# pamhomography - Man Page

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## Name

pamhomography — stretch/shrink a quadrilateral region of an image to

## 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.

## 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&times;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) &harr; (440, 0) and (0, 639) &harr; (639, 0).

Scaling is also straightforward. The following command scales down the image from 441&times;640 to 341&times;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&deg; 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:

## History

pamhomography was new in Netpbm 10.94 (March 2021).