New image registration method based on the physical forces

Transcription

1 Amin SADRI, Ali Asghr BEHESHTI SHIRAZI, Msoomeh ZAMENI Deprtment of Electricl Engineering, Irn University of Science nd Technology New imge registrtion method bsed on the physicl forces Abstrct. In this pper, we propose new method for imge registrtion nd templte mtching in which the registrtion prmeters re trnsltion nd rottion. This method is bsed on the physicl forces. The ssumption is tht imges re like chrged mterils tht ttrct ech other, which is unique feture of the proposed method. In this cse, one of the imges moves in the sme direction s the pplied force nd the other one is still. The movement of the imge continues until the resultnt force becomes zero. This pproch does not estimte the two prmeters seprtely, but they re estimted simultneously leding to better optimized set of registrtion prmeters. We compre the computtion cost of this lgorithm with other re bsed methods. In conclusion, we show tht the pproch is successful nd yields to better results thn mutul informtion nd correltion-like methods. Streszczenie. Przedstwiono now metodę rejestrcji obrzu bzując n sile przyciągni. Złożono, że obrz może wytwrzć siłę przyciągni. Przedstwiono symulcje i potwierdzono że proponown metod dje lepsze rezultty niż metody korelcyjne. (Now metod rejestrcji obrzu bzując n sile przyciągni) Keywords: registrtion, Pttern recognition, Are bsed methods. Słow kluczowe: rejestrcj obrzu, rozpoznwnie wzoru. 1.Introduction registrtion is determining the geometricl trnsformtion tht brings two sets of dt into coincidence in the sme coordinte system. registrtion plys criticlly importnt role s preprocessing step in mny computer vision pplictions nd imge processing. Zitov et l. [1] [] presented survey of recent imge registrtion techniques covering different ppliction res. They clssified registrtion methods into two ctegories: the re-bsed methods nd the feture-bsed methods. Unlike feture-bsed methods, re-bsed methods del with the imges without ttempting to detect specil objects. In this pper, we proposed new lgorithm tht tkes the re-bse pproch. The first ctegory of re bsed methods is crosscorreltion. This method is clssicl re-bsed method tht exploits the imge intensities directly [3], without ny structurl nlysis [1]. ( W E( W ))( I(, ) ( (, ) )) W i j E I i j CC( i, j) ( W E( W )) ( I(, ) ( (, ) )) W I i j E I i j ( i, j ) (1) This mesure of similrity is computed for window pirs from the reference nd sensed imges nd its mximum is serched. The window pirs for which the mximum is chieved re set s the corresponding ones. The CC bsed registrtion cn lso be successfully pplied when slight rottion nd scling re present. There re generlized versions of CC for the more geometriclly deformed imges. These methods compute the CC for ech ssumed geometric trnsformtion of the sensed imge window [4], nd they re ble to hndle even more complicted geometric deformtions thn the trnsltion-usully the similrity trnsform. Berthilsson [5] tried to register in this mnner even ffinely deformed imges. The fltness of the similrity mesure mxim (due to the self-similrity of the imges) nd high computtionl complexity re two min drwbcks of correltion-like methods. However, despite these limittions, the correltion like registrtion methods re still often used; prticulrly, on ccount of their esy hrdwre implementtion, which mkes them useful for rel-time pplictions. Fourier methods re the second ctegory of re bsed methods. Fourier methods re preferred when n ccelertion of the computtionl speed is needed or the imges re corrupted by frequency-dependent noise. These methods exploit the Fourier representtion of the imges in the frequency domin [6] [7]. The phse correltion method is bsed on the Fourier Shift Theorem [6] nd it ws proposed for the registrtion of the trnslted imges. Furthermore, it computes the cross-power spectrum of the reference nd the sensed imges nd the loction of the pek in its inverse is serched [1]. () F f F g * ( ) ( ) i( ux0 vy0 ) e * F( f ) F( g) The method shows strong robustness ginst the correlted nd frequency dependent noise nd non-uniform, time vrying illumintion disturbnces. The computtionl time svings re more significnt for lrge imges. Moreover, the ppliction of the phse correltion in 3D is described in [8]. The mutul informtion (MI) methods re the third group of the re-bsed methods. They hve ppered recently nd represent the most powerful technique in multimodl registrtion. The MI, originting from informtion theory, is mesure of sttisticl dependency between two dt sets. It is prticulrly suitble for the registrtion of imges from different modlities. MI between two rndom vribles X nd Y is given by (3) MI ( X, Y ) H ( Y ) H ( Y X ) H ( X ) H ( Y ) H ( X, Y ) where H(X) =-Ex (log (P(X))) is entropy of rndom vrible nd P(X) represents the probbility distribution of X. The method is bsed on the mximiztion of MI [9]. Some lgorithms in computer science re inspired by nturl phenomen such s Genetic Algorithm, Neurl Networks, nd Ant Algorithm. The proposed lgorithm which is introduced in this pper is inspired by the mechnics nd the electromgnetic. In this method, we use the electrosttic force between chrges nd define n equivlent force between the imge pixels from the reference nd the sensed imge. By this definition, similr pixels bsorb ech other more thn dissimilr pixels. By mens of this virtul force nd other mechnicl rules, n lgorithm for registrtion of two imges is developed. The proposed method is described in section nd the simultion results re given in section 3. We discuss bout the method in section 4. Finlly, section 5 is devoted to conclusion. PRZEGLĄD ELEKTROTECHNICZNY (Electricl Review), ISSN , R. 87 NR 6/011 53

2 . The Proposed Method.1. Introduction to the Method This section presents the min ide of the proposed method tht will be discussed in detils in the next prts. In this method ech of the imges is considered s chrged object, supposing tht the sensed imge is ble to slide on the referenced imge. In ech step, the sensed imge moves to its counterprt in the referenced imge nd gets closer to it (Fig 1 nd Fig.B). The question is tht, how the mplitude nd direction of the force is obtined? In other words, how the trnsltion of the sensed imge is estimted? To explin the nswer it should be mentioned tht the initil position of the sensed imge is chosen rndomly. In ddition, physicl model is used to estimte the movement vector in ech step. In this model, every pixel is considered s chrged point. The pixels of the referenced imge pply forces to the pixels of the sensed imge. These forces hve been defined in wy tht the pixels with the sme color ttrct ech other. So, by this definition, the sensed imge ttrcts its counterprt nd moves towrds it. Therefore, the sensed imge gets closer to its counterprt in ech step nd finlly they mtch... The Force between the two imges Consider pir of gryscle imges, A nd B, where B is the sensed nd A is the referenced imge. These imges re shown in Fig 1. Here, we ttempt to find the trnsltion prmeters nd the rottion ngle. First n initil position for the imge B is chosen then the forces re computed to detect the correct position of B. To compute the resultnt force between the imges the following eqution is used: (4) F f ( p, AB pa qb where f(p, is the force between p nd q. So, the resultnt force for ech point of the imge B should be computed, nd then ll these forces summed up to obtin the resultnt force. where Q1 nd Q re the chrges of the points p nd q, k is constnt, nd d is the distnce between p nd q. Although we use electrosttic force, the sme formultions re not pplied. Therefore, it is suggested tht the mgnitude of the force between p nd q should be clculted s follows: (6) F ( 3 p, F1 ( p, F ( p, F ( p, where F1 is function of the pixel vlues of p nd q, F is the force tht mkes the similr objects closer to ech other, nd finlly F3 is the friction force. Direction of F(p, pq (Fig 1). is the sme s the direction of vector If p nd q hve the sme gry level, F1 must hve the mximum vlue. In this method the following eqution ws used for F1 (7) 1 F1 1( Cq C p) where Cq is the gry level of q, Cp is the gry level of p, nd 1 nd re constnt. This eqution suggests tht if the pixel vlues of p nd q hve significnt difference, F1 becomes negligible. Bsed on this definition, the similr prts ttrct ech other. According to Eq. (5), the closer chrges pply more force to ech other. We suggest Eq. (8) for F. This function increses when the distnce between p nd q decreses. (8) 1 F d 3 where 3 is positive constnt tht void the division by zero nd d is the distnce between p nd q. For better convergence of the lgorithm, it is supposed tht friction increses when the similr prts re close to mtch. The friction cn be useful here becuse it decreses the movement when the similr prts re close to ech other. In order to dd the friction to our formul, we ssume tht there is surfce between the imges. In this cse, we hve verticl (fv) nd horizontl (fh) forces which verticl force cuses the friction. Fig.A shows this sitution. (9) (10) f h f sin f v f cos Fig 1. B slides on the surfce until it mtches with its counterprt. It is supposed tht every pixel in n imge is point in its respective object, nd the gry level of pixel is considered s the chrge of the respective point. Therefore, bsed on these ssumptions the force between the imges ws computed. In electromgnetic, the force between p nd q is [10]: (5) Q Q F k d 1 f nd α re shown in Fig. From the (4) nd (6) equtions it cn be inferred tht fv increses when d decreses nd when fv increses friction increses too. So, the following eqution for F3 is proposed. F 3 d (11) This mens tht when the points re close to ech other the friction force increses due to the increse of the verticl force - which is ginst the movement. As previously ws discussed, these functions re different from their physicl counterprts. They re obtined experimentlly. For instnce, bsed on the physicl rules the friction is subtrcted from the force nd resists the movement. However, in our formultion we need force to 54 PRZEGLĄD ELEKTROTECHNICZNY (Electricl Review), ISSN , R. 87 NR 6/011

3 stop the movement completely when we get the mtching; moreover, dissimilr pixels should not pply force to ech other. Therefore, these forces re multiplied. Now for the purpose of obtining the resultnt force for one point, we should sum ll the forces tht pply to tht point (see (1)). F F( p, p qb (1) In the Eq. (1), the force tht pplies to the pixel p of imge A is computed. F x m (14) m F 1 F (15) where x is the movement vector nd m is sclr used to normlize vector F. White vector in Fig 3.A shows the estimted movement vector nd Fig 3.B shows the new position of the sensed imge. Fig 3. A: Estimted movement vector, B: New position of sensed imge fter pplying the estimted vector Fig. A: Two imges with surfce between them; B: The reference nd the sensed imge nd surfce between them Fig 4. The moment of force (Torque) Finlly to obtin resultnt force for the imge, Fp should be clculted. (13) F F F( p, AB pa p paqb In other words, for ech point in A such s p, first the resultnt force tht pplies to p is clculted. Then ll of these forces re summed to obtin the resultnt force tht pplies to A..3. Estimting the Movement After finding the resultnt force, the next step is to estimte the movement nd the rottion ngle. Then we slide (move nd rotte) imge B on the surfce until it mtches its counterprt. In the proposed method, trnsltion nd rottion prmeters re clculted using the resultnt force. Therefore, we don t need full serch of rottion nd trnsltion to find the best mtch, becuse the mgnitude nd direction of force my give the trnsltion nd rottion size. To estimte the trnsltion, the resultnt force between the imges should be normlized. Fig 5. Some pixels of the sensed imge ( B). Point C is the center of the imge B..4 Estimting the Rottion Angle To estimte the rottion ngle, the moment of the forces or torque should be clculted. The ssumption is tht the imge rottes round its center point; then the torque is clculted by multiplying the distnce by the verticl force (Fig 4). So, fter computing the resultnt forces of the point the torque is clculted using the following equtions: (16) r F PRZEGLĄD ELEKTROTECHNICZNY (Electricl Review), ISSN , R. 87 NR 6/011 55

4 r F sin (17) where is the torque vector tht is perpendiculr to the plne, r is the lever rm vector (vector from the xis to the point of the force ppliction), nd F is the force vector. Furthermore, denotes cross product nd θ is the ngle between the force vector nd the moment rm vector. If r nd F hs the sme direction, becomes zero nd the imge dose not rotte. For exmple, in Fig 5 the forces tht re pplied to the pixels p nd q, mke the imge rotte; but the moment of the force tht is pplied to s is zero. However, the sum of the moments produces the resultnt moment; then the rottion ngle is estimted using the resultnt moment (Fig 5). So, the Eq. (18) is used to estimte the rottion ngle of the imge A. p pa (18) J where τp is the moment of Fp (the resultnt force tht is pplied to pixel p of the imge A), θ is the estimted ngle, nd J is sclr used to normlize the moment. J is equl to the number of the pixels of the imge A. After estimting the movement nd the rottion, imge B moves to new position nd gin the forces re computed. This process will be repeted until the resultnt force is equl to zero. However, the direction nd the size of the movement depend on the resultnt force. The flowchrt of the proposed method is illustrted in Fig 6. Fig 6. The flowchrt of the lgorithm 3. Simultion Results Hving explined the lgorithm, the next step is to evlute the performnce of the proposed registrtion pproch nd exmine the precision of the registrtion. In this regrd, we try to hve enough exmples to show tht the proposed lgorithm works properly. Therefore, the imges of the Cmer mn nd Len re considered s the referenced imges. The referenced nd the sensed imges re shown in Fig 7 nd Fig 8. Then, the sensed imges with different rottion ngles from different prts of the referenced imge re chosen. Both of the referenced imges re nd the sensed imges It should be mentioned tht in ll of the following experiments, 1,, nd 3 were 0.04, 0.7, nd.5 respectively, which they were obtined experimentlly. For ech experiment first reference, sensed imge, nd n initil sitution re chosen for the sensed imge. Then the lgorithm is run nd the trnsltion nd the rottion of the sensed imge re clculted in ech step. In this cse, if the trnsltion is less thn 3 pixels or the rottion is less thn 3 degrees, the lgorithm is terminted. Finlly, the number of the steps nd registrtion errors re reported. Tbles 1- demonstrte twenty experiments tht the sensed imge, the referenced imge, nd the initil position of the sensed imge re different in ech experiment. The first position of the sensed imge is described s initil vlue. Moreover, x nd y show the initil coordintes of the sensed imge nd θ is the degree tht the sensed imge should rotte to mtch its counterprt. The resultnt force is clculted nd the registrtion prmeters updte in ech repetition of the lgorithm. Consequently, the lgorithm is repeted until the vrition of the registrtion prmeters becomes negligible (less thn 3 pixels for x nd y, nd less thn 3 degree for the rottion ngle). Tbles 1- indicte tht the proposed lgorithm works properly. Clerly, the lgorithm is converged in ll of the twenty experiments nd the verge of the number of the itertions is 7.5. Despite of the fct tht error of 3 pixels nd 56 PRZEGLĄD ELEKTROTECHNICZNY (Electricl Review), ISSN , R. 87 NR 6/011

5 3 degrees is reltively high vlue, the proposed method cn be quite useful. This is becuse obtining the exct position from the pproximte position is not so hrd. Fig 7. A: The Cmer mn (Reference ) B-D: The sensed imges Tble 1. The simultion results for imges in Fig 7 (Cmer Mn) Initil vlue Number Error of ex ey eθ x y θ itertions (pixel) (pixel) (degree) B B B B C C C D D D Tble. The simultion results for the imges in Fig 8 (Len) Initil vlue Number Error sensed of ex ey eθ x y θ itertions pixel pixel degree B B B B C C C D D D Fig 8. A: Len (Reference ) B-D: The sensed imges Some steps of n experiment re illustrted in Fig 9. In this Fig the referenced imge nd the position of the sensed imge re shown fter first, fourth nd sixth itertions. In this cse the rottion ngle is 7 nd the number of the itertions is 5. If we run the lgorithm fter the 5th itertion the sensed imge does not move nymore. 4. Discussion of proposed method 4.1. Computtion Reduction In this section we try to confirm the proposed method to reduce the computtion, nd s result, the lgorithm becomes fster. The min ide is tht it is not necessry to clculte the force between ech pixel of the referenced nd the sensed imge. Therefore, some pixels re chosen insted of ll. Fig 9. () The initil position of the imges. The positions of the imges fter (b) one (c) four (d) six itertions. This suggestion comes from the fct tht the energy of the low frequency in n imge is high nd we hve not so mny chnges in n imge. As result, djcent pixels probbly hve the sme color. So, first some pixels from the imges rndomly re chosen using uniform distribution, nd then the forces between these pixels re clculted. Assuming tht αa nd αb re the percentge of the selected pixels of the reference nd the sensed imge, respectively, the lgorithm becomes (αa*αb)-1 times fster. The reson is tht the number of clculted forces reduce to (αa*αb) of its originl vlue. In ddition, pixels which re fr from ech other pply negligible force; therefore, it is not necessry to clculte the force between these pixels. In this section, the force between two pixels is ignored providing tht the distnce between them is more thn 40 pixels. The performnce of this method is reported for the different percentges of the selected pixel in tbles 3 nd 4. PRZEGLĄD ELEKTROTECHNICZNY (Electricl Review), ISSN , R. 87 NR 6/011 57

6 The performnce of the lgorithm under different situtions is evluted. In cse tht the rtio of the selected pixels is bout 8% for the sensed nd % for the referenced imges, the performnce is cceptble. Therefore the computtion is reduced nd the lgorithm is bout 500 times fster. As it is seen in tbles 3-4, the number of the itertion nd the errors does not chnge under this sitution so much. Tble 3. Errors of the different percentges of the selected pixels. The reference imge is Cmermn nd the sensed imge is Fig 7.B. Referenced (%) Number Error (%) of itertions ex (pixel) ey (pixel) eθ (degree) Tble 4. Errors of the different percentges of the selected pixels. The reference imge is Len nd the sensed imge is Fig 8.D. Referenced Number Error (%) (%) of itertions ex (pixel) ey (pixel) eθ (degree) The Order of the Algorithm We begin this section by observing tht the computtionl cost of the proposed lgorithm stems mostly from the computtion of the force between the two points. This cse is the vluble computtionlly, becuse it is the most repeted process. However, the other steps in the lgorithm hve negligible cost. Suppose tht B (sensed imge) is n x y imge nd A (referenced imge) is n m n imge. the force between q nd some point in A should be clculted. Eq. (19) gives the totl number of the computtion. n n m x y k (19) PA A B where αa nd αb represent the rtio of the selected pixels for the reference nd the sensed imge, k is the number of itertions, nd npa is the number of the clculted forces between the two pixels. Therefore, npa is proportionl to the squre of m nd n. Computing the order of the proposed lgorithm, the next step is compring it with nother method such s the cross correltion nd the mutul informtion methods. In order to use full serch, the CC for ech ssumed geometric trnsformtion of the imge B is computed. Therefore, the similrity mesure (CC or MI) is clculted for the window pirs from the sensed nd the reference imges nd lso its mximum is investigted through full serch. Accordingly, the window pirs for which the mximum is chieved re set s the corresponding ones. The number of x y rectngles in n m n rectngle is ( m x 1) ( n y 1) [1]. If the ngle between the sensed nd the referenced imge is not zero, the totl number of the geometric trnsformtion of the sensed ( m x 1) ( n y 1) t imge is bins. Using CC s similrity mesure we hve: n (0) CC ( m x 1) ( n y 1) x y tbins n (1) CC m n x y tbins m x, n y where tbins is the number of the ngle bins nd ncc shows pproximtely the number of the computtions. The cost of single computtion of the MI of two imges depends on the number of pixels in imges, x y, nd lso on the number of the bins used to form the histogrm. The computtionl cost reltive to the number of histogrm bins, nbins used in the computtion, is (nbins). When used for imge registrtion, the totl cost is then function of the number of steps where the MI is computed. This vlue is bout (m-x+1) (n-y+1) tbins. [11] n () MI ( x y nbins) ( m x 1) ( n y 1) tbins n (3) MI ( x y nbins) m ntbins m x, n y The equtions (19-1) prove tht the computtion cost of the proposed lgorithm does not depend on tbins unlike the other two lgorithms. Furthermore, αa*αb is insignificnt (bout 0.001) nd k is pproximtely 8. The comprison of the computtion required by the CC, MI, nd PA (the proposed lgorithm) registrtion methods is given in tble 5 (the ssumption is tht nbins=3, k=8 nd tbins=180). The vlues re the number of the clcultion such s summing nd multiplying. As result, the computtion cost of proposed lgorithm is cceptble. In the cse tht the computtion cost of the proposed method is more thn tht of the fullserch, the proposed method is useless. Tble 5. The number of the opertions for the cross correltion (CC), the mutul informtion (MI), nd the proposed lgorithm (PA) Size of Referenced Size of Number of Opertions ( 106) (Full Serch) CC MI PA Comprison of the Proposed Algorithm nd the Steepest Decent This section looks t the comprison of the lgorithm with the two optimiztion methods, in terms of the computtion nd convergence. When we serch for the mximum vlue of the CC or MI, we cn use the Steepest Decent insted of the full serch. Regrding the serch strtegy, steepest decent hs less computtion thn full serch but the min drwbcks of it is the locl mximum. Then, the Steepest Decent is used s the serch strtegy nd the CC nd MI s the similrity mesures. As result, the Steepest Decent is fster thn our lgorithm but the region of the convergence for the lgorithm is quite lrger. So, the following experiment evluted the robustness of the lgorithm concerning to the strting point. The following procedures were followed for the purpose of this study: First, reference nd sensed imge were 58 PRZEGLĄD ELEKTROTECHNICZNY (Electricl Review), ISSN , R. 87 NR 6/011

7 chosen. Then, for ech pir of the imges, 5 different initil positions were considered nd in ech cse the lgorithm ws run. So, for ech lgorithm the computtion time ws reported. The pproch ws implemented on the Pentium CoreDue processor, 1 GB RAM, 1.8 GHz PC in MATLAB environment. In ddition, the size of the step of the Steepest Decent lgorithm ws 3. In other words, the registrtion prmeters incresed nd decresed by 3 units in ech step, nd the best nswer ws chosen by using the similrity mesure. Tbles 6-7 show the simultion results for the Len nd Cmermn imges. In these tbles, θ, x, nd y indicte the differences between the initil position nd the correct position of the sensed imges. The sign - in the tbles shows tht the lgorithm did not converge. It cn be inferred from these two tbles tht when the sensed imge nd its counterprt re close to ech other, the MI nd CC get converge fster thn the proposed lgorithm. However, when the imges re not close to ech other the proposed method converges unlike the other two lgorithms. Therefore, the dvntge of the proposed method over the other methods is the lrge region of the convergence Convergence The purpose of this section is to show; intuitively, tht the convergence is gurnteed. In other words, fter severl itertions, the registrtion prmeters re obtined independent of the initil position of the sensed imge. Fig 10 shows the CC grph of the imges of Fig 8.B nd Len. As it is seen, there re severl locl mximums nd the Steepest Decent is sensitive to these mximums. Tbles 8 show the simultion results for the Len nd Cmermn imges. It is observed from Tble 5 tht the region of the convergence of the proposed lgorithm is quite lrger thn the other two lgorithms. Tble 6. The comprison of the lgorithms for the imge, Len, nd the imges of Fig 8. Computtion time x y θ (second) CC MI PA Fig 8.B Fig 8.B Fig 8.B Fig 8.B Fig 8.B Fig 8.D Fig 8.D Fig 8.D Fig 8.D Fig 8.D Fig 8.C Fig 8.C Fig 8.C Fig 8.C Fig 8.C Tble 7. The comprison of the lgorithms for the imge, Cmer mn, nd the imges of Fig 7. Computtion time x y θ CC MI PA Fig 7.B Fig 7.B Fig 7.B Fig 7.B Fig 7.B Fig 7.D Fig 7.D Fig 7.D Fig 7.D Fig 7.D Fig 7.C Fig 7.C Fig 7.C Fig 7.C Fig 7.C Fig 11 nd 1 show quiver grphs. Every vector in the quiver grphs shows the movement vector when the smller imge situted in the plce of the vector. In fct in order to obtin Fig 1 we run the proposed lgorithm for 19 0 (the number of the vectors) times nd ech time the smller imge is situted in different plce. In Fig 1, the movement vectors re obtined from the proposed lgorithm; on the contrry, in Fig 11 they re obtined from the Steepest Decent. As it is seen, there is few locl mximum for the proposed lgorithm. So, in this exmple the convergence is gurnteed nd it does not depend on the position of the smller imge. In other words, unlike the other two lgorithms, it moves to the correct position independent of the initil position of the sensed imge. Tble 8. Comprison of the region of convergence Reference Region of Convergence (%) CC MI PA Len Fig 8.B Len Fig 8.C Len Fig 8.D Cmermn Fig 7.B Cmermn Fig 7.C Cmermn Fig 7.D Fig 10. Cross-correltion grph for the smple s PRZEGLĄD ELEKTROTECHNICZNY (Electricl Review), ISSN , R. 87 NR 6/011 59

8 show tht this new pproch is very effective in terms of speed nd region of convergence. b Fig 11. Quiver grph for () MI lgorithm (b) CC lgorithm. Fig 1. Quiver grph for proposed lgorithm 5. Conclusion This study presented n imge registrtion lgorithm bsed on the physicl forces. The method used some of the mechnic principles s friction, mss, nd resultnt force to estimte the registrtion prmeters. We ssumed these imges s chrged mterils but with the opposite chrges. So, they ttrct ech other nd the virtul forces helped to find the registrtion prmeters. Consequently, the smller imge moved to mtch the bigger one. For better convergence of the lgorithm we supposed tht the friction increses when the imges re close to mtching the position. The experimentl results REFERENCES [1] Brbr Zitov, Jn Flusser, registrtion methods: survey, nd Vision Computing, Vol 1, pp , 003. [] L.M.G. Fonsec, B.S. Mnjunth, Registrtion techniques for multi-sensor remotely sensed imgery, photo-grmmetric Engineering nd Remote Sensing 6 (1996) [3] W.K. Prtt, Digitl Processing, Third Edition, Wiley, New York, 001. [4] A.wong, Dvid A.Clusi, ARRSI:Automted Registrtion of remote-sensing imges, IEEE Trnsctions on Geoscience nd Remote Sensing, Vol. 45, No 5,MAY 007. [5] R.Berthilsson, Affine correltion, Proceedings of the Interntionl Conference on Pttern Recognition ICPR 98, pp , Brisbne, Austrli, [6] R.N. Brcewell, The Fourier Trnsform nd Its Applictions, McGrw-Hill, New York, [7] A. Abche, F.Ycoub, A.Mlouf, E.Krm, Registrtion bsed on Neurl Network nd Fourier Trnsform", IEEE EMBS Annul Interntionl Conference, 006. [8] L.Lucchese, G. Doretto, G.M. Cortelzzo, A frequency domin technique for rnge dt registrtion, IEEE Trnsctions on Pttern Anlysis nd Mchine Intelligence 4 (00) [9] P.Viol, W.M. Wells, Alignment by mximiztion of mutul informtion,interntionl Journl of Computer Vision 4 (1997) [10] D. Cheng, Electromgnetic Field nd Wve, nd Edn, pp [11] A. Cole-Rhodes, L. Johnson, J. LeMoigne, Multiresolution Registrtion of Remote Sensing ry by Optimiztion of Mutul Informtion Using Stochstic Grdient, IEEE Trnsctions on Processing, VOL. 1, NO. 1, DECEMBER 003 [1] R. P. Grimldi. Discrete nd Combintoril Mthemtics: An Applied Introduction. Addison-Wesley, New York, nd edition, June Authors: Amin Sdri, Deprtment of Electricl Engineering, Irn University of Science nd Technology, _sdri@elec.iust.c.ir Ali Asghr Beheshti Shirzi, Deprtment of Electricl Engineering, Irn University of Science nd Technology, beheshti@iust.c.ir Msoomeh Zmeni, Deprtment of Computer Engineering, Irn University of Science nd Technology, zmeni_m@comp.iust.c.ir 60 PRZEGLĄD ELEKTROTECHNICZNY (Electricl Review), ISSN , R. 87 NR 6/011