NAME
PDLA::Image2D  Miscellaneous 2D image processing functions
DESCRIPTION
Miscellaneous 2D image processing functions  for want of anywhere else to put them.
SYNOPSIS
use PDLA::Image2D;
FUNCTIONS
conv2d
Signature: (a(m,n); kern(p,q); [o]b(m,n); int opt)
2D convolution of an array with a kernel (smoothing)
For large kernels, using a FFT routine, such as fftconvolve() in PDLA::FFT
, will be quicker.
$new = conv2d $old, $kernel, {OPTIONS}
$smoothed = conv2d $image, ones(3,3), {Boundary => Reflect}
Boundary  controls what values are assumed for the image when kernel
crosses its edge:
=> Default  periodic boundary conditions
(i.e. wrap around axis)
=> Reflect  reflect at boundary
=> Truncate  truncate at boundary
=> Replicate  repeat boundary pixel values
Unlike the FFT routines, conv2d is able to process bad values.
med2d
Signature: (a(m,n); kern(p,q); [o]b(m,n); int opt)
2D medianconvolution of an array with a kernel (smoothing)
Note: only points in the kernel >0 are included in the median, other points are weighted by the kernel value (medianing lots of zeroes is rather pointless)
$new = med2d $old, $kernel, {OPTIONS}
$smoothed = med2d $image, ones(3,3), {Boundary => Reflect}
Boundary  controls what values are assumed for the image when kernel
crosses its edge:
=> Default  periodic boundary conditions (i.e. wrap around axis)
=> Reflect  reflect at boundary
=> Truncate  truncate at boundary
=> Replicate  repeat boundary pixel values
Bad values are ignored in the calculation. If all elements within the kernel are bad, the output is set bad.
med2df
Signature: (a(m,n); [o]b(m,n); int __p_size; int __q_size; int opt)
2D medianconvolution of an array in a pxq window (smoothing)
Note: this routine does the median over all points in a rectangular window and is not quite as flexible as med2d
in this regard but slightly faster instead
$new = med2df $old, $xwidth, $ywidth, {OPTIONS}
$smoothed = med2df $image, 3, 3, {Boundary => Reflect}
Boundary  controls what values are assumed for the image when kernel
crosses its edge:
=> Default  periodic boundary conditions (i.e. wrap around axis)
=> Reflect  reflect at boundary
=> Truncate  truncate at boundary
=> Replicate  repeat boundary pixel values
med2df does not process bad values. It will set the badvalue flag of all output piddles if the flag is set for any of the input piddles.
box2d
Signature: (a(n,m); [o] b(n,m); int wx; int wy; int edgezero)
fast 2D boxcar average
$smoothim = $im>box2d($wx,$wy,$edgezero=1);
The edgezero argument controls if edge is set to zero (edgezero=1) or just keeps the original (unfiltered) values.
box2d
should be updated to support similar edge options as conv2d
and med2d
etc.
Boxcar averaging is a pretty crude way of filtering. For serious stuff better filters are around (e.g., use conv2d with the appropriate kernel). On the other hand it is fast and computational cost grows only approximately linearly with window size.
box2d does not process bad values. It will set the badvalue flag of all output piddles if the flag is set for any of the input piddles.
patch2d
Signature: (a(m,n); int bad(m,n); [o]b(m,n))
patch bad pixels out of 2D images using a mask
$patched = patch2d $data, $bad;
$bad
is a 2D mask array where 1=bad pixel 0=good pixel. Pixels are replaced by the average of their nonbad neighbours; if all neighbours are bad, the original data value is copied across.
This routine does not handle bad values  use patchbad2d instead
patchbad2d
Signature: (a(m,n); [o]b(m,n))
patch bad pixels out of 2D images containing bad values
$patched = patchbad2d $data;
Pixels are replaced by the average of their nonbad neighbours; if all neighbours are bad, the output is set bad. If the input piddle contains no bad values, then a straight copy is performed (see patch2d).
patchbad2d handles bad values. The output piddle may contain bad values, depending on the pattern of bad values in the input piddle.
max2d_ind
Signature: (a(m,n); [o]val(); int [o]x(); int[o]y())
Return value/position of maximum value in 2D image
Contributed by Tim Jeness
Bad values are excluded from the search. If all pixels are bad then the output is set bad.
centroid2d
Signature: (im(m,n); x(); y(); box(); [o]xcen(); [o]ycen())
Refine a list of object positions in 2D image by centroiding in a box
$box
is the fullwidth of the box, i.e. the window is +/ $box/2
.
Bad pixels are excluded from the centroid calculation. If all elements are bad (or the pixel sum is 0  but why would you be centroiding something with negatives in...) then the output values are set bad.
cc8compt
Connected 8component labeling of a binary image.
Connected 8component labeling of 0,1 image  i.e. find separate segmented objects and fill object pixels with object number. 8component labeling includes all neighboring pixels. This is just a frontend to ccNcompt. See also cc4compt.
$segmented = cc8compt( $image > $threshold );
cc4compt
Connected 4component labeling of a binary image.
Connected 4component labeling of 0,1 image  i.e. find separate segmented objects and fill object pixels with object number. 4component labling does not include the diagonal neighbors. This is just a frontend to ccNcompt. See also cc8compt.
$segmented = cc4compt( $image > $threshold );
ccNcompt
Signature: (a(m,n); int+ [o]b(m,n); int con)
Connected component labeling of a binary image.
Connected component labeling of 0,1 image  i.e. find separate segmented objects and fill object pixels with object number. See also cc4compt and cc8compt.
The connectivity parameter must be 4 or 8.
$segmented = ccNcompt( $image > $threshold, 4);
$segmented2 = ccNcompt( $image > $threshold, 8);
where the second parameter specifies the connectivity (4 or 8) of the labeling.
ccNcompt ignores the badvalue flag of the input piddles. It will set the badvalue flag of all output piddles if the flag is set for any of the input piddles.
polyfill
fill the area of the given polygon with the given colour.
This function works inplace, i.e. modifies im
.
polyfill($im,$ps,$colour,[\%options]);
The default method of determining which points lie inside of the polygon used is not as strict as the method used in pnpoly. Often, it includes vertices and edge points. Set the Method
option to change this behaviour.
Method  Set the method used to determine which points lie in the polygon. => Default  internal PDLA algorithm => pnpoly  use the pnpoly algorithm
# Make a convex 3x3 square of 1s in an image using the pnpoly algorithm
$ps = pdl([3,3],[3,6],[6,6],[6,3]);
polyfill($im,$ps,1,{'Method' =>'pnpoly'});
pnpoly
'points in a polygon' selection from a 2D piddle
$mask = $img>pnpoly($ps);
# Old style, do not use
$mask = pnpoly($x, $y, $px, $py);
For a closed polygon determined by the sequence of points in {$px,$py} the output of pnpoly is a mask corresponding to whether or not each coordinate (x,y) in the set of test points, {$x,$y}, is in the interior of the polygon. This is the 'points in a polygon' algorithm from http://www.ecse.rpi.edu/Homepages/wrf/Research/Short_Notes/pnpoly.html and vectorized for PDLA by Karl Glazebrook.
# define a 3sided polygon (a triangle)
$ps = pdl([3, 3], [20, 20], [34, 3]);
# $tri is 0 everywhere except for points in polygon interior
$tri = $img>pnpoly($ps);
With the second form, the x and y coordinates must also be specified.
B< I<THIS IS MAINTAINED FOR BACKWARD COMPATIBILITY ONLY> >.
$px = pdl( 3, 20, 34 );
$py = pdl( 3, 20, 3 );
$x = $img>xvals; # get x pixel coords
$y = $img>yvals; # get y pixel coords
# $tri is 0 everywhere except for points in polygon interior
$tri = pnpoly($x,$y,$px,$py);
polyfillv
return the (dataflown) area of an image described by a polygon
polyfillv($im,$ps,[\%options]);
The default method of determining which points lie inside of the polygon used is not as strict as the method used in pnpoly. Often, it includes vertices and edge points. Set the Method
option to change this behaviour.
Method  Set the method used to determine which points lie in the polygon. => Default  internal PDLA algorithm => pnpoly  use the pnpoly algorithm
# increment intensity in area bounded by $poly using the pnpoly algorithm
$im>polyfillv($poly,{'Method'=>'pnpoly'})++; # legal in perl >= 5.6
# compute average intensity within area bounded by $poly using the default algorithm
$av = $im>polyfillv($poly)>avg;
rot2d
Signature: (im(m,n); float angle(); bg(); int aa(); [o] om(p,q))
rotate an image by given angle
# rotate by 10.5 degrees with antialiasing, set missing values to 7
$rot = $im>rot2d(10.5,7,1);
This function rotates an image through an angle
between 90 and + 90 degrees. Uses/doesn't use antialiasing depending on the aa
flag. Pixels outside the rotated image are set to bg
.
Code modified from pnmrotate (Copyright Jef Poskanzer) with an algorithm based on "A Fast Algorithm for General Raster Rotation" by Alan Paeth, Graphics Interface '86, pp. 7781.
Use the rotnewsz
function to find out about the dimension of the newly created image
($newcols,$newrows) = rotnewsz $oldn, $oldm, $angle;
PDLA::Transform offers a more general interface to distortions, including rotation, with various types of sampling; but rot2d is faster.
rot2d ignores the badvalue flag of the input piddles. It will set the badvalue flag of all output piddles if the flag is set for any of the input piddles.
bilin2d
Signature: (I(n,m); O(q,p))
Bilinearly maps the first piddle in the second. The interpolated values are actually added to the second piddle which is supposed to be larger than the first one.
bilin2d ignores the badvalue flag of the input piddles. It will set the badvalue flag of all output piddles if the flag is set for any of the input piddles.
rescale2d
Signature: (I(m,n); O(p,q))
The first piddle is rescaled to the dimensions of the second (expanding or meaning values as needed) and then added to it in place. Nothing useful is returned.
If you want photometric accuracy or automatic FITS header metadata tracking, consider using PDLA::Transform::map instead: it does these things, at some speed penalty compared to rescale2d.
rescale2d ignores the badvalue flag of the input piddles. It will set the badvalue flag of all output piddles if the flag is set for any of the input piddles.
fitwarp2d
Find the bestfit 2D polynomial to describe a coordinate transformation.
( $px, $py ) = fitwarp2d( $x, $y, $u, $v, $nf, { options } )
Given a set of points in the output plane ($u,$v
), find the bestfit (using singularvalue decomposition) 2D polynomial to describe the mapping back to the image plane ($x,$y
). The order of the fit is controlled by the $nf
parameter (the maximum power of the polynomial is $nf  1
), and you can restrict the terms to fit using the FIT
option.
$px
and $py
are np
by np
element piddles which describe a polynomial mapping (of order np1
) from the output (u,v)
image to the input (x,y)
image:
x = sum(j=0,np1) sum(i=0,np1) px(i,j) * u^i * v^j
y = sum(j=0,np1) sum(i=0,np1) py(i,j) * u^i * v^j
The transformation is returned for the reverse direction (ie output to input image) since that is what is required by the warp2d() routine. The applywarp2d() routine can be used to convert a set of $u,$v
points given $px
and $py
.
Options:
FIT  which terms to fit? default ones(byte,$nf,$nf)
 FIT

FIT
allows you to restrict which terms of the polynomial to fit: only those terms for which the FIT piddle evaluates to true will be evaluated. If a 2D piddle is sent in, then it is used for the x and y polynomials; otherwise$fit>slice(":,:,(0)")
will be used for$px
and$fit>slice(":,:,(1)")
will be used for$py
.
The number of points must be at least equal to the number of terms to fit ($nf*$nf
points for the default value of FIT
).
# points in original image
$x = pdl( 0, 0, 100, 100 );
$y = pdl( 0, 100, 100, 0 );
# get warped to these positions
$u = pdl( 10, 10, 90, 90 );
$v = pdl( 10, 90, 90, 10 );
#
# shift of origin + scale x/y axis only
$fit = byte( [ [1,1], [0,0] ], [ [1,0], [1,0] ] );
( $px, $py ) = fitwarp2d( $x, $y, $u, $v, 2, { FIT => $fit } );
print "px = ${px}py = $py";
px =
[
[12.5 1.25]
[ 0 0]
]
py =
[
[12.5 0]
[ 1.25 0]
]
#
# Compared to allowing all 4 terms
( $px, $py ) = fitwarp2d( $x, $y, $u, $v, 2 );
print "px = ${px}py = $py";
px =
[
[ 12.5 1.25]
[ 1.110223e16 1.1275703e17]
]
py =
[
[ 12.5 1.6653345e16]
[ 1.25 5.8546917e18]
]
# A higherdegree polynomial should not affect the answer much, but
# will require more control points
$x = $x>glue(0,pdl(50,12.5, 37.5, 12.5, 37.5));
$y = $y>glue(0,pdl(50,12.5, 37.5, 37.5, 12.5));
$u = $u>glue(0,pdl(73,20,40,20,40));
$v = $v>glue(0,pdl(29,20,40,40,20));
( $px3, $py3 ) = fitwarp2d( $x, $y, $u, $v, 3 );
print "px3 =${px3}py3 =$py3";
px3 =
[
[6.4981162e+08 71034917 726498.95]
[ 49902244 5415096.7 55945.388]
[ 807778.46 88457.191 902.51612]
]
py3 =
[
[6.2732159e+08 68576392 701354.77]
[ 48175125 5227679.8 54009.114]
[ 779821.18 85395.681 871.27997]
]
#This illustrates an important point about singular value
#decompositions that are used in fitwarp2d: like all SVDs, the
#rotation matrices are not unique, and so the $px and $py returned
#by fitwarp2d are not guaranteed to be the "simplest" solution.
#They do still work, though:
($x3,$y3) = applywarp2d($px3,$py3,$u,$v);
print approx $x3,$x,1e4;
[1 1 1 1 1 1 1 1 1]
print approx $y3,$y;
[1 1 1 1 1 1 1 1 1]
applywarp2d
Transform a set of points using a 2D polynomial mapping
( $x, $y ) = applywarp2d( $px, $py, $u, $v )
Convert a set of points (stored in 1D piddles $u,$v
) to $x,$y
using the 2D polynomial with coefficients stored in $px
and $py
. See fitwarp2d() for more information on the format of $px
and $py
.
warp2d
Signature: (img(m,n); double px(np,np); double py(np,np); [o] warp(m,n); { options })
Warp a 2D image given a polynomial describing the reverse mapping.
$out = warp2d( $img, $px, $py, { options } );
Apply the polynomial transformation encoded in the $px
and $py
piddles to warp the input image $img
into the output image $out
.
The format for the polynomial transformation is described in the documentation for the fitwarp2d() routine.
At each point x,y
, the closest 16 pixel values are combined with an interpolation kernel to calculate the value at u,v
. The interpolation is therefore done in the image, rather than Fourier, domain. By default, a tanh
kernel is used, but this can be changed using the KERNEL
option discussed below (the choice of kernel depends on the frequency content of the input image).
The routine is based on the warping
command from the Eclipse datareduction package  see http://www.eso.org/eclipse/  and for further details on image resampling see Wolberg, G., "Digital Image Warping", 1990, IEEE Computer Society Press ISBN 0818689447).
Currently the output image is the same size as the input one, which means data will be lost if the transformation reduces the pixel scale. This will (hopefully) be changed soon.
$img = rvals(byte,501,501);
imag $img, { JUSTIFY => 1 };
#
# use a notparticularlyobvious transformation:
# x = 10 + 0.5 * $u  0.1 * $v
# y = 20 + $v  0.002 * $u * $v
#
$px = pdl( [ 10, 0.5 ], [ 0.1, 0 ] );
$py = pdl( [ 20, 0 ], [ 1, 0.002 ] );
$wrp = warp2d( $img, $px, $py );
#
# see the warped image
imag $warp, { JUSTIFY => 1 };
The options are:
KERNEL  default value is tanh
NOVAL  default value is 0
KERNEL
is used to specify which interpolation kernel to use (to see what these kernels look like, use the warp2d_kernel() routine). The options are:
 tanh

Hyperbolic tangent: the approximation of an ideal box filter by the product of symmetric tanh functions.
 sinc

For a correctly sampled signal, the ideal filter in the fourier domain is a rectangle, which produces a
sinc
interpolation kernel in the spatial domain:sinc(x) = sin(pi * x) / (pi * x)
However, it is not ideal for the
4x4
pixel region used here.  sinc2

This is the square of the sinc function.
 lanczos

Although defined differently to the
tanh
kernel, the result is very similar in the spatial domain. The Lanczos function is defined asL(x) = sinc(x) * sinc(x/2) if abs(x) < 2 = 0 otherwise
 hann

This kernel is derived from the following function:
H(x) = a + (1a) * cos(2*pi*x/(N1)) if abs(x) < 0.5*(N1) = 0 otherwise
with
a = 0.5
and N currently equal to 2001.  hamming

This kernel uses the same
H(x)
as the Hann filter, but witha = 0.54
.
NOVAL
gives the value used to indicate that a pixel in the output image does not map onto one in the input image.
warp2d_kernel
Return the specified kernel, as used by warp2d
( $x, $k ) = warp2d_kernel( $name )
The valid values for $name
are the same as the KERNEL
option of warp2d().
line warp2d_kernel( "hamming" );
AUTHORS
Copyright (C) Karl Glazebrook 1997 with additions by Robin Williams (rjrw@ast.leeds.ac.uk), Tim Jeness (timj@jach.hawaii.edu), and Doug Burke (burke@ifa.hawaii.edu).
All rights reserved. There is no warranty. You are allowed to redistribute this software / documentation under certain conditions. For details, see the file COPYING in the PDLA distribution. If this file is separated from the PDLA distribution, the copyright notice should be included in the file.