Download SWA (Sliding Window Algorithm) V1.0 User·s Guide

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Carine Babusiaux
DASGAL, UMR 8633 du CNRS, Observatory of Paris-Meudon-Nançay
5, Place J. Janssen, 92195 Meudon Cedex
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SWA is a star detection algorithm that has been developed during a
study on possible algorithms for GAIA on board detection. Here is
presented the principle of SWA, the procedures to use it easily and
the results obtained through simulations.
20 nov 1999
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Content _________________________________________________________________________ 2
Introduction______________________________________________________________________ 3
I. SWA’s principle_________________________________________________________________ 4
a) STEP 1 : Peak test ____________________________________________________________ 4
b) STEP 2 : Sky Background calculation ___________________________________________ 5
c) STEP 3 : Signal to Noise Ration calculation _______________________________________ 5
d) STEP 4 : Parameters estimation ________________________________________________ 5
II. The C program _________________________________________________________________ 6
a) Program organisation _________________________________________________________ 6
b) Global Parameters ___________________________________________________________ 6
c) Organisation of the procedures _________________________________________________ 7
III. Results_______________________________________________________________________ 8
a) Detection rate and false detections ______________________________________________ 8
b) Parameters estimation ________________________________________________________ 8
References _______________________________________________________________________ 8
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SWA (Sliding Window Algorithm) is an algorithm based on an original idea of Erik
Høg. His idea (Høg 1999) was to develop an algorithm based on GAIA’s characteristics, as
opposed to a descendant method that consists in adapting a general algorithm already well
tested, like APM (Irwin 1985), to the GAIA’s characteristics. A first study of both ideas (Luri
1998) has been made. A more detailed study (Arenou & Babusiaux 1999) trying to use the
advantages of both APM and Erik Høg’s idea gave birth to this first version of SWA
algorithm.
SWA has been made only to detect punctual sources. In the idea of Erik Høg, another
algorithm will be developed to detect extended sources.
The principle of SWA is to use a sliding window to estimate the background locally. For
each sample (2*2 pixel in ASM1), there are 4 main steps :
(i) test if the sample seems to be a significant peak.
(ii) estimation of the local sky background near the peak using the sliding window.
(iii) calculation of the signal to noise ratio ; if this ratio is higher than a fixed limit, the peak
is accepted as a detection.
(iv) calculation of the object parameters (position, magnitude).
SWA is still in development ; in this paper is presented the version of September 99 for
ASM1 programmed in the C language. ASM3 could use the same algorithm with different
values of some parameters and some specifications, in particular for the study of binaries.
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peak
samples used to compute background
samples used to compute signal
(1 sample = 2*2 pixel = 74.4 * 223.2 mas)
Fig. 1 : SWA’s sliding window
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Peak test
Background estimation
Signal to Noise Ratio
SNR > 1.5
Centroïding
Photometry
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1. Preliminary thresholding to improve computation time
As the lecture noise in ASM1 is 10.9 e- and the magnitude limit is 21, one can estimate
that it is not useful to look at samples whose value is under 18 e- (this correspond to a star of
magnitude 21 centred between 4 samples). This very simple preliminary thresholding can
save a lot of computation time in fields without any particular sky background.
2. V8 peak test on filtered image
As the noise in GAIA’s image is very important, we use, as proposed in APM (Irwin
1985), a smoothing filter to reduce false detections. The best one tested for the moment is the
binomial filter :
1 2 1
2 4 2
1 2 4
A peak is defined in this filtered image as a sample whose value is higher than his 8
adjacent samples.
3. Khi2 test
To eliminate peaks only due to noise, we use a Khi2 test on the 9 samples centred
around the peak at the threshold of 3 gaussian sigma.
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The local sky background is estimated using the 72 samples of the sliding window
centred around the peak (fig. 1) with the method of the trimmed median : the median of the
72 samples is first calculated, and the samples whose value is at less than 3 sigma from this
median are kept to compute the median again. The median is computed using the Hoare’s
method, 20% quicker than the classical method using a preliminary sort of all the values.
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The signal is calculated here by a simple aperture photometry on the 9 samples around
the peak.
The noise is computed taking into account the photon noise, the RON and the standard
error estimated in the calculation of the background.
The peak is accepted as a detection if the signal to noise ratio (SNR) is higher than 1.5.
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1. centroïding
In this version, the centre of the object is given by the barycentre of the 25 samples
centred around the peak if the object is brighter than 16 magnitude and the 9 surrounding
samples otherwise. It is a compromise between a better precision for bright stars, a low
contamination by noise samples for faint ones, and a quick computation time.
For faint stars (magnitude > 19), a PSF fitting centroïding is a better method, but it is two
times slower in computation time ; the barycentre centroïding should give a sufficient
precision on position in order to follow the object in the other fields, but we will need the
PSF to correct the shift due to the aberration in ASM1 (this has not yet been tested).
2. photometry
In this version, we use the corrected aperture photometry ; the PSF photometry gives
worse results because the PSF is so sheer that this photometry depends too much on a good
precision on the centroïding.
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This algorithm has been tested on FITS images simulated by the program genimg
(Arenou 1999). Since the FITS images generated are oriented like the GAIA field of view and
since a FITS image is read line by line, the program makes a rotation of the image in order to
simulate the continuous lecture of the sky. With SWA’s algorithm, the program just needs to
know all the samples in the sliding window (21*11 samples) for the detection of one star. So
this program reads the fits image line by line, updating a table of 21 across-scan columns,
and for each sample of the central column, use the principle of the SWA algorithm (peak
finding, signal to noise ratio estimation, parameters estimation) to detect stars.
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RFITS.c :
MEDIAN.c :
declaration of the global variables
main
all the procedures of SWA : peak test, background, SNR, photometry
and centroïding estimation.
procedures to read the fits image
procedure to calculate the median
PSF.tab :
table containing the value of the theoretical PSF of the CCD
GLOBAL.h :
SWA.c :
PROCEDURES.c :
The input of the program is just the name of the FITS image, simulated for ASM1. To
use the algorithm for another part of GAIA, some global variables of GLOBAL.h, like the
value of RON and the SNR limit, must be changed.
The output is a .SWA giving the position of the star (in fraction of sample along scan
and across scan, with (1,1) for the centre of the first sample read), the corrected magnitude,
the value of the local background, and the signal to noise ratio of the detection.
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1.
Technical parameters
• The program is made to work on sample values coded with double precision, but the
RFITS procedures can read an image with 32 as well as 64 bits (BitPix) per sample. FesSwap
indicates if RFITS needs to swap the byte (1) or not (0).
• dimAL and dimAC give the dimension of the image, and Nbelts gives the number of
samples of the whole image.
2.
Parameters for a continuous lecture
• The 21 columns that need to be in memory to detect stars in the central column are stored
in the table IMAGE.
• The peak finding step needs the values of the filtered image around the sample ; to win
some computation time, it keeps in memory a table FILTER of 3 columns of the filtered
image, that is updated, as IMAGE at each new column read.
3.
GAIA’s parameters
• Global parameters to compute the magnitude : zero_mag (magnitude zero) and exp_time
(exposition time).
• Rnoise_sqr is the square of the GAIA’s lecture noise (here is used the RON of ASM1).
• PSF_tab is a table containing the values of the theoretical PSF given by L.Lindegren [2].
The values are given with an oversampling of 8. In this version of the program, it just
needs a radius of 31 values ( = PSF_NX = PSF_NY) around the central sub-sample
(PSF_X0,PSF_Y0). shift_sum9 is calculated from PSF_tab to have a corrected magnitude.
4.
SWA’s parameters
• SWA estimates the background using a window of Nbsamples around the peak, stored
in the table Window.
• The SNR limit used to accept a detection is given by SNRlim_sqr.
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To help for a quick look on the C program, here is presented a flow chart of the different
calls of procedures. The detail of the procedures are given in SWA’s principle.
main _detection
main
Peak
initializations
BG_SIGNAL_SNR_calcul
read new column
update buffers
SNR > 1.5
main_detection
Centroiding
magnitude calculus
EOF
EOF
end of
column
END
back to
main
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The images on which the algorithm has been tested are generated by the simulation
(Arenou 1999). Different type of images have been tested : image more or less dense, with a
uniform background or with an important background simulated thanks to HST images.
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On images simulated without any particular background, the detection rate is better
than 95% for stars of magnitude 20 and 60% for stars of magnitude 21. The detection rate
decreases with the field density, but the false detections in independent. On average, there
is less than 10 false detections by CCD. Some false detections can appear with a magnitude
brighter than 20 ; those detections are due to noise situated on the wings of bright stars.
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Centroïding precision is near 1/10ème sample at magnitude 20 (7mas), and 1/5ème sample
at 21 (15 mas). But those numbers have been calculated with images simulated with a PSF
without aberration. The precision should be worth with the real PSF, but it depends on the
correction used that has not been tested yet ;
Magnitude precision is 0.15 mag. at 20 magnitude, and 0.3 mag. at 21. A bias can be
observed from magnitude 20.5, just because it is under the detection limit : stars detected are
those whose flux has been over-estimated.
This first version of SWA has given good results, but it can still be improved. In
particular, the centroïding must be corrected using PSF_tab. The transit between ASM1 and
ASM3 must be simulated to estimate the final detection rate. Moreover, in ASM3, a special
case for binaries should be added.
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F. Arenou, C. Babusiaux (1999) « Simulations et algorithmes de détection pour GAIA »
Atelier Gaia (simulations on line at http://wwhip.obspm.obspm.fr/cgi-bin/genimg)
E. Høg (1999) « Sky survey and photometry by GAIA satellite » SAG_CUO_53
M. Irwin (1985) « Automatic analysis of crowded fields » MNRAS 214, 575-604
L. Lindegren (1998) « Point Spread Functions for GAIA including aberrations » SAG_LL_025
X. Luri (1998 ) « SM detection : APM and Høg algorithm » SAG_IWG_003
Sedjewich R. « Algorithms in C » Add_Wesley