5th International Conference on Measurement, Instrumentation and Automation (ICMIA 2016) Star image identification uninfluenced by rotation

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1 5th Internatonal Conference on Measurement, Instrumentaton and Automaton (ICMIA 2016) Star mage dentfcaton unnfluenced by rotaton Jang D1,a, Zhang Ke1, Lv Mebo1 1 Nortwestern Polytechncal Unversty, X an, Chna a cndyjangd@sna.com Key words: mage dentfcaton; rotaton; star sensor; gude catalog Abstract: All-sky autonomous star map dentfcaton has come up wth hgher requrement on calculatng speed and storage space. Error caused by rotaton and locaton nose nfluences the performance of star mage dentfcaton algorthms. So varous algorthms nclude procedure of rotatng star mage to the poston where the algorthm plans. That wll have a negatve effect on enhancng the performance of dentfcaton. Ths paper presented a recognton method unnfluenced by rotaton. The rotaton error s elmnated automatcally n recognton course. Both poston and magntude nformaton are consdered n t. The smulaton result ndcates that t cost less storage space and the accuracy was ncreased. Introducton It often occurs that gude stars are rotated off ther actual postons when star mages are photographed n CCD cameras[1]. Thus, most star dentfcaton methods come up wth procedures ncludng rotatng the stars to postons they plan. For eample, the grd algorthm. However, the speed of dentfcaton wll be reduced f we conduct rotaton procedures. On the other hand, stars magntude s often gnored n the match between mages acqured and those n gude star database[2][3]. Ths artcle presents an algorthm elmnatng the rotaton n star mages observed. It also takes star magntude nto consderaton to dentfy stars n mages. Method descrptons The algorthm chooses stars n Hpparcos catalog wth magntude lower than 7 to buld a gude catalog for gudance stars. The catalog contans 7548 stars. In the meantme, we assume that the star sensor s feld of vew s 12 by 12, and the sze of mage plane s 512 by 512 pels. Method to generate star mages for match N cos δ sn(α α ) = 2 tan(fov / 2) (sn δ sn δ + cos δ cos δ cos(α α )) N y (sn δ cos δ cos δ sn δ cos(α α )) y = 2 tan(fovy / 2) (sn δ sn δ + cos δ cos δ cos(α α )) (1) Equaton (1) s used to calculate the coordnate (,y) of each star captured by CCD camera. In Equaton (1), δ rght ascenson of each star n the star table chosen, α declnaton of each star n the star table chosen, δ rght ascenson of the star whch s ponted to by as of vew, α declnaton of the star whch s ponted to by as of vew The authors - Publshed by Atlants Press 673

2 The sze of mage plane s N N y, whch s pels here, The star sensor s feld of vew s FOV FOV y, whch s here. The stars magntude M s converted to grayscale G accordng to Equaton (2). 255 G= 2.51 M 1 (2) Fgure 1 llustrates an eample of star mage n gude star database. It s generated va smulaton accordng to Equaton (1) and (2) wthout rotaton. In Fgure 1, camera s as of vew ponts to the star of rght ascenson 41h and declnaton 1h 2 54 wth magntudes shown as gray scale of star spots.it s smplfed so as to be observed more clearly. Gude templates In ths artcle we regard rght ascenson and declnaton of each star n Hpparcos catalog n celestal coordnate system as the drecton of vsual as and smulate ts correspondng star mage, then we acqure 7548 star mages. They are regarded as gude templates. In fact, the algorthm doesn t smulate mages, but only calculate out 7548 matres of gray scales correspondng to these star mages. So the calculaton speed can be enhanced. Then we calculate the features of these templates. We defne the feature as below. m k P = G () ( ) + ( y y ) (3) 2 2 k = 1 In Equaton (3), P k refers to the k th feature and the sequence numbers of the features are the same wth the stars sequence numbers n gude star catalog; s the sequence number of the stars captured n the k th star mage, and the sequence number s made from left to rght and from top to bottom n the mage; G () s the grayscale of the th star n the mage; and y are star spot s coordnate values n mage space coordnate system ; and y refer to the of the mage and they are all 256 here. That s to say, there are 7548 features as the bass for pattern match afterwards. Moreover, we store the grayscale of central pel of the mages whch are taken as gude templates [4]. And we gve these grayscales the same sequence numbers wth the features [5]. We defne the star whch satsfes the condtons below as the man star n the star mage observed. The condtons are: t has the magntude lower than the other stars wthn a range. The range s that the angular separaton between the man star and the others s less than p FOV. In ths artcle, we set p = 0.3. It s possble that an observed mage wll contan several man stars. The algorthm chooses the man star whch s nearest to the center of the mage as the only man star. Then we translate ths star to the center. And wth ths procedure, the whole mage s translated. In order to elmnate the nfluence of translaton to the greatest etent, we epand the mage to the sze of 1.5N. Thus a new mage on the bass of the former one s generated. After ths step, we calculate the feature P of the new mage accordng to Equaton (4). m 2 2 ( ) ( j ) ( j ) (4) j= 1 P= G j + y y j s the sequence number of the spot whch satsfes Equaton (5) and has a brghtness larger than 0 n the observed star mage and the sequence number s made from left to rght and from top to bottom n the mage; 674

3 2 2 2 ( j ) ( yj y) R R=512 +, (5) G( j ) s the grayscale of the jth star n the mage; and y are star spot s coordnate values n mage space coordnate system ; j j and y refer to the of the mage and they are all 384 here. observaton templates The algorthm presented n ths paper constructed an observaton template as s llustrated. When calculatng the feature of the observaton template, the star spot out of the range of Equaton (5) won t be ncluded because we ntend to fnd the stars whch can match those n one gude template around the only man star. The purpose of epandng the feld of vew when constructng observaton template s to avod loss n the course of translaton. P s compared wth P ( = 1,2, L, k) one by one. The gude templates whch the algorthm s searchng for has feature that s at the same order of magntude wth P. We need to set a threshold value for match course. If the dfference between P and P s less than the threshold value, then the gude template correspondng to P s possble to be the match concluson. Ths s the ntal fltrate course. If a gude template has a feature satsfyng the threshold value, we compare the grayscale value of the central pel n ts grayscale matr wth the grayscale value of the central pel n observed star mage. The former grayscale value s stored n advance. Theoretcally, f the two grayscale values are equal to each other, the algorthm wll certfy the star correspondng to gude template s the man star n observed star mage. Smulaton eamples In order to verfy the algorthm n ths artcle, we generated a star mage as s shown n Fgure2 wth a random drecton of vsual as and assume that t s the mage observed through star sensor n operaton. Fgure 2 contans more than 10 man stars. The algorthm certfed that the only man star s the pel spot of the coordnate (226,213) n the mage. Its grayscale s Then the mage was translated so that the man star could be at the center of the new mage generated by translaton, as s shown n Fgure 3. It corresponds to a grayscale matr J. Accordng to Equaton (4), the feature 4 of J s P= Fgure 1 Images n database of gudng stars Fgure 2 Star mage observed by star sensor In ths eample, we set 150 as the threshold value. The result of match s the gude template 4 No.1648 wth P = and the grayscale value of the central pel n the 1648th gude

4 template s equal to We smulated the star mage of No.1648 as s shown n Fgure 4 to prove the result s accurate. Fgure 3 Star mage observed after translaton Fgure 4 the gude template No.1648 The spot of coordnate (226,213) n Fgure 2 s eactly the central star n Fgure 4. It means that the star whch s represented by the spot of coordnate (226,213) n Fgure 2 s the 1648th star n gude catalog. The star has rght ascenson 11h and declnaton -10h It can be seen that even f rotaton error s added to the mage observed, ts feature won t change. That s decded by the defnton of the feature. So n the course of star mage dentfcaton, the rotaton off orgnal star postons can be totally elmnated. The part above presented the effectveness of the algorthm n dealzed condton. It can be nferred that f Equaton (4) s used to calculate the feature of mages wth nose, the spots wth grayscale more than 0 wll ncrease a lot. And ths won t accord wth the real stuaton. To solve the problem, the algorthm adopted a lmtng prncple that only f the pel has the grayscale value more than that of Grade 7 star, ts grayscale wll be ncluded to calculate the feature of star mage. 71 That means addng a constrant condtong( j) 255/2.51 = to Equaton (4). In observed star mages wth nose, the result of pattern dentfcaton may be that several gude templates all satsfy the constrant condton set by the algorthm. At that tme, the algorthm wll choose the gude template whch has the least dfference n feature and central pel s magntude wth observaton template. Epermental results We generated 1000 drectons of vsual as randomly to test the success rate of man star dentfcaton. In the condton where grayscale value nose of 0.1 unts standard devaton and locaton nose of 0.5 pels standard devaton (nose referred to n ths paper are all Gaussan nose) were added to observed star mages, the rate that the only man star of each observed star mage was recognzed successfully s 95.7%. Performance on elmnatng error Seen from the smulaton result, the algorthm s performance to elmnate error caused by rotaton n captured star mage s obvous. For eample, Fgure 5 s an mage smulated as observed star mage contanng grayscale value nose of 0.1 unts standard devaton and locaton nose of 0.5 pels standard devaton. By the algorthm n ths paper, we got the result of star mage dentfcaton, whch was that the only man star n Fgure 5 s the 1800th star n gude star catalog. When we set the drecton of vsual as as the drecton of that star [6], we got the gude template correspondng to the observed mage, as s llustrated n Fgure

5 Fgure 5 observed mage Fgure 6 result of dentfcaton We can see that the two mages are almost opposte to each other, however, the result of match s accurate. Actually there was no procedure of rotaton n the course of star pattern recognton, but the result showed that the algorthm could dentfy the man star correctly even there was a large etent of rotaton between the observed mage and gude template. performance comparson The performances of trangle algorthm, match group algorthm, grd algorthm and the algorthm n ths artcle are shown n Table 1 [7][8]. The operaton condton of the three algorthms s the same wth that of the algorthm presented n ths paper. Table 1 Performance comparson of varous dentfcaton algorthms Algorthm Run tme(s) Memory requrement(mb) Trangle Match group Grd Method of ths artcle We can see that the memory cost of ths algorthm s a lot less compared wth the other three algorthms n Table 1. That s because t only needs space to store the features of dfferent gude templates and magntudes of gude stars. In Fgure 7, four curves represent the percentage of star felds dentfed over 500 random orentatons of the sensor. The locaton error was held constant wth a standard devaton of 0.5 pels. The standard devaton for the brghtness error s shown along the horzontal as n unts stellar magntude. In Fgure 8, four curves represent the percentage of star felds dentfed over 500 random orentatons of the sensor. The brghtness error was held constant wth a standard devaton of 0.3 unts stellar magntude. The standard devaton for the locaton error s shown along the horzontal as n pels. Conclusons Ths artcle presented algorthm for star mage dentfcaton unnfluenced by rotaton. The feature defned n the algorthm elmnates the nfluence from rotaton error. Thus the procedure for mage processng before pattern recognton can be elmnated. That s an advantage compared wth tradtonal algorthms of star mage dentfcaton. The result of smulaton ndcated the 677

6 performance of ths algorthm aganst locaton error and magntude error s ecellent and the tme and storage cost for dentfcaton s optmzed. 100 Fgure 7 Rate of dentfcaton wth several methods wth magntude error changng rate of dentfcaton(%) grd trangle match group method n artcle locaton error n p els Fgure 8 Rate of dentfcaton wth several methods wth locaton error changng References [1] Zhang Le, He Xn, We Zhonghu, Lu Yanjun, and Guo Jngmng. Modfcaton of trangle dentfcaton algorthm [J]. Optcs and precson engneerng. 2010, (2): [2] Ln Tao, Zhou Janl, Zhang Junpng, Ja Xaoguang, and Qan Guohu. All-sky automated quaternary star pattern recognton [J]. Journal of astronautcs. 2000, 21(2) : [3] Zhang Shaod, Wang Yanje, and Sun Hongha. Applcaton of trangulaton and RBF neural network to star pattern recognton[j]. Optcs and precson engneerng. 2012, (2): [4] LI L-hong, XU Hong-ze, ZHANG Fu-en. A knd of mproved grd algorthm for all-sky autonomous star feld dentfcaton [J], Optcal Technque, 2000, 26(3): [5] We Xn-guo, Zhang Guang-jun, Jang Je. A star map dentfcaton algorthm usng radal and cyclc features [J], Opto-Electronc Engneerng, 2004, 31(8): 4-7. [6] Padgett C, Kreutz-Delgado K, Udomkesmalee S. Evaluaton of star dentfcaton technques[j], Journal of Gudance, Control and Dynamcs, 1997, 20(2): [7] M. S. Scholl. Star-Feld Identfcaton for Autonomous Atttude Determnaton [J]. Journal of Gudance, control and dynamcs, 1995,18(1): [8] K.Ho. A survey of algorthms for star dentfcaton wth low-cost star trackers [J]. Acta astronautca. 2012, (73):