# pamhomography

Updated: 03 January 2021
Table of Contents

## 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.

pamhomography transforms a quadrilateral—not necessarily rectangular—region of an image, 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 -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 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.

-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.

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.

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" 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:

        (147, 51) (316, 105) (402, 595) (92, 560)
          (0,  0) (440,   0) (440, 639)  (0, 639)

then

        pamhomography -mapfile park_row_rect.map park_row.ppm > park_row_rect.ppm

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

        147 51 316 105 402 595 92 560 0 0 440 0 440 639 0 639

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:

        pamhomography -to "50,0 390,0 440,200 0,200" park_row.ppm > park_row_trap.ppm

As a very simple example,

        pamhomography -to "440,0 0,0 0,639 440,639" park_row.ppm > park_row_flip.ppm

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:

        pamhomography -to "0,0 340,0 340,539 0,539" park_row.ppm > park_row_small.ppm

Let's add 100 pixels of tan border to the above. We use -view and -fill to accomplish that task:

        pamhomography -to "0,0 340,0 340,539 0,539" -view "-100,-100 440,639" -fill tan park_row.ppm > park_row_small_border.ppm

We can add a border without having to scale the image:

        pamhomography -view "-100,-100 540,739" -fill tan park_row.ppm > park_row_border.ppm

The -view option can also be used to extract a rectangle out of an image, discarding the rest of the image:

        pamhomography -view "130,10 205,80" park_row.ppm > park_row_cut.ppm

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:

        pamhomography -from "185,300 310,325 320,425 180,405" -to "185,300 310,325 320,425 180,405" park_row.ppm > park_row_cut_2.ppm

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:

         189  -67
         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:

        pamhomography -mapfile park_row_rot30.map park_row.ppm > park_row_rot30.ppm

## SEE ALSO

- pamcut
- pamenlarge
- pamflip
- pamperspective
- pamscale
- pamstretch
- pam
- pnmmargin
- pnmpad
- pnmrotate
- pnmshear

## 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