pamhomography(1) General Commands Manual pamhomography(1)
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NAME
pamhomography - map one arbitrary quadrilateral image region to another
SYNOPSIS
pamhomography
[-from=coords]
[-to=coords]
[-mapfile=map_file]
[-view=coords]
[-fill=color]
[pam_file]
You can abbreviate any option to its shortest unique prefix. You can
use two hyphens instead of one to delimit an option. You can separate
an option from its value with whitespace instead of =.
DESCRIPTION
This program is part of Netpbm ⟨http://netpbm.sourceforge.net/⟩ .
pamhomography transforms a quadrilateral-not necessarily rectangular-
region of an image, producing a new image.
You can do any affine image transformation
⟨https://en.wikipedia.org/wiki/Affine_transformation#Image_transformation⟩
: translation, reflection, scaling, rotation, and shearing/skewing.
However, pamhomography additionally can do bilinear transforms, which
means it can warp any quadrilateral to any other quadrilateral, even
when this mapping cannot be described using a single set of linear
equations. This can be useful, for example, for creating perspective
views of rectangular images or for reverse-mapping a perspective view
back to a rectangular projection.
OPTIONS
In addition to the options common to all programs based on libnetpbm
(most notably -quiet, see Common Options
⟨http://index.html#commonoptions⟩ ), pamhomography recognizes the fol-
lowing command line options:
-from=coords
This defines the source quadrilateral. coords is a list of four
integer-valued (x, y) coordinates. If you do not
specify -from, the source quadrilateral is taken to be the
four
corners of the input image in clockwise order, starting from
the upper
left.
-to=coords
This defines the target quadrilateral. coords is a list of four
integer-valued (x, y) coordinates. If you do not specify -to,
the target quadrilateral is taken to be the four corners of the
input image in clockwise order, starting from the upper left.
-mapfile=map_file
This names a text file that describes the mapping from the
source to the target quadrilateral. The file map_file must con-
tain either eight integer-valued (x, y) coordinates, being the
four source coordinates followed by the corresponding four tar-
get coordinates, or only four (x, y) coordinates, being only the
four target coordinates. In the latter case, the source quadri-
lateral is taken to be the four corners of the input image in
clockwise order, starting from the upper left.
-view=coords
This defines the target view. coords is a list of two integer-
valued (x, y) coordinates: the upper left and lower right bound-
aries, respectively, of the pixels that will be visible in the
output image. If -view is not specified, the target view will
fit precisely the target quadrilateral.
-fill=color
This is the color with which the program fills all pixels that
lie outside of the target quadrilateral. Specify the color as
described for the
argument of the pnm_parsecolor() library routine
⟨http://libnetpbm_image.html#colorname⟩ .
The default is black, and for images with a transparency plane,
transparent.
Cooordinates should normally be specified in clockwise order. The syn-
tax is fairly flexible: all characters other than the plus sign, minus
sign, and digits are treated as separators. Although coordinates need
to be integers, they may lie outside the image's boundary.
If you specify -mapfile along with -from and/or -to, -from and -to
override the quadrilaterals specified by map_file.
PARAMETERS
pamhomography's only parameter, pam_file, is the name of the
file containing the input image. If you don't specify pam_file, the
image comes from Standard Input.
NOTES
The output image uses the same Netpbm format as the input image.
Simple transformations are best handled by other Netpbm programs, such
as those listed in the 'SEE ALSO' ⟨#SEE-ALSO⟩ section below. Use
pamhomography for more sophisticated transformations such as perspec-
tive adjustments, rotations around an arbitrary point in the image, ex-
traction of non-rectangular quadrilaterals, shearings by coordinates
rather than by angle, and, in general, all transformations that are
most easily expressed as mapping four points in one image to four
points in another image.
EXAMPLES
The following examples use the park_row.ppm ⟨park_row.ppm⟩ test image,
which is a
photograph of New York City's Park Row Building
⟨https://commons.wikimedia.org/wiki/File:15_Park_Row_3.JPG⟩ , scaled to
441×640, converted to a PPM file, and redistributed under the
terms of the
GFDL ⟨https://en.wikipedia.org/wiki/GNU_Free_Documentation_License⟩ .
The first example showcases the real power of bilinear transformations.
Assuming park_row_rect.map has the following contents:
(0, 0) (440, 0) (440, 639) (0, 639)
then
projects the building's facade from a perspective view to a rectilinear
front-on view. Remember that pamhomography ignores the parentheses and
commas used in park_row_rect.map; they merely make the file more human-
readable. We equivalently could have written
or any of myriad other variations.
pamhomography can warp the image to a trapezoid to make it look like
it's leaning backwards in 3-D:
As a very simple example,
flips the image left-to-right. Note that in this case the target quad-
rilateral's coordinates are listed in counterclockwise order because
that represents the correspondence between points (0, 0) ↔ (440,
0) and (0, 639) ↔ (639, 0).
Scaling is also straightforward. The following command scales down the
image from 441×640 to 341×540:
Let's add 100 pixels of tan border to the above. We use -view and -fill
to accomplish that task:
We can add a border without having to scale the image:
The -view option can also be used to extract a rectangle out of an im-
age, discarding the rest of the image:
Specifying the same set of coordinates to -from and -to has the same
effect but also allows you to extract non-rectangular quadrilaterals
from an image:
Rotation is doable but takes some effort. The challenge is that you
need to compute the rotated coordinates yourself. The matrix expression
to rotate points \((x_1, y_1)\) \((x_2, y_2)\), \((x_3, y_3)\), and
\((x_4, y_4)\) clockwise by \(\theta\) degrees around point \((c_x,
c_y)\) is
\[ \begin{bmatrix} 1 & 0 & c_x \\ 0 & 1 & c_y \\ 0 & 0 & 1 \end{bma-
trix} \begin{bmatrix} \cos \theta & -\sin \theta & 0 \\ \sin \theta &
\cos \theta & 0 \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} 1 & 0 & -c_x
\\ 0 & 1 & -c_y \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} x_1 & x_2 &
x_3 & x_4 \\ y_1 & y_2 & y_3 & y_4 \\ 1 & 1 & 1 & 1 \end{bmatrix}
\quad. \]
For example, to rotate park_row.ppm 30° clockwise around (220, 320)
you would compute
\[ \begin{bmatrix} 1 & 0 & 220 \\ 0 & 1 & 320 \\ 0 & 0 & 1 \end{bma-
trix} \begin{bmatrix} \cos 30^{\circ} & -\sin 30^{\circ} & 0 \\ \sin
30^{\circ} & \cos 30^{\circ} & 0 \\ 0 & 0 & 1 \end{bmatrix} \begin{bma-
trix} 1 & 0 & -220 \\ 0 & 1 & -320 \\ 0 & 0 & 1 \end{bmatrix} \be-
gin{bmatrix} 0 & 440 & 440 & 0 \\ 0 & 0 & 639 & 639 \\ 1 & 1 & 1 & 1
\end{bmatrix} = \begin{bmatrix} 189.4744 & 570.5256 & 251.0256 &
-130.0256 \\ -67.1281 & 152.8719 & 706.2621 & 486.2621 \\ 1.0000 &
1.0000 & 1.0000 & 1.0000 \end{bmatrix} \quad, \]
round these coordinates to integers, transpose the matrix, and produce
the following map file, park_row_rot30.map:
571 153
251 706
-130 486
(These are the 'to' coordinates; we use the default, full-image 'from'
coordinates.) The mapping then works as in all of the preceding exam-
ples:
SEE ALSO
•
pamcut(1)
•
pamenlarge(1)
•
pamflip(1)
•
pamperspective(1)
•
pamscale(1)
•
pamstretch(1)
•
pam(1)
•
pnmmargin(1)
•
pnmpad(1)
•
pnmrotate(1)
•
pnmshear(1)
HISTORY
pamhomography was new in Netpbm 10.94 (March 2021).
AUTHOR
Copyright © 2020 Scott Pakin, scott+pbm@pakin.org
Table of Contents
•
SYNOPSIS ⟨#SYNOPSIS⟩
•
DESCRIPTION ⟨#DESCRIPTION⟩
•
OPTIONS ⟨#OPTIONS⟩
•
PARAMETERS ⟨#PARAMETERS⟩
•
NOTES ⟨#NOTES⟩
•
EXAMPLES ⟨#EXAMPLES⟩
•
SEE ALSO ⟨#SEE-ALSO⟩
•
HISTORY ⟨#HISTORY⟩
•
AUTHOR ⟨#AUTHOR⟩
DOCUMENT SOURCE
This manual page was generated by the Netpbm tool 'makeman' from HTML
source. The master documentation is at
http://netpbm.sourceforge.net/doc/pamhomography.html
netpbm documentation 03 January 2021 pamhomography(1)
Generated by dwww version 1.15 on Sat Jun 29 02:22:29 CEST 2024.