This test page includes saturation examples of ppmhsy, including the newest
version, 1.2, with gamma correction.
We compare the results with results from Gimp and Imagemagick, which use
variants of the HLS model.  Note that Gimp uses much the same algorithms as
the popular Photoshop.
Saturation by a factor of more than 2 in gimp is done by saturating twice by
100%.

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Note: most saturation increases tested here are very heavy, up to a factor of
4.  This is to show the effect of the algorithms more clearly. Usually, you'll
only want to saturate up to a factor of 1.5 or perhaps 2.


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Desaturation.  From left to right: original, gimp desaturated, ppmhsy 1.1 (no
gamma correction), ppmhsy 1.2 (gamma correction).  Note: this image clearly
demonstrates the desaturation problem with regular HSV or HLS colour spaces.
Results from imagemagick are identical to gimp. The ppmhsy rendering results
in a faithful greyscale image. Note that the Gimp greyscale mode produces an
image similar to the ppmhsy image.

<BR> <img src="saturation-orig.jpg"> <img
src="saturation-grey-gimp.jpg"> <img src="saturation-grey-ppmhsy.jpg"> <img
src="saturation-grey-ppmhsy-gamma.jpg">

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A more blatant example of the HSV/HLS brightness problem can be seen when one
takes an image with primary colours.  With help of such an image, it is also
possible to see differences in different Y formulas.  <a
href="y-value.html">See the page on Y values.</a>


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Increasing saturation 4x.  From left to right: original, gimp, ppmhsy 1.1,
ppmhsy 1.2.
Note: gimp looks reasonably neat here, but the greens are brightened and the
blues are darkened.  Ppmhsy compensates by adding extra red and blue, which
amplifies noise in the dark areas.  The newest version of ppmhsy with gamma
correction corrects the noise problem in the dark areas.

<BR>
<img src="saturation-orig.jpg">
<img src="saturation-4x-gimp.jpg">
<img src="saturation-4x-ppmhsy.jpg">
<img src="saturation-4x-ppmhsy-gamma.jpg">
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The need for gamma correction is apparent here. A much clearer example of this
is found in the image below.  From left to right:  original, gimp desaturated,
ppmhsy desaturated without gamma correction, ppmhsy desaturated with gamma
correction.  Note: Gimp renders the blue and red waves too bright.  Ppmhsy
without gamma correction makes the waves disappear completely (gimp greyscale
mode produces a similar result).  Ppmhsy with gamma correction produces a more
accurate result.  Even the bright bands around the edges of the blue and red
waves are rendered faithfully.  <BR>

<img src="example1.png">
<img src="example1-gimp.png">
<img src="example1-nogamma.png">
<img src="example1-gamma.png">

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Increasing saturation 4x.  From left to right: original, gimp, imagemagick,
ppmhsy 1.1, ppmhsy 1.2.  Note: the yellows in the flower's heart are
brightened in gimp and imagemagick, causing ugly contrast in the shadows.
This effect already happens at 2x saturation.  At 4x saturation, we also get
terrible noise in the blues, which seems to be a result of the great
brightness differences between small differences of H or S of blue/cyan for
equal L.  It is not present in the ppmhsy version. Oddly, the noise in the
Gimp version is worse (see below).  There is little difference between ppmhsy
with and without gamma correction here.

<BR>
<img src="pic1.jpg">
<img src="sat-pic1-4x-gimp.jpg">
<img src="sat-pic1-4x-imagemagick.jpg">
<img src="sat-pic1-4x-pnmhsy.jpg">
<img src="sat-pic1-4x-ppmhsy-gamma.jpg">
<P>

<!--
Increasing saturation 2x.  Left: original. Middle: gimp. Right: ppmhsy<BR>
<img src="pic2.png">
<img src="sat-pic2-2x-gimp.png">
<img src="sat-pic2-2x-pnmhsb.png">
<P>-->

<!--
Increasing saturation 4x.  From left to right: original, gimp, imagemagick,
ppmhsy 1.1, ppmhsy 1.2.  Note: in the gimp and imagemagick versions, the pink
clouds at the top left and the very top right contrast oddly with the blue
sky, with a dark rim around them.  Again we see noise in the blues, which is
again worse in gimp.  Neither are present in the ppmhsy versions.
Again, there is little difference between ppmhsy
with and without gamma correction here.
<BR>

<img src="pic3.jpg">
<img src="sat-pic3-4x-gimp.jpg">
<img src="sat-pic3-4x-imagemagick.jpg">
<img src="sat-pic3-4x-pnmhsy.jpg">
<img src="sat-pic3-4x-ppmhsy-gamma.jpg">
<P>-->

To further test my hypotheses about the noise in the blue-cyan areas, I did a
4x saturation on a simple blue-cyan gradient.  The results are quite
surprising.  From left to right: original, gimp, imagemagick, ppmhsy 1.1,
ppmhsy 1.2.  There is terrible banding in the gimp image, indicating some
kind of serious rounding error, which may result from the fact that gimp uses
8-bit integers to represent the HLS values.  The imagemagick image looks quite
smooth, but has a steep brightness gradient about 1/3 from the bottom
(strongest at H=192), which is further proof of the theory about the
brightness noise. The difference between ppmhsy with and without gamma
correction is very clear here: without gamma correction it is too bright and
there is a small bright band around H=200.

<BR>
<img src="cyantest.png">
<img src="cyantest-gimp.png">
<img src="cyantest-imagemagick.png">
<img src="cyantest-ppmhsb.png">
<img src="cyantest-ppmhsy-gamma.png">
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So, it appears that for H around 190-200, varying H or S with equal L is
likely to cause visible brightness differences, resulting in noise.
Furthermore, we may conclude that the gimp (version 1.2.3) algorithm is
defective, and should be fixed.

<P>

Another situation where cyans can easily be shown to be troublesome are hue
shifts.  Say, I want to prove that I am an alien by turning a picture of
myself cyan.  Left: original. Middle: Gimp, 180 deg. hue shift.  Right:
ppmhsy, 180 deg. hue shift.  Of all possible hue shifts, this one turns out
worst in Gimp.  The ppmhsy rendering shows that the HSY model is also suitable
for hue operations.

<BR> <img src="mugshot.jpg"> <img
src="mugshot-gimp.jpg"> <img src="mugshot-ppmhsy.jpg">


<!--

Increasing saturation 4x.  From left to right: original, gimp, ppmhsb, ppmhsb
darkened. Note: the gimp version makes the background too deep pink, and
decreases the contrast in the hair in front of the eye. The skin is a bit more
pinkish than the ppmhsb version.  The darkened ppmhsb doesn't look quite cool,
probably because the white areas in the picture are overexposed areas, and
turn grey when darkened, making them look unnatural.
<BR>
<img src="pic4.png">
<img src="sat-pic4-4x-gimp.png">
<img src="sat-pic4-4x-pnmhsb.png">
<img src="sat-pic4-4x-pnmhsb-darkened.png">
<P>

Increasing saturation 3x.  From left to right:
original,gimp,imagemagick,ppmhsb,original.
Note: gimp and imagemagick are almost but not quite the same.
Both increase the brightness of the greens in the sweater, and on the face (in
particular around the chin).


<BR>

<img src="portrait1.png"> <img src="sat-portrait1-gimp.png"> <img
src="sat-portrait1-imagemagick.png">
<img
src="sat-portrait1-xv40p.png">
<img src="sat-portrait1-ppmhsb.png"> <img
src="portrait1.png"> <P> Increasing saturation 3x.  From left to right:
original,gimp,imagemagick,ppmhsb,original.  Note: this is not a very good
image, and saturation clearly amplifies noise.  The greenish parts of the skin
are brightened in gimp and imagemagick, which causes the skin to get
blotchier.

<BR>

<img src="portrait2.png">
<img src="sat-portrait2-gimp.png">
<img src="sat-portrait2-imagemagick.png">
<img src="sat-portrait2-xv40p.png">
<img src="sat-portrait2-ppmhsb.png">
<img src="portrait2.png">
-->


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<address>Boris van Schooten,  boris@13thmonkey.org</address>