### GAUSMOOTH

Smooths a one- or two-dimensional image using a Gaussian filter

#### Description:

This application smooths an NDF  using a one- or two-dimensional symmetrical Gaussian point spread function (PSF) of specified width, or widths and orientation. Each output pixel is the PSF-weighted mean of the input pixels within the filter box.

The NDF may have up to three dimensions. If it has three dimensions, then the filter is applied in turn to each plane in the cube and the result written to the corresponding plane in the output cube. The orientation of the smoothing plane can be specified using the AXES parameter.

#### Usage:

gausmooth in out fwhm

#### Parameters:

This parameter is only accessed if the NDF has exactly three significant pixel axes. It should be set to the indices of the NDF pixel axes which span the plane in which smoothing is to be applied. All pixel planes parallel to the specified plane will be smoothed independently of each other. The dynamic default is the indices of the first two significant axes in the NDF. []
The x and y sizes (in pixels) of the rectangular region over which the Gaussian PSF should be applied at each point. The smoothing PSF will be set to zero outside this rectangle, which should therefore be sufficiently large not to truncate the PSF too early. A square region is defined should only one size be given. For a one-dimensional or circular Gaussian a second size is ignored. Two values are expected when an elliptical PSF is requested (see the description of Parameter FWHM).

The values given will be rounded up to positive odd integers if necessary. If a null (!) value is supplied, the value used is just sufficient to accommodate the Gaussian PSF out to a radius of 3 standard deviations. Note that the time taken to perform the smoothing increases in approximate proportion to the value of this parameter for a circular Gaussian, and in proportion to the product of the two box sizes for an elliptical Gaussian. [!]

This specifies whether a circular or elliptical Gaussian point-spread function is used in smoothing a two-dimensional image. If one value is given it is the full-width at half-maximum of a one-dimensional or circular Gaussian PSF. (Indeed only one value is permitted for a one-dimensional array.) If two values are supplied, this parameter becomes the full-width at half-maximum of the major and minor axes of an elliptical Gaussian PSF. Values between 0.1 and 10000.0 pixels should be given. Note that unless a non-default value is specified for the BOX parameter, the time taken to perform the smoothing will increase in approximate proportion to the value(s) of FWHM. The suggested default is the current value.
The input NDF containing the one-, two-, or three-dimensional image to which Gaussian smoothing is to be applied.
The orientation of the major axis of the elliptical Gaussian PSF, measured in degrees in an anti-clockwise direction from the x axis of the NDF. ORIENT is not obtained if FWHM has one value, i.e. a circular Gaussian PSF will be used to smooth the image, or the input NDF is one-dimensional. The suggested default is the current value.
##### OUT = NDF (Write)
The output NDF which is to contain the smoothed image.
The title for the output NDF. A null value will cause the title of the input NDF to be used. [!]
If the input image contains bad pixels, then this parameter may be used to determine the number of good pixels which must be present within the PSF area before a valid output pixel is generated. It can be used, for example, to prevent output pixels from being generated in regions where good pixels are only present in the wings of the PSF.

By default, a null (!) value is used for WLIM, which causes the pattern of bad pixels to be propagated from the input image to the output image unchanged. In this case, smoothed output values are only calculated for those pixels which are not bad in the input image.

If a numerical value is given for WLIM, then it specifies the minimum PSF-weighted fraction of good pixels which must be present in the PSF area (i.e. box) in order to generate a good output pixel. The maximum value, in the absence of bad pixels, is unity. If the specified minimum fraction of good input pixels is not present, then a bad output pixel will result, otherwise a smoothed output value will be calculated. The value of this parameter should lie between 1E-6 and 1.0. [!]

#### Examples:

gausmooth image1 image2 5.0
Smooths the two-dimensional image held in the NDF structure image1 using a symmetrical Gaussian PSF with a full-width at half-maximum of 5 pixels. The smoothed image is written to image2. If any pixels in the input image are bad, then the corresponding pixels in the output image will also be bad.
gausmooth spectrum1 spectrum2 5.0 box=9
Smooths the one-dimensional image held in the NDF structure spectrum1 using a symmetrical Gaussian PSF with a full-width at half-maximum of 5, and is evaluated over a length of 9 pixels. The smoothed image is written to spectrum2. If any pixels in the input image are bad, then the corresponding pixels in the output image will also be bad.
gausmooth in=a out=b fwhm=3.5 box=31
Smooths the two-dimensional image held in the NDF structure a, writing the result into the structure b. The Gaussian smoothing PSF has a full-width at half-maximum of 3.5 pixels and is evaluated over a large square of size 31x31 pixels.
gausmooth in=a out=b fwhm=[4,3] orient=52.7 box=[29,33]
Smooths the two-dimensional image held in the NDF structure a, writing the result into the structure b. The elliptical Gaussian smoothing PSF has full-width at half-maximum of 4 pixels along its major axis and three pixels along its minor axis, and is evaluated over a large rectangle of size 29x33 pixels. The major axis of the PSF is oriented 52.7 degrees anti-clockwise from the x axis of the data array.
gausmooth ngc1097 ngc1097s fwhm=7.2 wlim=0.1
Smooths the specified image data using a Gaussian PSF with a full-width at half-maximum of 7.2. An output value is calculated for any pixel for which the PSF-weighted fraction of good input pixels is at least 0.1. This will cause the smoothing operation to fill in moderately sized regions of bad pixels.

#### Timing

For a circular PSF, the execution time is approximately proportional to the number of pixels in the image to be smoothed and to the value given for the BOX parameter. By default, this latter value is proportional to the value given for FWHM. For an elliptical PSF, the execution time is approximately proportional to the number of pixels in the image to be smoothed and to the product of the values given for the BOX parameter. By default, these latter values are approximately proportional to the values given for FWHM. Execution time will be approximately doubled if a variance array is present in the input NDF.

#### Related Applications

KAPPA: BLOCK, CONVOLVE, FFCLEAN, MATHS, MEDIAN, PSF; FIGARO: ICONV3, ISMOOTH, IXSMOOTH, MEDFILT.