### CENTROID

Finds the centroids of star-like features in an NDF

#### Description:

This routine takes an NDF  and returns the co-ordinates of the centroids of features in its data array given approximate initial co-ordinates. A feature is a set of connected pixels which are above or below the surrounding background region. For example, a feature could be a star or galaxy on the sky, although the applications is not restricted to two-dimensional NDFs.

Four methods are available for obtaining the initial positions, selected using Parameter MODE:

• from the parameter system (see Parameter INIT);

• Using a graphics cursor to indicate the feature in a previously displayed data array (see Parameter DEVICE);

• from a specified positions list (see Parameter INCAT); or

• from a simple text file containing a list of co-ordinates (see Parameter COIN).

In the first two modes the application loops, asking for new feature co-ordinates until it is told to quit or encounters an error.

The results may optionally be written to an output positions list which can be used to pass the positions on to another application (see Parameter OUTCAT), or to a log file geared more towards human readers, including details of the input parameters (see parameter LOGFILE).

The uncertainty in the centroid positions may be estimated if variance values are available within the supplied NDF (see Parameter CERROR).

#### Usage:

centroid ndf [mode] $\left\{\right\$
init coin=? incat=?
[search] [maxiter] [maxshift] [toler]
mode

#### Parameters:

A string determining the co-ordinate Frame  in which positions are to be stored in the output catalogue associated with parameter OUTCAT. The string supplied for CATFRAME can be one of the following options.
• A domain name  such as SKY, AXIS, PIXEL.

• An integer value giving the index of the required Frame.

• An IRAS90 Sky Co-ordinate System (SCS) values such as "EQUAT(J2000)" (see SUN/163).

If a null (!) value is supplied, the positions will be stored in the current Frame. [!]

The epoch at which the sky positions stored in the output catalogue were determined. It will only be accessed if an epoch value is needed to qualify the co-ordinate Frame specified by COLFRAME. If required, it should be given as a decimal years value, with or without decimal places ("1996.8" for example). Such values are interpreted as a Besselian epoch if less than 1984.0 and as a Julian epoch otherwise.
If TRUE, errors in the centroided position will be calculated. The input NDF must contain a VARIANCE component in order to compute errors. [FALSE]
Name of a text file containing the initial guesses at the co-ordinates of features to be centroided. Only accessed if Parameter MODE is given the value "File". Each line should contain the formatted axis values for a single position, in the current Frame  of the NDF. Axis values can be separated by spaces, tabs or commas. The file may contain comment lines with the first character # or !.
If TRUE, a detailed description of the co-ordinate Frame in which the centroided positions will be reported is displayed before the positions themselves. [current value]
The graphics device which is to be used to give the initial guesses at the centroid positions. Only accessed if parameter MODE is given the value "Cursor". [Current graphics device]
If TRUE, then the supplied guesses for the centroid positions will be included in the screen and log file output, together with the accurate positions. [current value]
A catalogue containing a positions list giving the initial guesses at the centroid positions, such as produced by applications CURSOR, LISTMAKE. Only accessed if parameter MODE is given the value "Catalogue".
An initial guess at the co-ordinates of the next feature to be centroided, in the current co-ordinate Frame of the NDF (supplying a colon ":" will display details of the current co-ordinate Frame). The position should be supplied as a list of formatted axis values separated by spaces or commas. INIT is only accessed if parameter MODE is given the value "Interface". If the initial co-ordinates are supplied on the command line only one centroid will be found; otherwise the application will ask for further guesses, which may be terminated by supplying the null value (!).
Name of the text file to log the results. If null, there will be no logging. Note this is intended for the human reader and is not intended for passing to other applications. [!]
Only accessed if Parameter MODE is given the value "Cursor". It indicates which positions are to be marked on the screen using the marker type given by Parameter MARKER. It can take any of the following values.
• "Initial": The position of the cursor when the mouse button is pressed is marked.

• "Centroid": The corresponding centroid position is marked.

• "None": No positions are marked.

[current value]

This parameter is only accessed if Parameter MARK is set TRUE. It specifies the type of marker with which each cursor position should be marked, and should be given as an integer PGPLOT marker type. For instance, 0 gives a box, 1 gives a dot, 2 gives a cross, 3 gives an asterisk, 7 gives a triangle. The value must be larger than or equal to $-$31. [current value]
Maximum number of iterations to be used in the search. It must be in the range 1–9. The dynamic default is 3. [9]
Maximum shift in each dimension allowed between the guess and output positions in pixels. Each must lie in the range 0.0–26.0. If only a single value is given, then it will be duplicated to all dimensions. The dynamic default is half of SEARCH $+$ 1. [9.0]
The mode in which the initial co-ordinates are to be obtained. The supplied string can be one of the following values.
• "Interface" — positions are obtained using Parameter INIT.

• "Cursor" — positions are obtained using the graphics cursor of the device specified by Parameter DEVICE.

• "Catalogue" — positions are obtained from a positions list using Parameter INCAT.

• "File" — positions are obtained from a text file using Parameter COIN.

[current value]
The NDF structure containing the data array to be analysed. In cursor mode (see Parameter MODE), the run-time default is the displayed data, as recorded in the graphics database. In other modes, there is no run-time default and the user must supply a value. []
The number of simulations or realisations using the variance information in order to estimate the error in the centroid position. The uncertainty in the centroid error decreases as one over the square root of NSIM. The range of acceptable values is 3–10000. [100]
##### OUTCAT = FILENAME (Write)
The output catalogue in which to store the centroided positions. If a null value (!) is supplied, no output catalogue is produced. See also Parameter CATFRAME. [!]
A group of attribute settings describing the style to use when drawing the graphics markers specified by Parameter MARK.

A comma-separated list of strings should be given in which each string is either an attribute setting, or the name of a text file preceded by an up-arrow character "^". Such text files should contain further comma-separated lists which will be read and interpreted in the same manner. Attribute settings are applied in the order in which they occur within the list, with later settings overriding any earlier settings given for the same attribute.

Each individual attribute setting should be of the form:

$<$name$>$=$<$value$>$

where $<$name$>$ is the name of a plotting attribute, and $<$value$>$ is the value to assign to the attribute. Default values will be used for any unspecified attributes. All attributes will be defaulted if a null value (!)—the initial default—is supplied. To apply changes of style to only the current invocation, begin these attributes with a plus sign. A mixture of persistent and temporary style changes is achieved by listing all the persistent attributes followed by a plus sign then the list of temporary attributes.

See Section E for a description of the available attributes. Any unrecognised attributes are ignored (no error is reported). [current value]

TRUE, if array features are positive above the background. [TRUE]
Size in pixels of the search box to be used. If only a single value is given, then it will be duplicated to all dimensions so that a square, cube or hypercube region is searched. Each value must be odd and lie in the range 3–51. [9]
A title to store with the output catalogue specified by Parameter OUTCAT, and to display before the centroid positions are listed. If a null (!) value is supplied, the title is taken from any input catalogue specified by Parameter INCAT, or is a fixed string including the name of the NDF. [!]
Accuracy in pixels required in centroiding. Iterations will stop when the shift between successive centroid positions is less than the accuracy. The accuracy must lie in the range 0.0–2.0. [0.05]

#### Results Parameters

##### CENTRE = LITERAL (Write)
The formatted co-ordinates of the last centroid position, in the current Frame of the NDF.
##### ERROR = LITERAL (Write)
The errors associated with the position written to Parameter CENTRE.
##### XCEN = LITERAL (Write)
The formatted x co-ordinate of the last centroid position, in the current co-ordinate Frame of the NDF.
##### XERR = LITERAL (Write)
The error associated with the value written to Parameter XCEN.
##### YCEN = LITERAL (Write)
The formatted y co-ordinate of the last centroid position, in the current co-ordinate Frame of the NDF.
##### YERR = LITERAL (Write)
The error associated with the value written to Parameter YCEN.

#### Examples:

centroid cluster cu
This finds the centroids in the NDF called cluster via the graphics cursor on the current graphics device.
centroid cluster cu search=21 mark=ce plotstyle=’colour=red’
This finds the centroids in the NDF called cluster via the graphics cursor on the current graphics device. The search box for the centroid is 21 pixels in each dimension. The centroid positions are marked using a red symbol.
centroid cluster i "21.7,5007.1"
This finds the centroid of the object in the two-dimensional NDF called cluster around the current Frame co-ordinate (21.7,5007.1).
centroid arp244(6„) i "40,30" toler=0.01
This finds the two-dimensional centroid of the feature near pixel (6,40,30) in the three-dimensional NDF called arp244 (assuming the current co-ordinate Frame of the NDF is PIXEL). The centroid must be found to 0.01 pixels.
centroid cluster cu xcen=(xp) ycen=(yp)
This finds the centroid of an object in the two-dimensional NDF called cluster using a graphics cursor, and writes the centroid co-ordinates to ICL variables XP and YP for use in other applications.
centroid cluster mode=file coin=objects.dat logfile=centroids.log
This finds the centroids in the NDF called cluster. The initial positions are given in the text file objects.dat in the current co-ordinate Frame. A log of the input parameter values, initial and centroid positions is written to the text file centroids.log.
centroid cluster mode=cat incat=a outcat=b catframe=ecl
This example reads the initial guess positions from the positions list in file a.FIT, and writes the accurate centroid positions to positions list file b.FIT, storing the output positions in ecliptic co-ordinates. The input file may, for instance, have been created using the application CURSOR.

#### Notes:

• All positions are supplied and reported in the current co-ordinate Frame of the NDF. A description of the co-ordinate Frame being used is given if Parameter DESCRIBE is set to a TRUE value. Application WCSFRAME can be used to change the current co-ordinate Frame of the NDF before running this application if required.

• In Cursor or Interface mode, only the first 200 supplied positions will be stored in the output catalogue. Any further positions will be displayed on the screen but not stored in the output catalogue.

• The centroid positions are not displayed on the screen when the message filter environment variable MSG_FILTER is set to QUIET. The creation of output parameters and files is unaffected by MSG_FILTER.

#### Estimation of Centroid Positions

Each centroid position is obtained by projecting the data values within a search box centred on the supplied position, on to each axis in turn. This forms a set of profiles for the feature, one for each axis. An estimate of the background at each point in these profiles is made and subtracted from the profile. This flattens the profile backgrounds, removing any slope in the data. Once the profiles have been flattened in this way, and estimate of the background noise in each is made. The centroid of the feature is then found using only the data above the noise level.

Successive estimates of the centroid position are made by using the previous estimate of the centroid as the initial position for another estimation. This loop is repeated up to a maximum number of iterations, though it normally terminates when a desired accuracy has been achieved.

The achieved accuracy is affected by noise, and the presence of non-Gaussian or overlapping features, but typically an accuracy better than 0.1 pixel is readily attainable for stars. The error in the centroid position may be estimated by a Monte-Carlo method using the data variance to generate realisations of the data about the feature (see Parameter CERROR). Each realisation is processed identically to the actual data, and statistics are formed to derive the standard deviations.

#### Related Applications

KAPPA: PSF, CURSOR, LISTSHOW, LISTMAKE.