Manual: pamhomography
pamhomography(1) General Commands Manual pamhomography(1)
NAME
pamhomography - stretch/shrink a quadrilateral region of an image to
another quadrilateral shape
SYNOPSIS
pamhomography
[-from=coords]
[-to=coords]
[-mapfile=map_file]
[-view=coords]
[-fill=color]
[-verbose
[pam_file]
You can abbreviate any option to its shortest unique prefix. You can use two hyphens instead of one to delimit an op‐
tion. You can separate an option from its value with whitespace instead of =.
DESCRIPTION
This program is part of Netpbm .
pamhomography stretches and shrinks an arbitrary quadrilateral portion of an input image you specify (not necessarily
rectangular), into a new quadrilateral shape you specify, producing a new image.
You can do any affine image transformation : translation, reflection, scaling, rotation, and shearing/skewing. How‐
ever, 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 ),
pamhomography recognizes the following 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 the
source with either -from or -mapfile, the source quadrilateral
is the entire input image.
-to=coords
This defines the target quadrilateral. coords is a list of four integer-valued (x, y) coordinates. If you do
not specify the target with either -to or -mapfile, the target quadrilateral is the same as the entire input
image.
-mapfile=map_file
This names a text file that describes the mapping from the source to the target quadrilateral. The file
map_file must contain either eight integer-valued (x, y) coordinates, being the four source coordinates fol‐
lowed by the corresponding four target coordinates, or only four (x, y) coordinates, being only the four tar‐
get coordinates. In the latter case, the source quadrilateral is taken to be the four corners of the input im‐
age in clockwise order, starting from the upper left.
Anything you specify with -to or -from overrides what is in
this file.
-view=coords
This defines the target view. coords is a list of two integer-valued (x, y) coordinates: the upper left and
lower right boundaries, 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. Spec‐
ify the color as described for the argument of the pnm_parsecolor() library routine .
The default is black, and for images with a transparency plane, transparent.
-verbose
This makes the program issue some informational messages about what it is doing.
Cooordinates should normally be specified in clockwise order. The syntax 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.
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' section be‐
low. Use pamhomography for more sophisticated transformations such as perspective adjustments, rotations around an
arbitrary point in the image, extraction 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 test image, which is a photograph of New York City's Park Row Building
, scaled to 441×640, converted to a PPM file, and redistributed under the terms of the GFDL .
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 quadrilateral's coordinates are listed in counter‐
clockwise 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 image, 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-rec‐
tangular 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
\[ \begin{bmatrix} 1 & 0 & c_x \\ 0 & 1 & c_y \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} \cos \theta & -\sin \theta &
0 \\ \sin \theta & \cos \theta & 0 \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} 1 & 0 & -c_x \\ 0 & 1 & -c_y \\ 0 & 0 &
1 \end{bmatrix} \begin{bmatrix} x_1 & x_2 & x_3 & x_4 \\ y_1 & y_2 & y_3 & y_4 \\ 1 & 1 & 1 & 1 \end{bmatrix} \quad.
\]
For example, to rotate park_row.ppm 30° clockwise around (220, 320) you would compute
\[ \begin{bmatrix} 1 & 0 & 220 \\ 0 & 1 & 320 \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} \cos 30^{\circ} & -\sin
30^{\circ} & 0 \\ \sin 30^{\circ} & \cos 30^{\circ} & 0 \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} 1 & 0 & -220 \\ 0
& 1 & -320 \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} 0 & 440 & 440 & 0 \\ 0 & 0 & 639 & 639 \\ 1 & 1 & 1 & 1
\end{bmatrix} = \begin{bmatrix} 189.4744 & 570.5256 & 251.0256 & -130.0256 \\ -67.1281 & 152.8719 & 706.2621 &
486.2621 \\ 1.0000 & 1.0000 & 1.0000 & 1.0000 \end{bmatrix} \quad, \]
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 examples:
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
• DESCRIPTION
• OPTIONS
• PARAMETERS
• NOTES
• EXAMPLES
• SEE ALSO
• HISTORY
• 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 04 December 2022 pamhomography(1)