TIME_REQUIREMENTS · BUGS · SEE_ALSO

## NAME

frmedian -- quantize and ring median filter a list of input images

## USAGE

`frmedian input output rinner router`

## PARAMETERS

- input
- List of input images.

- output
- List of 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 images replaces the original image.

- rinner, router
- The inner and outer semi-major axes of the ring filter in pixels. If rinner is set to 0.0 then the ring filter becomes a circular filter.

- ratio = 1.0
- The ratio of the semi-minor axis to the semi-major axes of the ring filter. If ratio is 1.0 the ring filter is circularly symmetric.

- theta = 0.0
- The position angle of the major axis of the ring filter. Theta is measured counter-clockwise in degrees from the x axis and must be between 0 and 180 degrees.

- 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 those suitable for the 16 bit twos complement data 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 hmin and hmax in the integer representation of the input image.

- unmap = yes
- Frmedian rescale the integer values to numbers between zmin and zmax by default. If the user wishes to preserve the mode 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

FRMEDIAN takes a list of input images *input*
and produces a set of filtered
output images *output*
. The filter consists of a sliding
circular / elliptical or annular circular / elliptical window whose size
and orientation is determined
by the *rinner*
, *router*
, *ratio*
, and *theta*
parameters.
The center pixel in the window is replaced by the median of the pixels in the
window, where the median of a sequence of numbers is defined to be
the value of the (n + 1) / 2 number in the ordered sequence.
Out of bounds pixel references are handled by setting the parameter
*boundary*
. The principal function of the circular / elliptical filters
is to smooth an image using a circularly / elliptically symmetric filter.
The principal function of the circular / elliptical ring filter is to
remove objects from the image which have a scale length of rinner and
replace them with an estimate of the local background value.

If *zmin*
= *hmin*
and *zmax*
= *hmax*
, FRMEDIAN 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 to 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, page 209.

The properties of the ring median filter and its application to astronomical data analysis problems is summarized in the article "A Ring Median Filter for Digital Images" (Secker, J., 1995, PASP, 107, 496-501) and reference therein.

## EXAMPLES

1. Median filter a 16 bit CCD image using a circular ring filter with an inner radius of 4 pixels and a width of 1 pixel.

im> frmedian input output 4.0 5.0 hmin=-32768 hmax=32767 \ >>> zmin=-32768. zmax=32767.

2. Median filter a KPNO PDS image using a circular ring filter of outer radius 3.

im> frmedian input output 0.0 3.0 hmin=0 hmax=4095 zmin=0. zmax=4095.

3. Median filter an 8 bit image using the same filter used in example 2.

im> frmedian input output 0.0 3.0 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. Use a ring filter of inner radius 5.0 and width 0.5 pixels.

im> frmedian input output 5.0 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 using a circular filter of outer radius 5.0.

im> frmedian dev$pix output 0.0 5.0 hmin=-1 hmax=20000 zmin=-1.0 \ >>> zmax=20000 zloreject=5 zhireject=20000

## TIME REQUIREMENTS

It requires approximately 30 and 22 cpu seconds to median filter a 512 by 512 square integer image with a circular filter of radius 5 pixels and a ring filter of inner and outer radii of 4.0 and 5.0 pixels respectively. (SPARCStation2).

## BUGS

This technique is most suitable for integer data and data which has not been calibrated. For non-integer data the calculated median is an approximation only.

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