Provided by: pdl_2.007-2build1_amd64 bug

NAME

       PDL::Image2D - Miscellaneous 2D image processing functions

DESCRIPTION

       Miscellaneous 2D image processing functions - for want of anywhere else to put them.

SYNOPSIS

        use PDL::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 "PDL::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 median-convolution 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 median-convolution 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 bad-value 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 bad-value 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 non-bad 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 non-bad 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 full-width 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 8-component labeling of a binary image.

       Connected 8-component labeling of 0,1 image - i.e. find separate segmented objects and
       fill object pixels with object number.  8-component labeling includes all neighboring
       pixels.  This is just a front-end to ccNcompt.  See also cc4compt.

        $segmented = cc8compt( $image > $threshold );

   cc4compt
       Connected 4-component labeling of a binary image.

       Connected 4-component labeling of 0,1 image - i.e. find separate segmented objects and
       fill object pixels with object number.  4-component labling does not include the diagonal
       neighbors.  This is just a front-end to ccNcompt.  See also cc8compt.

        $segmented = cc4compt( $image > $threshold );

   ccNcompt
         Signature: (a(m,n); [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 bad-value flag of the input piddles.  It will set the bad-value 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 PDL 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 2-D 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 PDL by Karl Glazebrook.

         # define a 3-sided 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 PDL 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.
       77-81.

       Use the "rotnewsz" function to find out about the dimension of the newly created image

         ($newcols,$newrows) = rotnewsz $oldn, $oldm, $angle;

       PDL::Transform offers a more general interface to distortions, including rotation, with
       various types of sampling; but rot2d is faster.

       rot2d ignores the bad-value flag of the input piddles.  It will set the bad-value 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 bad-value flag of the input piddles.  It will set the bad-value 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 PDL::Transform::map instead: it does these things, at some speed penalty compared to
       rescale2d.

       rescale2d ignores the bad-value flag of the input piddles.  It will set the bad-value flag
       of all output piddles if the flag is set for any of the input piddles.

   fitwarp2d
       Find the best-fit 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 best-fit (using singular-
       value 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
       "np-1") from the output "(u,v)" image to the input "(x,y)" image:

         x = sum(j=0,np-1) sum(i=0,np-1) px(i,j) * u^i * v^j
         y = sum(j=0,np-1) sum(i=0,np-1) 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)
         THRESH  - in svd, remove terms smaller than THRESH * max value
                   default is 1.0e-5

       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.

       THRESH
           Remove all singular values whose valus is less than "THRESH" times the largest
           singular value.

       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]
          [  1.110223e-16 -1.1275703e-17]
         ]
         py =
         [
          [         -12.5  1.6653345e-16]
          [          1.25 -5.8546917e-18]
         ]

   applywarp2d
       Transform a set of points using a 2-D 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 2-D 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 data-reduction 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 0-8186-8944-7).

       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 not-particularly-obvious 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 as

             L(x) = sinc(x) * sinc(x/2)  if abs(x) < 2
                  = 0                       otherwise

       hann
           This kernel is derived from the following function:

             H(x) = a + (1-a) * cos(2*pi*x/(N-1))  if abs(x) < 0.5*(N-1)
                  = 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 with "a = 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 PDL
       distribution. If this file is separated from the PDL distribution, the copyright notice
       should be included in the file.