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      Identical to MEDIAN or SMOOTH but handle edges and allow iterations.


      Computes the average and/or median of pixels in moving box,
      replacing center pixel with the computed average and/or median,
      (using the IDL SMOOTH() or MEDIAN() functions).
      The main reason for using this function is the options to
      also process the pixels at edges and corners of image, and,
      to apply iterative smoothing simulating convolution with Gaussian,
      and/or to convolve image with a Gaussian kernel. Users might also
      look at the function ESTIMATOR_FILTER() introduced in IDL 7.1.

Calling Sequence

      Result = filter_image( image, SMOOTH=width, MEDIAN = width, /ALL_PIXELS
                              /ITERATE, FWHM =, /NO_FT_CONVOL)


      image = 2-D array (matrix)

Optional Input Keywords

      SMOOTH = scalar (odd) integer specifying the width of a square box
              for moving average, in # pixels. /SMOOTH means use box
              width = 3 pixels for smoothing.
        MEDIAN = scalar (usually odd) integer specifying the width of square
              moving box for median filter, in # pixels. /MEDIAN means use
              box width = 3 pixels for median filter.
      /ALL_PIXELS causes the edges of image to be filtered as well. This
              is accomplished by reflecting pixels adjacent to edges outward
              (similar to the /EDGE_WRAP keyword in CONVOL).
              Note that this is a different algorithm from the /EDGE_TRUNCATE
              keyword to SMOOTH or CONVOL, which duplicates the nearest pixel.
      /ITERATE means apply smooth(image,3) iteratively for a count of
              (box_width-1)/2 times (=radius), when box_width >= 5.
              This is equivalent to convolution with a Gaussian PSF
              of FWHM = 2 * sqrt( radius ) as radius gets large.
              Note that /ALL_PIXELS is automatically applied,
              giving better results in the iteration limit.
              (also, MEDIAN keyword is ignored when /ITER is specified).
      FWHM_GAUSSIAN = Full-width half-max of Gaussian to convolve with image.
                      FWHM can be a single number (circular beam),
                      or 2 numbers giving axes of elliptical beam.
      /NO_FT_CONVOL causes the convolution to be computed directly,
              with intrinsic IDL CONVOL function. The default is to use
              FFT when factors of size are all LE 13. Note that
              external function convolve.pro handles both cases)

Optional Input/output Keyword

    PSF = Array containing the PSF used during the convolution. This
          keyword is only active if the FWHM_GAUSSIAN keyword is also
          specified. If PSF is undefined on input, then upon output it
          contains the Gaussian convolution specified by the FWHM_GAUSSIAN
          keyword. If the PSF array is defined on input then it is used
          as the convolution kernel, the value of the FWHM_GAUSSIAN keyword
          is ignored. Typically, on a first call set PSF to an undefined
          variable, which can be reused for subsequent calls to prevent
          recalculation of the Gaussian PSF.


      Function returns the smoothed, median filtered, or convolved image.
      If both SMOOTH and MEDIAN are specified, median filter is applied first.
      If only SMOOTH is applied, then output is of same type as input. If
      either MEDIAN or FWHM_GAUSSIAN is supplied than the output is at least
      floating (double if the input image is double).


      To apply 3x3 moving median filter and
      then 3x3 moving average, both applied to all pixels:
              Result = filter_image( image, /SMOOTH, /MEDIAN, /ALL )
      To iteratively apply 3x3 moving average filter for 4 = (9-1)/2 times,
      thus approximating convolution with Gaussian of FWHM = 2*sqrt(4) = 4 :
              Result = filter_image( image, SMOOTH=9, /ITER )
      To convolve all pixels with Gaussian of FWHM = 3.7 x 5.2 pixels:
              Result = filter_image( image, FWHM=[3.7,5.2], /ALL )

External Calls

      function psf_gaussian
      function convolve
      pro factor
      function prime ;all these called only if FWHM is specified


      If both /ALL_PIXELS (or /ITERATE) keywords are set then
      create a larger image by reflecting the edges outward, then call the
      IDL MEDIAN() or SMOOTH() function on the larger image, and just return
      the central part (the original size image).
      NAN values are recognized during calls to MEDIAN() or SMOOTH(), but
      not for convolution with a Gaussian (FWHM keyword supplied).


      Written, 1991, Frank Varosi, NASA/GSFC.
      FV, 1992, added /ITERATE option.
      FV, 1993, added FWHM_GAUSSIAN= option.
      Use /EVEN call to median, recognize NAN values in SMOOTH
                  W. Landsman June 2001
      Added PSF keyword, Bjorn Heijligers/WL, September 2001
      Keep same output data type if /ALL_PIXELS supplied A. Steffl Mar 2011

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