TIME_REQUIREMENTS · BUGS · SEE_ALSO

## NAME

fmedian -- quantize and box median filter a list of images

## USAGE

`fmedian input output xwindow ywindow`

## PARAMETERS

- input
- List of input images.

- output
- List of output filtered images. The number of input images must be the same as the number of output images. If the input image name equals the output image name the filtered image replaces the original image.

- xwindow, ywindow
- The size of the box median filter. Xwindow and ywindow must be odd. Even values for xwindow or ywindow will be rounded up to the nearest odd integer.

- hmin = -32768, hmax = 32767
- The histogram quantization parameters. Hmin and hmax define the minimum and maximum permitted values for the integer representation of the input image. The default values are appropriate for the 16 bit twos complement data values produced by current CCDs. Hmin and hmax should be chosen so as to minimize the space required to store the image histogram.

- zmin = INDEF, zmax = INDEF
- The data quantization parameters. Zmin and zmax default to the minimum and maximum pixel values in the input image. Pixel values from zmin to zmax are linearly mapped to integer values from hmin to hmax. If zmin = hmin and zmax = hmax, the image pixels are converted directly to integers. Image values less than or greater than zmin or zmax will default to hmin and hmax respectively.

- zloreject = INDEF, zhireject = INDEF
- The minimum and maximum good pixel values. Zloreject and zhireject default to zmin and zmax in the input data or equivalently to hmin and hmax in the integer representation of the input image.

- unmap = yes
- Fmedian rescales the integer values to numbers between zmin and zmax by default. If the user wishes to preserve the median of the quantized images the unmap parameter should be set to no.

- boundary = "nearest"
- The type of boundary extension. The options are:
- nearest
- Use the value of the nearest pixel.

- constant
- Use a constant value.

- reflect
- Reflect pixel values around the boundary.

- wrap
- Wrap pixel values around the boundary.

- constant = 0.
- The value for constant valued boundary extension.

- verbose = yes
- Print messages about actions taken by the task ?

## DESCRIPTION

FMEDIAN takes a list of input images *input*
and produces a set of filtered
output images *output*
. The filter consists of a sliding rectangular
*xwindow*
by *ywindow*
window whose function is to replace the
center pixel in the window with the median of the pixels in the
window. The median of a sequence of numbers is defined to be
the value of the (n + 1) / 2 pixel in the ordered sequence.
Out-of-bounds pixel references are handled by setting the parameter
*boundary*
.

If *zmin*
= *hmin*
and *zmax*
= *hmax*
,
FMEDIAN converts the image pixels directly to
integers. This operation may result in truncation of the pixel values
if the input image is not an integer image. Otherwise the
input pixel values from zmin to zmax are linearly mapped to integer
values from hmin to hmax. The histogram, median, and number of pixels less
than the median, are computed for the first window position. These
quantities are updated as the median filter moves one position.
The *unmap*
parameter is normally set so as to restore the output
pixel values to the range defined by zmin and zmax, but may be turned off
if the user wishes to examine the quantized pixels. The precision of the
median in integer space and pixel space is 1.0 and
(zmax - zmin) / (hmax - hmin) respectively.

The *zloreject*
and *zhireject*
parameters may be used to
reject bad data from the median filtering box. If no good
data is left in a give filtering box, then the median is set to zloreject
if the majority of the pixels are less than zloreject, or to zhireject
if the majority of pixels are greater than zhireject.

## REFERENCES

A description of the fast median algorithm used here can be found in "Topics in Applied Physics: Two-Dimensional Digital Signal Processing II: Transforms and Median Filters", Volume 43, 1981, Springer-Verlag, edited by T.S. Huang, p 209.

## EXAMPLES

1. Median filter a 16 bit CCD image using a 5 by 5 window.

im> fmedian input output 5 5 hmin=-32768 hmax=32767 \ >>> zmin=-32768. zmax=32767.

2. Median filter a KPNO PDS image using a 3 by 3 window.

im> fmedian input output 3 3 hmin=0 hmax=4095 zmin=0. zmax=4095.

3. Median filter an 8 bit image using a 3 by 3 window.

im> fmedian input output 3 3 hmin=0 hmax=255 zmin=0. zmax=255.

4. Median filter an image with real values from 0.0 to 1.0 with a precision of .003 and leave the output pixels in integer format.

im> fmedian input output 5 5 unmap- hmin=0 hmax=1000 zmin=0. \ >>> zmax=1.

5. Median filter the test image dev$pix rejecting any pixels < 5 or greater than 19935 from the medianing process.

im> fmedian dev$pix output 5 5 hmin=-1 hmax=20000 zmin=-1.0 \ >>> zmax=20000 zloreject=5 zhireject=20000

## TIME REQUIREMENTS

It requires approximately 4.5 and 5.8 CPU seconds to median filter an 512 by 512 square integer image with a 5 by 5 and 7 by 7 window respectively. (SPARCStation2).

## BUGS

This technique is most suitable for integer data or data which has not been calibrated. For non-integer data the calculated median may be an approximation, not an exact pixel value.

If the dynamic range of the data defined by hmin and hmax is large the memory requirements can become very large.

## SEE ALSO

median, frmedian