Provided by: netpbm_11.09.02-2_amd64 
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 option. 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. 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 ), 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 followed by the corresponding four target coordinates, or only four (x, y)
coordinates, being only the four target coordinates. In the latter case, the source quadrilateral
is taken to be the four corners of the input image 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. Specify 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 below. 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 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 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-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
\[ \begin{bmatrix} 1 & 0 & c_x \\ 0 & 1 & c_y \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} \cos \theta &
-\sin \theta & 0 \\ \sin \theta & \cos \theta & 0 \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} 1 & 0 & -c_x
\\ 0 & 1 & -c_y \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} x_1 & x_2 & x_3 & x_4 \\ y_1 & y_2 & y_3 & y_4
\\ 1 & 1 & 1 & 1 \end{bmatrix} \quad. \]
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)