1 Introduction. 2 The Problem and the present method. 2.1 The problem

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1 Stellar Image Interpretation System Using Artificial Neural Networks: II Bi-polar Function Case A. El-Bassuny Alawy, F. I. Y. Elnagahy, A. A. Haroon, Y. A. Azzam, B. Šimák A supervised Artificial Neural Network (ANN) based system is being developed employing the Bi-polar function for identifying stellar images in CCD frames. It is based on feed-forward artificial neural networks with error back-propagation learning. It has been coded in C language. The learning process was performed on a 341 input pattern set, while a similar set was used for testing. The present approach has been applied on a CCD frame of the open star cluster M67. The results obtained have been discussed and compared with those derived in our previous work employing the Uni-polar function and by a package known in the astronomical community (DAOPHOT-II). Full agreement was found between the present approach, that of Elnagahy et al, and the standard astronomical data for the cluster. It has been shown that the developed technique resembles that of the Uni-Polar function, possessing a simple, much faster yet reliable approach. Moreover, neither prior knowledge on, nor initial data from, the frame to be analysed is required, as it is for DAOPHOT-II. Keywords: neural networks, knowledge-based system, stellar images, image processing. 1 Introduction Not only is stel lar as tron omy the old est topic in astro - nomical stud ies, but it con tin ues to be of im por tance in astronomical re search. This is be cause stars are the prin ci ple ob jects from which oth ers are formed (bi nary and mul ti ple star sys tems, star clus ters and gal ax ies). Stel lar im ag ing has become an essential and effective technique in astronomy since the in ven tion of pho to graphic plates. Its im por tance increased with the ad vent of so phis ti cated low light level two dimension detectors such as Image Intensifier Tubes (IITs) and Charge Cou pled De vices (CCDs). By the end of the 1970 s, as tro nom i cal op ti cal ob ser va - tions had made a great leap with the use of cam eras equipped with CCD chips af ter their in ven tion at the Bell Lab. by W. Boyle and G. Smith [1]. This may be at trib uted to rea sons such as su pe rior quan tum ef fi ciency, large dy namic and spec - tral sen si tiv ity ranges, fairly uni form re sponse, high lin ear ity and rel a tively low noise in com par i son with other de tec tors, particularly photographic plates. In addition, digital image data is di rectly ac ces si ble with no need for mea sure ment or for cumbersome and imprecise calibration. The invention of CCD chips and their use co in cided with great ad vances in of elec tronic com put ing ma chines. As a con se quence of these advances, tremendous astronomical images have been acquired that need re li able, pre cise and fast re duc tion tech - niques and ap proaches. In the astronomical community various methods have been de signed, de vel oped, coded and ap plied. These are based on view ing the star im age through a math e mat i cal model [2, 3, 4], an em pir i cal model [5, 6, 7] or a semi-em pir i - cal model [8, 9]. The codes based on these mod els, usu ally a bi-vari ant Gaussi an func tion, re quire a user-com puter in ter - face fa cil ity for pro vid ing the form of the model adopted and also for set ting the ini tial val ues of the model pa ram e ters. Sev eral runs of such codes are nec es sary to op ti mise and derive the fi nal set of pa ram e ters, through some non-lin ear fit ting pro cess, to be ap pli ca ble for CCD frame re duc tion. Such cir cum stances re quire a fast com put ing ma chine pro - vided with a large mem ory and work ing space area as well as an ex pert user. How ever, in cor rect and/or false re sults are possible, mainly due to imprecise parameter estimates and/or improper user intervention. Re cently, we have de vel oped two ap proaches em ploy ing Artificial Intelligence techniques to recognise stellar images [10] besides deriving all relevant astronomical data [11]. In our previous communication [12], hereinafter Paper I, an Artificial Neural Network based system employing a Unipolar func tion was pro posed. Very good agree ment was achieved be tween the re sults of our sys tem and those ob tained by applying the most widely used soft ware in the as tro nom i cal com mu nity, DAOPHOT-II [13], through ap pli ca tion on a test case (a CCD frame of the star clus ter M67). In ad di tion, ex act co in ci dence was found be tween the re sults of Pa per I and the cluster standard data found in the astronomical literature and databases. In the pres ent work, a bi po lar func tion has been adopted and ap plied on the same frame, and the out come has been investigated and com pared with the pre vi ous ones. 2 The Problem and the present method 2.1 The problem As known and out lined in Pa per I, a CCD frame may contain entities that are images of astronomical objects (star, gal axy, etc.) as well as those caused by other sources (cos mic rays, noise etc.). All of them are gath ered at the same time and under the same atmospheric and instrumental conditions. After ac quir ing an im age, the frame needs to be re duced, first by iden ti fy ing the stel lar im ages among the oth ers and then by deriving their positions and magnitudes. The present work con cerns the first step. This has been real ised by a su per vised Ar ti fi cial Neu ral Net work based Sys tem (ANNS) as a dis crim i - nating approach. 24 Czech Technical University Publishing House

2 Acta Polytechnica Vol. 44 No. 1/ The architecture of the present ANNS The ANNS used here is sim i lar to that adopted in Pa per I. It com prises the two-layer for ward net work de picted in Fig. 1. It in cludes four and three neurones for the first (hid den) layer and the sec ond (out put) layer, re spec tively. The in put is z i (for i = 1 to 24) yield ing the hid den layer weight ma trix as v(4 24) and that of the out put as w(3 4). These are il lus - trated in the fig ure, which also shows the bi ases (v 1,0, v 2,0, v 3,0 & v 4,0 and w 1,0, w 2,0 & w 3,0 ) for the neurones of the lay - ers. The dis crim i nat ing func tion adopted is one of the known bi-po lar func tions given by the hy per bolic tan gent func tion as x 1 e F x 1 F x 1 x 1 e where (de scend ing fac tor) is an ar bi trarily small pos i tive value. First, the weights for this func tion have to be de ter mined through the learn ing pro cess on the se lected pat tern set. Secondly and be fore ap pli ca tion, both the func tion adopted and the weights de rived have to be ver i fied against a sim i lar known set. Finally, the func tion and its weights can be ap plied to an un known CCD frame to be re duced for the pur poses of discrimination. 2.3 Learning and test input patterns For the learn ing and test tasks, we adopted the same two pat tern sets used in Pa per I. In each set, a to tal of 341 in put pat terns are in cluded (119 stars, 111 cos mic ray events and 111 noises). It is ob vi ous that the pat tern sets are of large size and equally dis trib uted over the three en ti ties. This as sures proper learning and reliable weight determination. For the pur pose of learn ing, the set pat terns were ran dom ised and fed to the ANNS. Each pat tern con sists of the data of a 5 5 pixel ar ray cen tred at the peaked pixel taken from some CCD frames. The pat tern sam ples were se lected to rep re sent stars of dif fer ent bright ness and events of cos mic rays with dif fer ent en er gies as well as var i ous noise pat terns. In such a case, the data of the cen tral pix els of the pat terns dif fers widely. In or - der to per form the learn ing pro cess prop erly this data has to be scaled. This was achieved, for each pat tern, by nor mal is ing the data of all pix els to that of the cen tral pixel. This leads to the unity to all cen tral pix els of the pat terns. Fig. 2 dem on - strates the raw data, the im age and the 3-D view of a sam ple of these pat terns. For the im ages and 3-D views, nor mal ised data is used. It is ev i dent from the pat tern sets, as il lus trated in the figure, that: a) For a star, the data shows a grad ual de crease from the cen - tre out ward caus ing an ex tended bright area to the lim its of the im age and a pro nounced (but not ex treme) sharp peak in the 3-D view. b) For a cos mic sam ple, the cen tral pixel da tum is much larger than the data of the other 24 pix els, which is very close to each other with val ues much lower than those at the cen tre. This pro vides very sharp local ised peak in the 3-D view and highly con cen trated bright ness at the cen tre of the im age. c) For noise, the data of the ar ray is more or less close to each other and dis trib uted ran domly, caus ing some peaks of low height in the 3-D view, and a fea ture less im age. Fig. 1: The ar chi tec ture of the adopted ANNS Czech Technical University Publishing House 25

3 Fig. 2: Raw data, im age and a 3-D view of a star, cos mic and noise sam ples of the in put pat tern These discriminate characteristics of the three identities are very help ful in ap ply ing ANNS. 2.4 Training error and learning factors The train ing er ror and the learn ing fac tors adopted here are those de scribed in de tail by one of us else where [10] and sum ma rised in [12]. Among the dif fer ent types of er rors work able in ANN, the de ci sion er ror is in voked to ter mi nate the net work train ing pro cess. It was com puted for the en tire batch of train ing pat tern sam ples (P) via, Ed Nerr PK where K is the thresh old out put over one cy cle (set as 3) and N err is the to tal num ber of bit er rors re sulted. Re gard ing the learn ing mode, some pre cau tions were undertaken for the learn ing fac tors in or der to avoid the pitfalls generally associated with error minimisation tech - niques, such as instability, oscillation, divergence and shallow lo cal min ima. First, the net work weights were in itial ised ran - domly to pos i tive val ues be tween 0.0 and 0.1, while neg a tive val ues be tween these lim its were as signed to the bi ases for the hid den and out put layer neu rons v i,0 and w i,0. Sec ondly, a value of 0.01 was set to the learn ing con stant that was found to accelerate the convergence without overshooting the so lu tion. Finally, the mo men tum term was set as 0.5 to speed up the con ver gence of the er ror back-prop a ga tion learn ing al go rithm. The learn ing fac tor and the mo men tum term values are in ac cor dance with the sim i lar val ues used in Paper I. 2.5 Training the present ANNS Ta ble 1 lists the de sired three com po nents of the out put patterns, O i, nom i nated for star, noise and cos mic event en ti - ties. In the learn ing mode, many cy cles were per formed through the adopted pat terns. At the be gin ning of any cy cle, N err was set to zero and all in put pat terns data were map - ped to the ANNS se quen tially. For each cy cle the first pat tern data was fed to the ANNS and the three out puts (i.e. ac tual out put) were com puted. For each one of these out puts the error as so ci ated was cal cu lated. The to tal num ber of bit er ror (i.e. N err ) has to be in creased if the dif fer ence be tween the desired out put (Ta ble 1) and the ac tual out put is equal to (or greater than) 0.1; then the weights of the out put and the hidden lay ers are ad justed, re spec tively. Then this pro cess is ap plied for the next pat tern, till the last one pro vid ing that the er ror of each pat tern is com puted. At the end of the cy cle, the decision error (E d ) is com puted. If E d is not equal to zero, the whole cy cle is re peated un til E d is zero and hence the learn ing task is com pleted. The de ci sion com po nents of the out put pat terns, O i, are given in Ta ble 2 for the three en ti ties (star, noise and cos mic ray event). These are used to gether with the adopted bi-po lar func tion and the de rived weights in or der to clas sify the unknown frame en ti ties. In such a case when Lo cal Cen tral Peaked Pixel (LCPP) is found the 5 5 pixel ar ray data is extracted and the ANNS is em ployed to com pute the rel e vant outputs and, applying the following: If O 1 > 0.9, O 2 < 0.1 and O 3 < 0.1 then the ob ject is a star image. If O 1 < 0.1, O 2 > 0.9 and O 3 < 0.1 then the ob ject is a noise. 26 Czech Technical University Publishing House

4 Acta Polytechnica Vol. 44 No. 1/2004 If O 1 < 0.1, O 2 < 0.1 and O 3 > 0.9 then the ob ject is a cos - mic event. Ta ble 1: De sired out put val ues for Star, Noise and Cos mic ray event O 1 O 2 O 3 Star Noise Cosmic Ray Ta ble 2: De ci sion out put val ues for Star, Noise and Cos mic ray event O 1 O 2 O 3 Star >0.9 <0.1 <0.1 Noise <0.1 >0.9 <0.1 Cosmic Ray <0.1 <0.1 > Implementation and test The pres ent ap proach was de vel oped to scan the CCD frame to re duce the search for any LCPP whose con tent is larger than those of the four ad ja cent pix els at the car di nal directions (see [10, 11]). If such a case is found, the data of the 5 5 pixel ar ray is then nor mal ised with re spect to the LCPP da tum and mapped to the ANN sys tem. The out puts ob tained are com pared to the de ci sion out put listed in Ta ble 2 to iden tify the im age iden tity type as star, noise or cos mic ray event within a value of 0.1, which has been adopted as the tolerance limit for learn ing (Sec. 2.5). The pres ent ANN system has been coded in C lan guage and has been tested through ap pli ca tion to the test pat tern set (Sec. 2.3). Ex act agree ment was found be tween the en ti ties re cog nised and the prior knowl edge on the pat terns adopted. 3 Application Af ter test ing the pres ent ANNS, it was ap plied on a stan - dard CCD frame pre vi ously ana lysed by dif fer ent meth ods in or der to ver ify the ca pa bil ity and lim i ta tions of the pres ent ANNS in com par i son with these meth ods and the known standard data. 3.1 The case adopted A CCD frame of the star clus ter M67 [14] was un der taken to ap ply the pres ent ANNS for the fol low ing rea sons: a) The clus ter is one of the stan dard, well-known and well - -stud ied star clus ters, where pre cise data on the stars in its vicinity is available from several publications and from an ac cu rate da ta base. The re gion of the clus ter im aged in the frame in cludes faint, in ter me di ate and bright stars, while some stars are close to gether and some are far apart. b) The frame can be con sid ered as an ideal case for stel lar CCD im ag ing where im ages of the stars are gen er ally circular. It was ob tained to gether with the widely used soft - ware DAOPHOT-II [13] and the rel e vant and nec es sary aux il iary files. Hence re duc tion of the frame us ing this code can be achieved prop erly. c) The frame was re duced by two other ap proaches through of Knowl edge Based Sys tem, KBS, [10, 11] and ANNS employing the Uni-po lar func tion [12]. These reasons facilitate an objective comparison of these approaches. The frame is pix els ac quired for a pe riod of 30 sec onds through the vi sual op ti cal band where CCD chips have max i mum quan tum ef fi ciency. The full well ca pac ity value is ADU (An a log-to-dig i tal con verter Unit). 3.2 Results and discussion The se lected case frame was re duced by ap ply ing the present ANNS ap proach as well as that of Pa per I and the DAOPHOT-II code. The last two ap proaches iden tify 134 and 137 star im ages, re spec tively. A com par i son be tween, and a dis cus sion of, these find ings are given in Pa per I. The ex e cu tion of the pres ent tech nique on the frame showed that: a) The max i mum pixel da tum is ADU, where sat u ra - tion oc curred. b) The frame back ground level is 21.0 (p.e. =±1.0). c) Three cos mic events have been iden ti fied. d) The frame con tains 131 stel lar im ages. The sec ond find ing (i.e. frame back ground level) is in good agree ment with that de rived pre vi ously as 21.1 [see 11]. The third find ing is ex actly like that iden ti fied by [10, 11]. The com put ing time is sim i lar to that needed for Pa per I, i.e., 45 sec onds em ploy ing a Pentium II PC (233 MHz Pro ces sor) for scan ning the im age, find ing the data lim its of the pix - els, dis play ing the frame via the mon i tor, re cog nis ing stel lar images and cos mic events and sav ing the out put in the rel e - vant files. Dur ing the rec og ni tion step, each star im age found was marked by an open cir cle while an open square is dis - played around each cos mic event. In the fol low ing, the pres ent re sults are dis cussed and com pared with those ob tained by the other two meth ods The Bi-po lar and the Uni-po lar func tion ANNS approaches Fig. 3 shows the re sults of ap ply ing the two codes. The two ap proaches agree about iden ti fy ing the three cos mic events. All stel lar im ages re cog nised in the pres ent work were iden ti - fied when the uni-po lar func tion was adopted in Pa per I. Three more stel lar im ages were found by ap ply ing the lat ter ap proach. For these im ages, it is worth while to state that: a) The cen tral pixel data are 33, 35 and 35 (see Ta ble 3). These val ues are very close to the frame back ground level (21) and very far from the sat u ra tion value (16252). This im plies that these are very faint stars hav ing a very low peak-to-back ground ra tio (com pare this data with the data in Fig. 2). Hence they are of much less as tro nom i cal importance. b) The star discriminator out put el e ment O 1 has the val ues 0.91, 0.92 and These val ues are lower than those of other stars, which are gen er ally larger than Czech Technical University Publishing House 27

5 Ta ble 3: 5 5 pixel ar ray data for the three very faint stars Star No. 1 Star No. 2 Star No lit er a ture (e.g. [15, 16, 17]). Be cause of the high bright ness of the star the four cen tral pix els are sat u rated, hav ing the full well ca pac ity value as (see Ta ble 4a). An other case was found and des ig nated by an open tri an gle in Fig. 4. In such cases the lo cal area of the frame is treated as two over lapped im ages by the DAOPHOT-II code, while it is skipped by the pres ent ap proach be cause no LCPP is found due to saturation. Finally, the sixth im age is at the frame top-left corner and de noted by an open square. On the one hand, one im age was iden ti fied in the pres ent work. On the other hand the other code as signed two im ages at al most the same po si - tion. Ac cord ing to POSS and the clus ter charts, there is one star only in this po si tion. In spec tion of the data in the pix els shows that the star im age de parts slightly from cir cu lar ity as no ra dial sym me try around the peaked pixel; the data shows al most two close peaks (see Ta ble 4b). Due to the prin ci ples of the pres ent tech nique, only one LCPP is adopted, lead ing to one star im age. In the DAOPHOT-II code, two over lapped images are considered. Fig. 3: Map of the im ages of stars re cog nised in the M67 star clus - ter frame (North is up and East to the left). See text. Filled cir cles: im ages iden ti fied by both Uni-po lar and Bi-po lar func tions Open cir cles: im ages iden ti fied by the Uni-po lar func tion only The Bi-po lar func tion ANNS ap proach ver sus the DAOPHOT-II code As sated above, ap ply ing the DAOPHOT-II code on the test case frame leads to rec og ni tion of 137 star im ages; out of these, 131 im ages were iden ti fied by the pres ent ap proach, show ing very good agree ment. These com mon im ages are dis played in Fig. 4 by filled cir cles. The re main ing six im ages are shown with dif fer ent sym bols, on which some com ments are given. First, three im ages (de noted by filled squares) are cen tred at the first or sec ond row (col umn) close to the frame bor der. The pres ent ap proach is not ap pli ca ble, since no 5 5 pixel ar ray data is avail able. Nev er the less such lo ca tions im - ply that the stars are par tially im aged and hence the im ages are of no im por tance from the as tro nom i cal point of view. Sec ondly, two other im ages (de noted by open cir cles) are assigned by the DAOPHOT-II code where no im ages could be found by the pres ent code. At this po si tion, only one very bright star can be seen from the Palomar Ob ser va tory Sky Sur vey (POSS) and the clus ter iden ti fi ca tion charts found in Fig. 4: Map of im ages of stars re cog nised in the M67 star clus ter frame (North is up and East to the left). See text. Filled cir cles: im ages iden ti fied by Bi-po lar func tion and DAOPHOT-II Open cir cles, square and tri an gle: im ages iden ti fied by DAOPHOT-II only 28 Czech Technical University Publishing House

6 Acta Polytechnica Vol. 44 No. 1/2004 Ta ble 4: 8 8 pixel ar ray data for the two stars iden ti fied by DAOPHOT-II a) data for the sat u rated star im age de noted by (D&S) in Fig b) data for the de formed star im age de noted by (D) in Fig Conclusions Some con clu sions can be drawn from the pres ent study: Both Uni-po lar and Bi-po lar func tions are good dis crim i - nat ing func tions when used in an ANN ap proach to iden tify stel lar im ages among the other en ti ties in a CCD frame. Both possess, in comparison with mathematical or empirical star image modelling, the following advantages: 1) Extremely short execution time. 2) Better and higher rec og ni tion abil ity. 3) The two meth ods do not re quire com pli cated non-lin ear fitting computation, user intervention, prior knowledge or ini tial val ues for the star model, a fast com puter or large HD free space. 4) The abil ity of the pres ent ap proach, i.e. dis play the im age and mark the en ti ties found is help ful for vi sual in spec tion and for eval u at ing the out come of the ANNS tech nique. 5) The re sults of the Bi-po lar func tion ap proach agree very well with those ob tained in the Uni-po lar func tion case, except for the im ages of the three very faint stars. How - ever this may be ac counted for by re duc ing the tol er ance value to be less than 0.1 adopted for the train ing er ror (Sec. 2.5) in or der to en hance the weights of the hid den and out put lay ers. The two ap proaches are lim ited for im ages cen tred within the frame up to the third pixel from the frame bor ders. Any im age out side such a re gion (even if it is a star im age) is of no astronomical significance, since it is an incomplete image. Hence this lim i ta tion can be ig nored. References [1] Boyle W. S., Smith G. E.: Charge Cou pled Semicon - ductor De vices. Bell Systems Technical Journal, Vol. 49 (1970), p [2] Blecha R.: Electronographic Stel lar Pho tom e try of Globular Clusters. Astronomy and Astrophysics, Vol. 135 (1984), p [3] Penny A., Dick ens R.: CCD Pho tom e try of the Glob u lar Cluster NGC6752. Monthly No tices of the Royal As tro nom i - cal Society, Vol. 220 (1986), p [4] Mateo M., Schechter P.: The DAOPHOT Two-Di men sional Photometry Program. Pro ceeding of the first ESO/ST-ECF Data Analysis Workshop, 1989, p. 69. [5] Tody D.: Stel lar Pho tom e try in Crowded Fields. SPIE, Vol. 264 (1980), p [6] Lupton R., Gunn J.: M13- Main Se quence Pho tom e try and the Mass Func tion. Astronomical Journal, Vol. 91 (1986), p [7] Linde P.: Highlights in Astronomy. Vol. 8 (1989), p [8] Stet son P.: DAOPHOT- A Com puter Pro gram for Crowded Fields Stellar Photometry. Publication of the Astronomical Society of the Pacific, Vol. 99 (1987), p [9] Gilliland R., Brown T.: Time-Re solved CCD Photo - metry of an En sem ble of Stars. Publication of the Astronomical Society of the Pacific, Vol. 100 (1988), p [10] Elnagahy F. I. Y.: MSc The sis, Fac ulty of En gi neering, Al-Azhar Univ., Cairo, Egypt, [11] Alawy A. El-Bassuny: Stel lar CCD Pho tom e try: New Approach, Principles and Application. Astrophysics and Space Sci ences, Vol. 277 (2001), p [12] Elnagahy F. I. Y., Alawy A. E., Simak B., Ella M., Madkour M.: Stellar Image Interpretation System using Artificial Neural Networks: Uni-polar Function Case. Acta Poly technica, Vol. 41, No. 6 (2001), p [13] Stetson P.: User s Man ual for DAOPHOT-II. Dominion Astrophysical Observatory, Victoria, Canada, [14] Bojan D.: [15] Eggen O., Sandage A.: New Pho to elec tric Ob ser va tions of Stars in the Old Ga lac tic Clus ter M67. Astrophysical Journal, Vol. 140 (1964), p [16] John son H., Sandage A.: The Ga lac tic Clus ter M67 and its Significance for Stellar Evolution. Astrophysical Journal, Vol. 121 (1955), p [17] Kent A. et al: CCD Pho tom e try of the Old Open Cluster M67. Astronomical Journal, Vol. 106 (1993), p Czech Technical University Publishing House 29

7 Assoc. Prof. Ahmed El-Bassuny Alawy Re searcher Ali Abdel Wahab Haroon, PhD Asst. Re searcher Eng. Yosry Ahmed Azzam, MSc Na tional Re search In sti tute of As tron omy and Geo phys ics (NRIAG) Helwan, Cairo, Egypt Doc. Ing. Boris Šimák, Csc. Eng. Farag Ibrahim Younis Elnagahy, MSc De part ment of Tele com mu ni ca tions En gi neering Czech Tech ni cal Uni ver sity in Prague Fac ulty of Elec tri cal En gi neering Technická Praha 6, Czech Re pub lic 30 Czech Technical University Publishing House