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fix typo - thanks peter luft
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zschuessler committed Nov 11, 2016
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Expand Up @@ -18,7 +18,7 @@ <h2>Introduction</h2>
<p>
The <a href="http://www.cie.co.at/index.php/LEFTMENUE/About+us">International Commission on Illumination</a>
(<em>CIE</em>) formed in the early 1900s to standardize the fields of
colorimetry, photometry, and imaging. The commission addressed the
colorimetry, photometry, and imaging. The commission addressed the
topic of color difference in 1976, introducing the world to the concept
of Delta E.
</p>
Expand All @@ -33,52 +33,52 @@ <h2>Defining Delta E</h2>
ΔE - (<em>Delta E, dE</em>) The measure of change in visual perception of two given colors.
</p>
<p>
Delta E is a metric for understanding how the human eye perceives color
difference. The term <em>delta</em> comes from mathematics, meaning change in
a variable or function. The suffix <em>E</em> references the German word
Delta E is a metric for understanding how the human eye perceives color
difference. The term <em>delta</em> comes from mathematics, meaning change in
a variable or function. The suffix <em>E</em> references the German word
<em>Empfindung</em>, which broadly means sensation.
</p>
<p>
On a typical scale, the Delta E value will range from 0 to 100.
</p>
<table>
<tbody>
<tr>
<tr>
<th>Delta E</th>
<th>Perception</th>
</tr>
<tr>
<tr>
<td><= 1.0</td>
<td>Not perceptible by human eyes.</td>
</tr>
<tr>
<tr>
<td>1 - 2</td>
<td>Perceptible through close observation.</td>
<td>Perceptible through close observation.</td>
</tr>
<tr>
<tr>
<td>2 - 10</td>
<td>Perceptible at a glance.</td>
</tr>
<tr>
<tr>
<td>11 - 49</td>
<td>Colors are more similar than opposite</td>
</tr>
<tr>
<tr>
<td>100</td>
<td>Colors are exact opposite</td>
</tr>
</tbody>
</table>
<p>
Take the table as a general guide; it’s possible to get a Delta E
value below 1.0 for two colors that appear different. This is
value below 1.0 for two colors that appear different. This is
the case with CIE76 and CIE94 formulas, in which saturation is
either not considered or not weighted properly.
</p>
<p>
Because of inconsistencies between the three algorithms, the
Because of inconsistencies between the three algorithms, the
exact meaning of Delta E changes slightly depending on which
formula is used. Think of Delta E less as a definitive answer,
formula is used. Think of Delta E less as a definitive answer,
and instead a helpful metric to apply to a specific use case.
</p>

Expand All @@ -99,7 +99,7 @@ <h3>Delta E 76</h3>
<figure>
<img src="{{ site.baseurl }}/img/formula-cie76.png" alt="CIE76 color difference formula" title="CIE76 color difference formula" />
<figcaption>The first-ever Delta E</figcaption>
</figure>
</figure>
<p>
Look familiar? Indeed, you're looking at a ripoff of the <a href="http://en.wikipedia.org/wiki/Euclidean_distance">Euclidean Distance</a>
formula. This makes sense, as CIELAB color space was created as a 3D
Expand All @@ -108,34 +108,34 @@ <h3>Delta E 76</h3>
<figure>
<img src="{{ site.baseurl }}/img/lab-space.png" alt="LAB color space distance example" title="LAB color space distance example" />
<figcaption>Two points in LAB color space</figcaption>
</figure>
</figure>
<p>
Alas, issues are afoot. The premise that LAB color space is
perfect in perceptual uniformity falls short, particularly with
differences in saturation. The example above demonstrates that
perfect in perceptual uniformity falls short, particularly with
differences in saturation. The example above demonstrates that
for hues in the same lightness it works well. But what happens
when we have two saturated colors of different hues?
</p>
<figure>
<img src="{{ site.baseurl }}/img/lab-space-2.png" alt="LAB color space distance comparison example" title="LAB color space distance comparison example" />
<figcaption>Two very different hues, highly saturated</figcaption>
</figure>
</figure>
<figure>
<img src="{{ site.baseurl }}/img/lab-swatch-comparison.png" alt="LAB color swatch comparison" title="LAB color swatch comparison" />
<figcaption>
A closer comparison of the two colors above. Are they similar?
<br/>
...indeed - they appear to be!
</figcaption>
</figure>
</figure>
<p>
The two above blocks represent the dark blue and dark red as
The two above blocks represent the dark blue and dark red as
graphed. CIE76 reports this difference as ΔE 10 (<em>perceptible at a glance</em>),
when by definition difference should fall in the ΔE~1-3 range
(<em>perceptible with close observation</em>).
</p>
<p>
Clearly saturation is a major problem for dE76. In the below
Clearly saturation is a major problem for dE76. In the below
example, blue highlights pixels that each algorithm has
determined as 25% within tolerance of pure saturation (black).
</p>
Expand All @@ -146,17 +146,17 @@ <h3>Delta E 76</h3>
</figcaption>
</figure>
<p>
Delta E can mean different things for a given use case. Here,
Delta E can mean different things for a given use case. Here,
if we wanted to come closer to matching all black color in CIE76,
we would pad the Delta E number more. (<em>Note this lends to
more error, as tolerance increases.</em>)
</p>
<p>
So when do we still use CIE76? The formula has the major advantage
of being a simple Euclidean Distance calculation: it’s faster
than the successive CIE formulas. It’s used in
performance-intensive situations that don’t require high
accuracy. Image processing and real-time post processing
of being a simple Euclidean Distance calculation: it’s faster
than the successive CIE formulas. It’s used in
performance-intensive situations that don’t require high
accuracy. Image processing and real-time post processing
of media is an example of where CIE76 would suffice.
</p>
<p>
Expand All @@ -166,9 +166,9 @@ <h3>Delta E 76</h3>
<!-- Delta E 94 -->
<h3>Delta E 94</h3>
<p>
In 1994, the original Delta E formula was improved. The new
In 1994, the original Delta E formula was improved. The new
formula would take into account certain weighting factors for
each lightness, chroma, and hue value. It also introduced the
each lightness, chroma, and hue value. It also introduced the
ability to add a modifier according to the use case: either
textile, or graphic arts.
</p>
Expand All @@ -178,15 +178,15 @@ <h3>Delta E 94</h3>
<figure>
<img src="{{ site.baseurl }}/img/formula-cie94.png" alt="CIE 94 formula" title="CIE 94 formula" />
<figcaption>
dE76 Formula
dE94 Formula
</figcaption>
</figure>

<p>
CIE94 introduced a conversion of the given Lab value into
CIE L*C*h (Lch). The two color models differ in that Lch
CIE L*C*h (Lch). The two color models differ in that Lch
represents hue as an angle instead of infinite points of color.
This allows us to more easily troubleshoot and perform
This allows us to more easily troubleshoot and perform
calculations on hue.
</p>
<figure>
Expand All @@ -206,22 +206,22 @@ <h3>Delta E 94</h3>
</figcaption>
</figure>
<p>
Given the two colors above, we can agree that the two are much
Given the two colors above, we can agree that the two are much
different in hue, but similar in overall lightness. CIE94
calculates ΔE 128 (<em>polar opposites</em>), while CIE2000 more
correctly calculates ΔE 49.4 (<em>middle of the road</em>).
</p>
<p>
CIE94 is very much Baby Bear in Goldilocks lore: It’s a middle of
the road formula where accuracy is necessary but not mission-critical.
the road formula where accuracy is necessary but not mission-critical.
It’s still often used in textiles and printing applications today.
</p>

<!-- CIE2000 -->
<h3>Delta E 2000</h3>
<p>
The CIE organization decided to fix the lightness inaccuracies
by introducing dE00. It’s currently the most complicated,
by introducing dE00. It’s currently the most complicated,
yet most accurate, CIE color difference algorithm available.
</p>
<figure>
Expand All @@ -232,7 +232,7 @@ <h3>Delta E 2000</h3>
</figure>
<p>
All this busy work gets us a more accurate lightness calculation.
We can see the difference in saturation weighting below.
We can see the difference in saturation weighting below.
This graph compares dE94 and dE00 in posing the question,
"Is pure green more similar to white or black?"
</p>
Expand All @@ -243,13 +243,13 @@ <h3>Delta E 2000</h3>
</figcaption>
</figure>
<p>
Bravo for dE00, which maintains the correct weighting as
Bravo for dE00, which maintains the correct weighting as
lightness fades from black to white. The formula concludes color
difference between green/black and green/white is moderate.
</p>
<p>
dE94 incorrectly concludes that black/green has roughly the same
color difference as white/green. It’s almost as if it couldn't
color difference as white/green. It’s almost as if it couldn't
weight saturation properly!
</p>
<figure>
Expand All @@ -259,16 +259,16 @@ <h3>Delta E 2000</h3>
</figcaption>
</figure>
<p>
Although the most accurate we have today, dE00 is not without
Although the most accurate we have today, dE00 is not without
fault. The most significant discontinuity occurs when compared
hues are 180° from each other (forcing a hue shift in the calculation).
hues are 180° from each other (forcing a hue shift in the calculation).
According to a <a href="http://www.ece.rochester.edu/~gsharma/ciede2000/ciede2000noteCRNA.pdf">Rochester CIE2000 Analysis paper</a>,
this could create a discontinuity of ΔE 0.2734. For all but the
most high accuracy use cases, this is negligible.
</p>
<p>
Remember: Delta E accuracy must be confirmed through the very
tool it was meant to remove subjectivity from -
Remember: Delta E accuracy must be confirmed through the very
tool it was meant to remove subjectivity from -
<em>a pair of human eyes.</em>
</p>

Expand All @@ -278,16 +278,16 @@ <h3>References</h3>
(2014). Retrieved from http://www.cie.co.at/
</li>
<li>
Sharma, G. (2004). The CIEDE2000 Color-Difference Formula:
Implementation Notes, Supplementary Test Data, and Mathematical
Observations. Retrieved from
Sharma, G. (2004). The CIEDE2000 Color-Difference Formula:
Implementation Notes, Supplementary Test Data, and Mathematical
Observations. Retrieved from
<a href="http://www.ece.rochester.edu/~gsharma/ciede2000/ciede2000noteCRNA.pdf">
http://www.ece.rochester.edu/~gsharma/ciede2000/ciede2000noteCRNA.pdf
</a>
</li>
<li>
Color Differences & Tolerances: Commercial Color Acceptability.
(2013, January 1). Retrieved from
Color Differences & Tolerances: Commercial Color Acceptability.
(2013, January 1). Retrieved from
<a href="http://industrial.datacolor.com/support/wp-content/uploads/2013/01/Color-Differences-Tolerances.pdf">
http://industrial.datacolor.com/support/wp-content/uploads/2013/01/Color-Differences-Tolerances.pdf
</a>
Expand All @@ -306,7 +306,7 @@ <h3>References</h3>
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var currentOffset;
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