### 4 Object detection and parameterisation – PISAFIND

PISAFIND performs image analysis on a 2-dimensional data frame. It has two basic modes of operation. The first is isophotal analysis in which pixels with data values above a given threshold are examined for connectivity and combined into objects. This type of analysis should be used on images that contain a heterogeneous collection of objects such as a mixture of stars and galaxies.

The second mode of operation is profile fitting in which an analytical stellar profile is fitted to the objects found by a preliminary isophotal analysis. This latter option should only be used in situations where all the images on a data frame have the same shape, such as in a star cluster. This type of analysis is also performed by the DAOPHOT [3] package which specializes in analysing crowded stellar fields. The determination of the best fit model parameters is performed by PISAFIT.

In crowded regions deblending of overlapping sources can be performed. The isophotal analysis does this by examining each object at a number of higher isophotes to see if the object splits into more than one component. The profile fitting does this by modelling the data with the analytic profiles and seeing if the fit can be improved by decreasing or increasing the number of objects, as well as altering their position and brightness. In both cases the intensity of the combined image is partitioned between the components to ensure conservation of flux.

If the objects have extensive wings to their intensity profiles then the simple isophotal analysis can underestimate the total intensity in an object; two options for estimating the total intensity are available. The first uses a circular aperture of specified radius within which you know the total light to be contained. The second uses an automatic curve of growth analysis in which the intensity within elliptical apertures of increasing size is measured until a maximum is reached. This is similar to a Kron-style analysis.

For the profile fitting case the intensity of an object is obtained by integrating under the analytic profile using the relevant parameters (the actual functions are described in appendix B). The analytic profile is made up of three components. The core of the profile is a Gaussian but below a given level an exponential function takes over. The two functions are under-pinned by a Lorentzian function which is summed over all regions. If the results of the analysis are to be compared to other frames then the magnitudes from the profile fitting have to be related to total magnitudes by analysing at least one object on the frame by both methods. The rest of the measurements can then be suitably scaled to give total magnitudes.

It is always a good idea to run the isophotal analysis on a frame before running any of the other options to check that there are no peculiarities, and in the case of deblending to check that the objects do not fragment too much. If the data is significantly oversampled (the point-spread function covers many pixels) then the data should be binned into a smaller array. There will be no significant loss of accuracy, but a great improvement in execution time.

A full list of the PISAFIND parameters is given in appendix A which should be consulted before running the application.

#### 4.1 Pre-processing of the image

PISAFIND expects there to be no background variation in the image array. Any such variations should be removed in advance with a suitable application, such as SURFIT in KAPPA [6]. The frame should also be clean of any defects and bad pixels.

#### 4.2 Restriction on input data

Currently PISAFIND works with INTEGER data in the range 0 to 32766. An array of real data in this range will be accepted by the routine but the following message will appear:

Input NDF is of type _REAL - this application can only process at
_WORD precision; significance may be lost

If the array contains data outside this range the program will abort with the following message:

! The input NDF contains "bad" pixels or values outside the range of
_WORD, these cannot be correctly handled by this application.

A previous restriction on the size of the input data has been removed, however, other limitations still apply. The maximum length of the first dimension of any input data is 10240 pixels. Objects cannot fragment into more than 200 pieces.

#### 4.3 Content of the results files

The results of the parameterisation analysis are written into two files.

The first file name is defined by the RESULTS parameter. There are eleven columns in the output file containing the following information :-

 Column Name Description 1 INDEX Index number of object. 2 XPOS X position of object in pixels. 3 YPOS Y position of object in pixels. 4 INTENSITY Integrated intensity of object. 5 NPIX Number of pixels above threshold. 6 PEAK Peak intensity of object in one pixel. 7 ELLIPT Ellipticity of object. 8 ANGLE Orientation of object, anti-clockwise from y-axis. 9 SXX Second moment of data in x. 10 SYY Second moment of data in y. 11 SXY Cross moment of data in x and y.

The SXX, SYY and SXY moments are defined as:

$SXX=\frac{\sum {x}^{2}{I}_{i}}{\sum {I}_{i}},\phantom{\rule{0.3em}{0ex}}\phantom{\rule{0.3em}{0ex}}SYY=\frac{\sum {y}^{2}{I}_{i}}{\sum {I}_{i}},\phantom{\rule{0.3em}{0ex}}\phantom{\rule{0.3em}{0ex}}SXY=\frac{\sum xy{I}_{i}}{\sum {I}_{i}}$

Where $x$ and $y$ are offsets from the centre of the object (determined by the centroid) and ${I}_{i}$ is the intensity in a pixel, corrected for the background contribution.

The ellipticity is defined by the equation:

$ell=\frac{a-b}{a}$

Where $a$ and $b$ are the semimajor and semiminor axes:
${a}^{2}=2\phantom{\rule{0.3em}{0ex}}\left(SXX+SYY\right)+2\phantom{\rule{0.3em}{0ex}}\sqrt{{\left(SXX-SYY\right)}^{2}+4\phantom{\rule{0.3em}{0ex}}SX{Y}^{2}}$

${b}^{2}=2\phantom{\rule{0.3em}{0ex}}\left(SXX+SYY\right)-2\phantom{\rule{0.3em}{0ex}}\sqrt{{\left(SXX-SYY\right)}^{2}+4\phantom{\rule{0.3em}{0ex}}SX{Y}^{2}}$

Note that these are intensity weighted rms-like distances. If you want to calculate values that go out to say the detection isophote then you should use the geometric formulae:
$a=\sqrt{\frac{NPIX}{\left(\pi \phantom{\rule{0.3em}{0ex}}\left(1-ELLIPT\right)\right)}}$

$b=a\phantom{\rule{0.3em}{0ex}}\left(1-ELLIPT\right)$

The results of the areal thresholding analysis are written to the file whose name is given by the SIZES parameter. There are nine columns in the output file, the last seven contain the number of pixels within the intensity thresholds : -

${I}_{i}={I}_{t}\ast {2}^{\left(i+2\right)},\phantom{\rule{3.04074pt}{0ex}}i=2,8$

where ${I}_{t}$ is the threshold intensity and ${I}_{i}$ is the object intensity above the threshold :-
 Column Name Description 1 INDEX Index number of object. 2 A1 Number of object pixels within threshold. 3 A2 Number of object pixels within i=2 threshold. 4 A3 Number of object pixels within i=3 threshold. 5 A4 Number of object pixels within i=4 threshold. 6 A5 Number of object pixels within i=5 threshold. 7 A6 Number of object pixels within i=6 threshold. 8 A7 Number of object pixels within i=7 threshold. 9 A8 Number of object pixels within i=8 threshold.

The RESULTS output of PISAFIND can be used as input to the aperture photometry program PHOTOM [4]. This could be exploited to automate the photometry of standard stars on CCD frames.