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Albert Gräf
Gem
Commits
01b1861d
Commit
01b1861d
authored
May 09, 2019
by
IOhannes m zmölnig
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COPYING.txt
View file @
01b1861d
GEM - Graphics Environment for Multimedia
Copyright © 1997-2000 Mark Danks
Copyright © Günter Geiger
Copyright © 2001-2019 IOhannes m zmölnig,
Copyright © 2003-2007 James Tittle II,
Copyright © 2003-2008 Chris Clepper
This program is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License
as published by the Free Software Foundation; either version 2
of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License along
with this program. If not, see <http://www.gnu.org/licenses/>.
In the official GEM distribution, the GNU General Public License is
in the file GnuGPL.LICENSE
---------------------------------------------------------
ACKNOWLEDGMENTS
---------------------------------------------------------
Not all of the source code provided here has entirely been written by me.
I would like to point at the great openGL-tutorials at http://nehe.gamedev.net
Since these are tutorials, there is no copyright notice here.
Some of the pix_fx code is borrowed from effecTV by Kentarou Fukuchi et al.
at http://effectv.sourceforge.net released under the Gnu GPL, some other pix_fx
code has been ported from Pete Warden's fine collection of FreeFrame plugins at
http://petewarden.com released under the Gnu GPL.
---------------------------------------------------------
OTHER COPYRIGHT NOTICES
---------------------------------------------------------
particle:
Author: David McAllister
davemc[AT]cs.unc.edu
http://www.cs.unc.edu/~davemc/Particle/
Copyright (c) 1998 David K. McAllister
License: GNU Lesser General Public License, version 2.1 or later
GEM - Graphics Environment for Multimedia
Copyright © 1997-2000 Mark Danks
Copyright © Günter Geiger
Copyright © 2001-2019 IOhannes m zmölnig,
Copyright © 2003-2007 James Tittle II,
Copyright © 2003-2008 Chris Clepper
This program is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License
as published by the Free Software Foundation; either version 2
of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License along
with this program. If not, see <http://www.gnu.org/licenses/>.
In the official GEM distribution, the GNU General Public License is
in the file GnuGPL.LICENSE
---------------------------------------------------------
ACKNOWLEDGMENTS
---------------------------------------------------------
Not all of the source code provided here has entirely been written by me.
I would like to point at the great openGL-tutorials at http://nehe.gamedev.net
Since these are tutorials, there is no copyright notice here.
Some of the pix_fx code is borrowed from effecTV by Kentarou Fukuchi et al.
at http://effectv.sourceforge.net released under the Gnu GPL, some other pix_fx
code has been ported from Pete Warden's fine collection of FreeFrame plugins at
http://petewarden.com released under the Gnu GPL.
---------------------------------------------------------
OTHER COPYRIGHT NOTICES
---------------------------------------------------------
particle:
Author: David McAllister
davemc[AT]cs.unc.edu
http://www.cs.unc.edu/~davemc/Particle/
Copyright (c) 1998 David K. McAllister
License: GNU Lesser General Public License, version 2.1 or later
GnuGPL.LICENSE.txt
View file @
01b1861d
This diff is collapsed.
Click to expand it.
abstractions/rgb2hsv-help.pd
View file @
01b1861d
#N canvas 172 190 600 500 10;
#X text 124 68 GEM object;
#X text 138 23 rgb2hsv;
#X text 89 388 convert between RGB colorspace and HSV colorspace;
#X text 91 412 RGB is red \, green \, blue;
#X text 91 434 HSV is hue \, saturation \, value (luminance);
#X obj 123 220 rgb2hsv;
#X msg 122 156 1 0 0;
#X msg 357 160 0 1 1;
#X obj 123 299 print hsv;
#X obj 357 303 print rgb;
#X obj 357 226 hsv2rgb;
#X msg 414 159 0.6 1 0.5;
#X msg 185 155 0 0.2 0.5;
#X text 215 21 hsv2rgb;
#X connect 5 0 8 0;
#X connect 6 0 5 0;
#X connect 7 0 10 0;
#X connect 10 0 9 0;
#X connect 11 0 10 0;
#X connect 12 0 5 0;
#N canvas 172 190 600 500 10;
#X text 124 68 GEM object;
#X text 138 23 rgb2hsv;
#X text 89 388 convert between RGB colorspace and HSV colorspace;
#X text 91 412 RGB is red \, green \, blue;
#X text 91 434 HSV is hue \, saturation \, value (luminance);
#X obj 123 220 rgb2hsv;
#X msg 122 156 1 0 0;
#X msg 357 160 0 1 1;
#X obj 123 299 print hsv;
#X obj 357 303 print rgb;
#X obj 357 226 hsv2rgb;
#X msg 414 159 0.6 1 0.5;
#X msg 185 155 0 0.2 0.5;
#X text 215 21 hsv2rgb;
#X connect 5 0 8 0;
#X connect 6 0 5 0;
#X connect 7 0 10 0;
#X connect 10 0 9 0;
#X connect 11 0 10 0;
#X connect 12 0 5 0;
doc/cMatrix.html
View file @
01b1861d
<html>
<head>
<title>
Matrix Operations for Image Processing
</title>
</head>
<body
bgcolor=
"#ffffff"
text=
"#000000"
>
<!--no_print-->
<br><center><table
width=
564
><tr><td>
<h2>
Matrix Operations for Image Processing
</h2>
<!--no_print-->
<h3>
Paul Haeberli
</h3>
<h3>
Nov 1993
</h3>
<img
src=
../tribar.gif
alt=
"Horiz Bar"
width=
561
height=
3
>
<h3>
Introduction
</h3>
<p>
Four by four matrices are commonly used to transform geometry for 3D
rendering. These matrices may also be used to transform RGB colors, to scale
RGB colors, and to control hue, saturation and contrast. The most important
advantage of using matrices is that any number of color transformations
can be composed using standard matrix multiplication.
<p>
Please note that for these operations to be correct, we really must operate
on linear brightness values. If the input image is in a non-linear brightness
space RGB colors must be transformed into a linear space before these
matrix operations are used.
<h3>
Color Transformation
</h3>
RGB colors are transformed by a four by four matrix as shown here:
<pre>
xformrgb(mat,r,g,b,tr,tg,tb)
float mat[4][4];
float r,g,b;
float *tr,*tg,*tb;
{
*tr = r*mat[0][0] + g*mat[1][0] +
b*mat[2][0] + mat[3][0];
*tg = r*mat[0][1] + g*mat[1][1] +
b*mat[2][1] + mat[3][1];
*tb = r*mat[0][2] + g*mat[1][2] +
b*mat[2][2] + mat[3][2];
}
</pre>
<h3>
The Identity
</h3>
This is the identity matrix:
<pre>
float mat[4][4] = {
1.0, 0.0, 0.0, 0.0,
0.0, 1.0, 0.0, 0.0,
0.0, 0.0, 1.0, 0.0,
0.0, 0.0, 0.0, 1.0,
};
</pre>
Transforming colors by the identity matrix will leave them unchanged.
<h3>
Changing Brightness
</h3>
To scale RGB colors a matrix like this is used:
<pre>
float mat[4][4] = {
rscale, 0.0, 0.0, 0.0,
0.0, gscale, 0.0, 0.0,
0.0, 0.0, bscale, 0.0,
0.0, 0.0, 0.0, 1.0,
};
</pre>
Where rscale, gscale, and bscale specify how much to scale the r, g, and b
components of colors. This can be used to alter the color balance of an image.
<p>
In effect, this calculates:
<pre>
tr = r*rscale;
tg = g*gscale;
tb = b*bscale;
</pre>
<h3>
Modifying Saturation
</h3>
<h3>
Converting to Luminance
</h3>
To convert a color image into a black and white image, this matrix is used:
<pre>
float mat[4][4] = {
rwgt, rwgt, rwgt, 0.0,
gwgt, gwgt, gwgt, 0.0,
bwgt, bwgt, bwgt, 0.0,
0.0, 0.0, 0.0, 1.0,
};
</pre>
Where rwgt is 0.3086, gwgt is 0.6094, and bwgt is 0.0820. This is the
luminance vector. Notice here that we do not use the standard NTSC weights
of 0.299, 0.587, and 0.114. The NTSC weights are only applicable to RGB
colors in a gamma 2.2 color space. For linear RGB colors the values above
are better.
<p>
In effect, this calculates:
<pre>
tr = r*rwgt + g*gwgt + b*bwgt;
tg = r*rwgt + g*gwgt + b*bwgt;
tb = r*rwgt + g*gwgt + b*bwgt;
</pre>
<h3>
Modifying Saturation
</h3>
To saturate RGB colors, this matrix is used:
<pre>
float mat[4][4] = {
a, b, c, 0.0,
d, e, f, 0.0,
g, h, i, 0.0,
0.0, 0.0, 0.0, 1.0,
};
</pre>
Where the constants are derived from the saturation value s
as shown below:
<pre>
a = (1.0-s)*rwgt + s;
b = (1.0-s)*rwgt;
c = (1.0-s)*rwgt;
d = (1.0-s)*gwgt;
e = (1.0-s)*gwgt + s;
f = (1.0-s)*gwgt;
g = (1.0-s)*bwgt;
h = (1.0-s)*bwgt;
i = (1.0-s)*bwgt + s;
</pre>
One nice property of this saturation matrix is that the luminance
of input RGB colors is maintained. This matrix can also be used
to complement the colors in an image by specifying a saturation
value of -1.0.
<p>
Notice that when
<code>
s
</code>
is set to 0.0, the matrix is exactly
the "convert to luminance" matrix described above. When
<code>
s
</code>
is set to 1.0 the matrix becomes the identity. All saturation matrices
can be derived by interpolating between or extrapolating beyond these
two matrices.
<p>
This is discussed in more detail in the note on
<a
href=
"../interp/index.html"
>
Image Processing By Interpolation and Extrapolation
</a>
.
<h3>
Applying Offsets to Color Components
</h3>
To offset the r, g, and b components of colors in an image this matrix is used:
<pre>
float mat[4][4] = {
1.0, 0.0, 0.0, 0.0,
0.0, 1.0, 0.0, 0.0,
0.0, 0.0, 1.0, 0.0,
roffset,goffset,boffset,1.0,
};
</pre>
This can be used along with color scaling to alter the contrast of RGB
images.
<h3>
Simple Hue Rotation
</h3>
To rotate the hue, we perform a 3D rotation of RGB colors about the diagonal
vector [1.0 1.0 1.0]. The transformation matrix is derived as shown here:
<p>
If we have functions:
<br><br>
<dl>
<dt><code>
identmat(mat)
</code>
<dd>
that creates an identity matrix.
</dl>
<dl>
<dt><code>
xrotatemat(mat,rsin,rcos)
</code>
<dd>
that multiplies a matrix that rotates about the x (red) axis.
</dl>
<dl>
<dt><code>
yrotatemat(mat,rsin,rcos)
</code>
<dd>
that multiplies a matrix that rotates about the y (green) axis.
</dl>
<dl>
<dt><code>
zrotatemat(mat,rsin,rcos)
</code>
<dd>
that multiplies a matrix that rotates about the z (blue) axis.
</dl>
Then a matrix that rotates about the 1.0,1.0,1.0 diagonal can be
constructed like this:
<br>
First we make an identity matrix
<pre>
identmat(mat);
</pre>
Rotate the grey vector into positive Z
<pre>
mag = sqrt(2.0);
xrs = 1.0/mag;
xrc = 1.0/mag;
xrotatemat(mat,xrs,xrc);
mag = sqrt(3.0);
yrs = -1.0/mag;
yrc = sqrt(2.0)/mag;
yrotatemat(mat,yrs,yrc);
</pre>
Rotate the hue
<pre>
zrs = sin(rot*PI/180.0);
zrc = cos(rot*PI/180.0);
zrotatemat(mat,zrs,zrc);
</pre>
Rotate the grey vector back into place
<pre>
yrotatemat(mat,-yrs,yrc);
xrotatemat(mat,-xrs,xrc);
</pre>
The resulting matrix will rotate the hue of the input RGB colors. A rotation
of 120.0 degrees will exactly map Red into Green, Green into Blue and
Blue into Red. This transformation has one problem, however, the luminance
of the input colors is not preserved. This can be fixed with the following
refinement:
<h3>
Hue Rotation While Preserving Luminance
</h3>
We make an identity matrix
<pre>
identmat(mmat);
</pre>
Rotate the grey vector into positive Z
<pre>
mag = sqrt(2.0);
xrs = 1.0/mag;
xrc = 1.0/mag;
xrotatemat(mmat,xrs,xrc);
mag = sqrt(3.0);
yrs = -1.0/mag;
yrc = sqrt(2.0)/mag;
yrotatemat(mmat,yrs,yrc);
matrixmult(mmat,mat,mat);
</pre>
Shear the space to make the luminance plane horizontal
<pre>
xformrgb(mmat,rwgt,gwgt,bwgt,
&lx,&ly,&lz);
zsx = lx/lz;
zsy = ly/lz;
zshearmat(mat,zsx,zsy);
</pre>
Rotate the hue
<pre>
zrs = sin(rot*PI/180.0);
zrc = cos(rot*PI/180.0);
zrotatemat(mat,zrs,zrc);
</pre>
Unshear the space to put the luminance plane back
<pre>
zshearmat(mat,-zsx,-zsy);
</pre>
Rotate the grey vector back into place
<pre>
yrotatemat(mat,-yrs,yrc);
xrotatemat(mat,-xrs,xrc);
</pre>
<h3>
Conclusion
</h3>
I've presented several matrix transformations that may be applied
to RGB colors. Each color transformation is represented by
a 4 by 4 matrix, similar to matrices commonly used to transform 3D geometry.
<p>
<a
href=
"matrix.c"
>
Example C code
</a>
that demonstrates these concepts is provided for your enjoyment.
<p>
These transformations allow us to adjust image contrast, brightness, hue and
saturation individually. In addition, color matrix transformations concatenate
in a way similar to geometric transformations. Any sequence of
operations can be combined into a single matrix using
matrix multiplication.
<!--no_print-->
<p>
<!--no_print-->
<center>
<!--no_print-->
<a
href=
../index.html#matrix
><img
src=
../gobot.gif
width=
564
height=
25
border=
0
></a>
<!--no_print-->
<br>
<!--no_print-->
</center>
<!--no_print-->
</td></tr></table></center>
</body>
</html>
<html>
<head>
<title>
Matrix Operations for Image Processing
</title>
</head>
<body
bgcolor=
"#ffffff"
text=
"#000000"
>
<!--no_print-->
<br><center><table
width=
564
><tr><td>
<h2>
Matrix Operations for Image Processing
</h2>
<!--no_print-->
<h3>
Paul Haeberli
</h3>
<h3>
Nov 1993
</h3>
<img
src=
../tribar.gif
alt=
"Horiz Bar"
width=
561
height=
3
>
<h3>
Introduction
</h3>
<p>
Four by four matrices are commonly used to transform geometry for 3D
rendering. These matrices may also be used to transform RGB colors, to scale
RGB colors, and to control hue, saturation and contrast. The most important
advantage of using matrices is that any number of color transformations
can be composed using standard matrix multiplication.
<p>
Please note that for these operations to be correct, we really must operate
on linear brightness values. If the input image is in a non-linear brightness
space RGB colors must be transformed into a linear space before these
matrix operations are used.
<h3>
Color Transformation
</h3>
RGB colors are transformed by a four by four matrix as shown here:
<pre>
xformrgb(mat,r,g,b,tr,tg,tb)
float mat[4][4];
float r,g,b;
float *tr,*tg,*tb;
{
*tr = r*mat[0][0] + g*mat[1][0] +
b*mat[2][0] + mat[3][0];
*tg = r*mat[0][1] + g*mat[1][1] +
b*mat[2][1] + mat[3][1];
*tb = r*mat[0][2] + g*mat[1][2] +
b*mat[2][2] + mat[3][2];
}
</pre>
<h3>
The Identity
</h3>
This is the identity matrix:
<pre>
float mat[4][4] = {
1.0, 0.0, 0.0, 0.0,
0.0, 1.0, 0.0, 0.0,
0.0, 0.0, 1.0, 0.0,
0.0, 0.0, 0.0, 1.0,
};
</pre>
Transforming colors by the identity matrix will leave them unchanged.
<h3>
Changing Brightness
</h3>
To scale RGB colors a matrix like this is used:
<pre>
float mat[4][4] = {
rscale, 0.0, 0.0, 0.0,
0.0, gscale, 0.0, 0.0,
0.0, 0.0, bscale, 0.0,
0.0, 0.0, 0.0, 1.0,
};
</pre>
Where rscale, gscale, and bscale specify how much to scale the r, g, and b
components of colors. This can be used to alter the color balance of an image.
<p>
In effect, this calculates:
<pre>
tr = r*rscale;
tg = g*gscale;
tb = b*bscale;
</pre>
<h3>
Modifying Saturation
</h3>
<h3>
Converting to Luminance
</h3>
To convert a color image into a black and white image, this matrix is used:
<pre>
float mat[4][4] = {
rwgt, rwgt, rwgt, 0.0,
gwgt, gwgt, gwgt, 0.0,
bwgt, bwgt, bwgt, 0.0,
0.0, 0.0, 0.0, 1.0,
};
</pre>
Where rwgt is 0.3086, gwgt is 0.6094, and bwgt is 0.0820. This is the
luminance vector. Notice here that we do not use the standard NTSC weights
of 0.299, 0.587, and 0.114. The NTSC weights are only applicable to RGB
colors in a gamma 2.2 color space. For linear RGB colors the values above
are better.
<p>
In effect, this calculates:
<pre>
tr = r*rwgt + g*gwgt + b*bwgt;
tg = r*rwgt + g*gwgt + b*bwgt;
tb = r*rwgt + g*gwgt + b*bwgt;
</pre>
<h3>
Modifying Saturation
</h3>
To saturate RGB colors, this matrix is used:
<pre>
float mat[4][4] = {
a, b, c, 0.0,
d, e, f, 0.0,
g, h, i, 0.0,
0.0, 0.0, 0.0, 1.0,
};
</pre>
Where the constants are derived from the saturation value s
as shown below:
<pre>
a = (1.0-s)*rwgt + s;
b = (1.0-s)*rwgt;
c = (1.0-s)*rwgt;
d = (1.0-s)*gwgt;
e = (1.0-s)*gwgt + s;
f = (1.0-s)*gwgt;
g = (1.0-s)*bwgt;
h = (1.0-s)*bwgt;
i = (1.0-s)*bwgt + s;
</pre>
One nice property of this saturation matrix is that the luminance
of input RGB colors is maintained. This matrix can also be used
to complement the colors in an image by specifying a saturation
value of -1.0.
<p>
Notice that when
<code>
s
</code>
is set to 0.0, the matrix is exactly
the "convert to luminance" matrix described above. When
<code>
s
</code>
is set to 1.0 the matrix becomes the identity. All saturation matrices
can be derived by interpolating between or extrapolating beyond these
two matrices.
<p>
This is discussed in more detail in the note on
<a
href=
"../interp/index.html"
>
Image Processing By Interpolation and Extrapolation
</a>
.
<h3>
Applying Offsets to Color Components
</h3>
To offset the r, g, and b components of colors in an image this matrix is used:
<pre>
float mat[4][4] = {
1.0, 0.0, 0.0, 0.0,
0.0, 1.0, 0.0, 0.0,
0.0, 0.0, 1.0, 0.0,
roffset,goffset,boffset,1.0,
};
</pre>
This can be used along with color scaling to alter the contrast of RGB
images.
<h3>
Simple Hue Rotation
</h3>
To rotate the hue, we perform a 3D rotation of RGB colors about the diagonal
vector [1.0 1.0 1.0]. The transformation matrix is derived as shown here:
<p>
If we have functions:
<br><br>
<dl>
<dt><code>
identmat(mat)
</code>
<dd>
that creates an identity matrix.
</dl>
<dl>
<dt><code>
xrotatemat(mat,rsin,rcos)
</code>
<dd>
that multiplies a matrix that rotates about the x (red) axis.
</dl>
<dl>
<dt><code>
yrotatemat(mat,rsin,rcos)
</code>
<dd>
that multiplies a matrix that rotates about the y (green) axis.
</dl>
<dl>
<dt><code>
zrotatemat(mat,rsin,rcos)
</code>
<dd>
that multiplies a matrix that rotates about the z (blue) axis.
</dl>
Then a matrix that rotates about the 1.0,1.0,1.0 diagonal can be
constructed like this:
<br>
First we make an identity matrix
<pre>
identmat(mat);
</pre>
Rotate the grey vector into positive Z
<pre>
mag = sqrt(2.0);
xrs = 1.0/mag;
xrc = 1.0/mag;
xrotatemat(mat,xrs,xrc);
mag = sqrt(3.0);
yrs = -1.0/mag;
yrc = sqrt(2.0)/mag;
yrotatemat(mat,yrs,yrc);
</pre>
Rotate the hue
<pre>
zrs = sin(rot*PI/180.0);
zrc = cos(rot*PI/180.0);
zrotatemat(mat,zrs,zrc);
</pre>
Rotate the grey vector back into place
<pre>
yrotatemat(mat,-yrs,yrc);
xrotatemat(mat,-xrs,xrc);
</pre>
The resulting matrix will rotate the hue of the input RGB colors. A rotation
of 120.0 degrees will exactly map Red into Green, Green into Blue and
Blue into Red. This transformation has one problem, however, the luminance
of the input colors is not preserved. This can be fixed with the following
refinement:
<h3>
Hue Rotation While Preserving Luminance
</h3>
We make an identity matrix
<pre>
identmat(mmat);
</pre>
Rotate the grey vector into positive Z
<pre>
mag = sqrt(2.0);
xrs = 1.0/mag;
xrc = 1.0/mag;
xrotatemat(mmat,xrs,xrc);
mag = sqrt(3.0);
yrs = -1.0/mag;
yrc = sqrt(2.0)/mag;
yrotatemat(mmat,yrs,yrc);
matrixmult(mmat,mat,mat);
</pre>
Shear the space to make the luminance plane horizontal
<pre>
xformrgb(mmat,rwgt,gwgt,bwgt,
&lx,&ly,&lz);
zsx = lx/lz;