling for a
calculation between the 167th and 168th color values, without floating point the
application would have to round to one or the other. The result of the final calculation
would be a color that is close but not accurate. Unfortunately, information is lost.
255
239
0
127
63
31
15
47
95
79
111
191
159
143
175
167.5 Although an 8-bit color channel
can’t display the color value
represented by 167.5, floating-point
calculations can use this value to
create a more accurate final color.
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