A Sub-Pixel Image Registration Technique with Applications to Defect Detection

Transcription

1 Internatonal Journal of Electrcal and Electroncs Engneerng 3:3 009 A Sub-Pxel Iage Regstraton Technque wth Applcatons to Defect Detecton Zhen-Hu Hu, Jyh-Shong Ju, and Mng-Hwe Perng Abstract Ths paper presents a useful sub-pxel age regstraton ethod usng lne segents and a sub-pxel edge detector. In ths approach, straght lne segents are frst extracted fro gray ages at the pxel level before applyng the sub-pxel edge detector. Next, all sub-pxel lne edges are apped onto the orentaton-dstance paraeter space to solve for lne correspondence between ages. Fnally, the regstraton paraeters wth sub-pxel accuracy are analytcally solved va two lnear least-square probles. The present approach can be appled to varous felds where fast regstraton wth sub-pxel accuracy s requred. To llustrate, the present approach s appled to the nspecton of prnted crcuts on a flat panel. Nuercal exaple shows that the present approach s effectve and accurate when target ages contan a suffcent nuber of lne segents, whch s true n any ndustral probles. Keywords Defect detecton, Iage regstraton, Straght lne segent, Sub-pxel. I. INTRODUCTION MAGE regstraton s the process of overlayng two or ore I ages of the sae scene wth the goal to deterne the geoetrc transforaton that algns the test age wth the reference age. It has becoe a fundaental task of age processng n varous applcatons such as teplate-based autoatc optcal nspectons (AOI), robot vson and age fuson. Concernng teplate-based autoatc nspectons, a coputatonally effcent regstraton ethod wth a very hgh accuracy s becong a crtcal factor n ther success due to rapd ncrease n crcut densty and the sze of a flat panel. In such ndustral applcatons, defects to be detected are becong saller and saller whle the nspecton te avalable for the task of AOI s not ncreased proportonally. Hence there arses the need of a precse and fast sub-pxel age regstraton ethod. Exstng age regstraton technques are generally classfed nto two categores: area-based and feature-based ethods [7]. Area-based ethods generally requre coputaton of ntensty correlaton between ages. Earler Fourer-based schees are only capable of atchng translated ages by eans of the shft property of Fourer transfor [0]. Mng-Hwe Perng s wth the Departent of Power Mechancal Engneerng, Natonal Tsng Hua Unversty, Hsnchu, 30043, Tawan, R. O. C. (phone: ; fax: ; e-al: hperng@pe.nth.edu.tw). Zhen-Hu Hu s wth the Departent of Power Mechancal Engneerng, Natonal Tsng Hua Unversty, Hsnchu, 30043, Tawan, R. O. C. Jyh-Shong Ju s wth the Departent of Power Mechancal Engneerng, Natonal Tsng Hua Unversty, Hsnchu, 30043, Tawan, R. O. C. To account for rotaton and scalng, Fourer-Melln transfor s adopted. Rotaton and scalng are represented as translatons n paraeter space and estated by phase correlaton [4]. Keller et al. [9] use the pseudopolar estaton to substantally prove approxatons of the polar and log-polar Fourer transfors of an age. In the above approaches, the overall coplexty s donated by FFT operatons, and optzed FFT pleentatons are necessary for a real-te perforance. However, as the an drawback of area-based ethods, the coputatonal coplexty easured by the nuber of transforaton grows rapdly as the requred accuracy ncreases. In contrast, feature-based ethods are coputatonally spler and faster. Tradtonally, the aorty of feature-based regstraton ethods consst of three essental steps: ()features detecton, ()features atchng, and (3)odel estaton to result n the relatve transforaton paraeters. In general, dstnct obects such as edges, corners, lne ntersectons and closed boundary regons are frst detected as features and represented by ther representatve ponts, the so called control ponts or feature ponts [7]. The second, and the ost crtcal, step s to establsh the correspondence between two sets of feature ponts n the absence of soe control ponts due to defect or partal occluson. For nstance, Stockan et al. [5] use lne ntersectons as control ponts and deterne the correspondence between the by eans of cluster analyss. However, the locatons of feature ponts are generally senstve to nose and lunance changes [4]. Accordngly, pont features do not ft the need of a precse regstraton proble. Lne features are ore relable than pont features n the proble of precse regstraton and are generally avalable n an-ade obects. When lne features are adopted, the Hough transfor can be appled to detect the locaton and orentaton of straght lnes [7], and the relatve rotaton angle between the reference and test ages can be obtaned by an angle dfference hstogra [6,]. However, the coputatonal effort based on the Hough transfor s too deandng for the task of autoatc optcal nspectons. For cases where regstraton accuracy s an portant concern, an teratve schee has been proposed at a cost of addtonal coputaton effort [6]. Alternatvely, the Hausdorff dstance and the ult-resoluton search of the transforaton space [,6] have also been proposed for age regstraton usng lne features. Y and Caps [6] use the orentaton, length and ddle pont of lne segents as atchng features. Unfortunately, ddle ponts are not relable features especally n the presence of occluson. Slarly, the ult-class technque usng the Hausdorff dstance ay suffer fro satches due to 3

2 Internatonal Journal of Electrcal and Electroncs Engneerng 3:3 009 sclassfed pxels []. As a result, none of the aforeentoned approaches can serve the need of fast and accurate sub-pxel regstraton (a) (b) Fg. Chan code dfference for straght lne segent n two cases. a Slanted straght lne segent. b Shft due to nose To overcoe the aforeentoned dffcultes n sub-pxel regstraton, ths paper presents a useful ethod eployng a sub-pxel lne edge detector [5,3]. In ths approach, straght lne segents are frst extracted fro the reference and the test ages at the pxel level before applyng the sub-pxel edge detector. Next, all sub-pxel lne edges are apped onto the orentaton-dstance paraeter space to solve for the correspondence between lne edges n the reference age and those n the test age. Fnally, the regstraton paraeters wth sub-pxel accuracy are solved va two lnear least-square probles. The present approach akes two basc assuptons. Frst, there are at least two or ore groups of parallel lne segents wth dfferent orentatons n the reference and test ages. Second, a rgd oton of rotaton and translaton occurred between these two ages, where a sall rotaton angle s assued. Many ndustral applcatons confor to these condtons, for exaple, ages of prnted crcuts. The rest of ths paper s organzed as follows. Secton presents a three-step process to extract straght lne segents as regstraton features. Secton 3 detals a two-stage atchng procedure to fnd correct correspondng pars of lne segents between two ages. In Sect. 4, two lnear least-square probles are then analytcally solved to obtan the regstraton paraeters. The applcaton of the present approach to defect detecton of prnted crcuts s reported n Sect. 5 before concludng ths paper. II. EXTRACTION OF SUB-PIXEL REGISTRATION FEATURES Ths secton descrbes n detals the process of extractng dstnctve regstraton features wth sub-pxel accuracy for the proposed ethod. Under the assupton of rgd oton, the relatve dstances between parallel lne segents are nvarant to rotaton and translaton, whch gves sgnfcant nforaton for the task of spatally algnng ages. Below, straght lne segents are frst extracted at the pxel level. Then, sub-pxel edge detecton s appled at a sall cost of addtonal coputatons. Fnally, the extracted lne segents are apped onto the orentaton-dstance paraeter space for feature atchng. To extract straght lne segents at the pxel level, edges are frst detected on the reference and test ages. Then, edge pxels are traced and lnked to for connected paths, fro whch straght lne segents can be acqured. Aong those avalable edge detectors [8], the Sobel operator s adopted n 0 0 ths paper due to ts nsenstvty to nose and effcency n coputaton. Note that we need to detect only strong edges whch do not necessarly for a closed loop, hence there s no need for coplex and te consung edge detectors such as the Canny edge detector [3]. Next, all connected paths are obtaned by scannng the edge ages usng chan code dfference [8]. The edge age s scanned fro left to rght and top to botto. Every edge pont s assgned a chan code dfference f one or ore 8-connected neghbors [8] exst. The search sequence for the next edge pxel of a connected path s antclockwse so that the drecton of each edge pxel to the next pxel can be unquely encoded even at branch ponts. If there are no further 8-connected neghbors, current searchng procedure for a connected path ends and we ove to the pxel next to the last startng pont for a new trackng. In ths anner, edge pxels that belong to the sae path can be grouped and recorded. A path length threshold s utlzed to reect sall edge segents and nose. After then, the chan code dfferences recorded n each selected path are surfed to deterne a straght lne segent. Snce chan code dfference characterzes edge drecton, a tran of all zero chan code dfferences anfests a straght lne segent, and all straght lne segents can be obtaned by countng consecutve chan code dfference. However, referrng to Fg., due to the dgtalzaton of lne edges nto dscrete pxels, both a slanted straght lne segent and a teporal shft away should be treated as parts of a straght lne segent. Please also notce that, later steps of the present approach can cope wth ssng lne segents, hence there s no need to fnd all lne segents but only a few. Ths property contrbutes to the robustness of the present approaches and save sgnfcant coputatonal te n handlng detals such as noses, weak edges and broken lne segents. In the present approach, the coplexty of searchng for O N for an edge age wth connected paths s at ost ( ep ) N edge pxels, and that of extractng straght lne segents s ep n the order of O( n cp ), where n cp denote the nuber of fltered connected paths. Several well-known ethods n the lterature for the extracton of straght lnes [,] can also be used nstead of the present procedure. However, the aforeentoned procedure s preferable because of ts coputatonal splcty. The resoluton of an agng devce s lted to pxel level only. To acheve a sub-pxel accuracy, a Zernke oent operator [5,3] s adopted n ths paper to pn pont the sub-pxel locatons of the edge ponts n the prevously extracted straght lne segents. Consder a sple D sub-pxel step edge odel as those n [5,3] to paraeterze every edge pont. A wndow of sze 5 5 pxels s eployed to calculate the Zernke oents. The rule of thub for deternng the wndow sze s that t should be large enough to cover the range of ntensty changes n the acqured edges to consder the blurrng effect of an agng lens. Due to length lt, detals of coputaton are referred to [5,3]. By eans of a few coputatons, the sub-pxel locaton paraeters for each 33

3 Internatonal Journal of Electrcal and Electroncs Engneerng 3:3 009 edge pont n the extracted straght lne segents can be obtaned. Before lne atchng and the estaton of transforaton paraeters, all straght lne segents wth sub-pxel locaton accuracy are represented n the polar for xcos + ysn = ρ. For a gven set of edge ponts n a straght lne segent, the paraeters (, ρ ) can be analytcally derved through a least-square fttng [8], and consequently, each straght lne segent s apped onto a pont (, ρ ) n the ρ axs,.e., the Hough space. The ert of usng ths polar for s stated n the followngs. Parallel straght lne segents can be apped near vertcally n the Hough space wth very close orentatons, whch s benefcal n establshng group atchng between the reference and test ages. For exaple, as shown n Fg., all lne segents are grouped nto dfferent sets accordng to ther orentatons and then group atchng can be easly acheved under the assupton of a sall rotaton. Copared to the technques based upon Hough transforaton pleentaton, the characterzaton of lne segents nto the Hough space presented n ths secton s explct, precse and effcent snce sub-pxel accuracy s realzed and no coprose between dscrete paraeter space and coputatonal coplexty exsts n deternng the pont locaton n the Hough space. In the next secton, the advantage of polar for representaton wll be further exploted. III. FINDING CORRESPONDING PAIRS OF LINE SEGMENTS In Sect., straght lne segents wth sub-pxel accuracy are extracted and characterzed nto the polar for. Here a two-stage atchng technque s proposed to effcently and robustly fnd ther par-wse correspondence. In the frst stage, the group atchng of straght lne segents s bult based on ther orentatons. Then lne correspondence n atched groups s dentfed n the second stage by usng the relatve dstance between straght lne segents. Ths atchng technque can cope wth partal atchng f soe lne segents are ssng on account of defects and/or occluson. In the followng all lne segents are frst classfed nto separate groups accordng to ther orentatons, then group atchng s establshed by usng averaged group orentatons. In ost potental applcatons of the present approach such as autoatc optcal nspecton n seconductor ndustres, straght lne segents are grouped nto dstnctve clusters, such as 0, 45, and 90. So a sple ethod lke quantzaton and accuulaton of the orentaton can be adopted to group those lne segents characterzed n the Hough space, and then each group can be represented by the average orentatons of those lne segents n the sae group. Accordngly, group atchng s acheved f the average group orentatons are atched. Referrng to Fg. whch llustrates an exaple of group atchng for a suffcently sall rotaton, let G = {,,, r} and G = {,,, s} denote the acqured group orentatons n the reference and test ages, respectvely, where r and s can be dfferent. Wthout loss of generalty, G and G are assued to be strctly ordered,.e., > + and + >. In the present approach, the relatve rotaton Δ between ages s assued to be suffcently sall such that Δ Ω, where Ω s the nu orentaton dfference aong all groups,.e., Ω n{n{ }, n{ }}. Hence t s easy to + + dentfy atched group orentatons (, ) f < ε, where ε s a atchng constant. By sequentally coparng the dscrnatve group orentatons and n G and G, for =,,, r and =,,, s, we can get all atched group orentatons {(, ),(, ),,( k, k) }. If two or ore pars of group orentatons are atched, then group atchng s copleted because they are provded wth the nu nforaton for transforaton paraeter estaton. A sple procedure for ths task as lsted n Table I wll be dscussed later. In the followng subsecton we wll proceed to tackle lne atchng between two atched groups. TABLE I A SIMPLE PROCEDURE FOR IDENTIFYING MATCHED DATA PAIR. Set atchng constant ε and stoppng threshold T sc ; Reset Tc = ; k =. For =,,, n do Whle Tc < T do sc For = k, k+, If d d ε, M ( T,:) = (, ) ; T = T + ; k = k+ c c To deal wth the proble of lne atchng depcted n Fg., we wll transcrbe the orgnal lne atchng proble nto a proble of data atchng between two real sets and present a sple soluton schee by takng advantages of the fact that the relatve dstance between straght lne segents are nvarant under rotaton and translaton. In the end of the prevous secton, each straght lne segent s characterzed n polar for. Therefore here we use Ρ= { ρ, ρ,, ρn} and P = { ρ, ρ,, ρ } to represent two atched groups n the reference and test ages, respectvely. P and P are also strctly ordered snce we can properly select one wth the largest length for those lne segents wth equal dstances to the orgn durng the process of lne segent extracton. Besdes, suppose that two baselne segents ρ b and ρ b n P and P have been deterned whle the selecton of baselne segents wll be dscussed later. Then the relatve dstance fro each lne segent n P and P to and c ρ b can be calculated to result n two strctly ordered real ρ b 34

4 Internatonal Journal of Electrcal and Electroncs Engneerng 3:3 009 sets, D = { d d = ρ ρb, =,,, n} and D = { d d = ρ ρ b, =,,, }. Next, a sple coparson procedure for dentfyng the correspondng pars of atched eleents between two real sets D and D s presented n Table I. We frst set constants ε and T SC, and ntalze paraeters k and T C. Then, d and d n D and D are copared sequentally to adt ther closeness. The data par ( d, d ) s adtted as atched f d d ε, where ε deternes the slarty of two real data. In practce, a counter can be used to count the nuber of atchng pars and to ternate the procedure when a specfed nuber of atchng s acheved. Please notce that a atched data par ( d, d ) ples that ( ρ, ρ ) s also atched par of lne segents because ther relatve dstances to the baselne segents are nearly the sae. As a result, atched lne segents n P and P can be acqured once the data atchng between D and D s copleted. Table II s the suary of the proposed algorth for lne atchng. Step. Step. Step 3. TABLE II ALGORITHM FOR LINE MATCHING Deterne the baselne segents ρ b and ρ b fro P and P. Copute the relatve dstance sets D and D. Fnd atched data pars M between D and D usng the sple procedure lsted n Table I. Moreover, because the task of lne atchng s copleted when a suffcent nuber of lnes are atched, the above atchng procedure can accoodate ssng lne segents. The queston reans how baselne segents are deterned. A workable approach s presented here to fnd all canddate baselnes. Let the relatve dstance between two neghborng straght lne segents n P and P be denoted as c ρ + ρ and c ρ + ρ, respectvely, and C { c =,,, n }, C { c =,,, }. If the relatve dstance par ( c, c ) are taken as nearly equal,.e., c c ε BT, then ρ and ρ can serve as a canddate baselne par. So we scan the relatve dfferences n C and C, and dentfy those pars ( c, c ) wth nearly equal relatve dstance by eans of the sae coparson procedure lsted n Table I, except for another atchng constant ε BT for baselne. It should be noted that, f there are n b canddate baselne segent pars, then at ost n b atchng procedures are requred n Table II to establsh the correspondence between lne segents n P and P. IV. ESTIMATION OF TRANSFORMATION PARAMETERS Once the lne correspondence between the reference and test ages s establshed, the present approach proceeds to estate the transforaton paraeters dscussed n ths secton. Under the assupton of a rgd oton, let the transforaton paraeters be the relatve rotaton angle Δ and the relatve translaton ( x, y) t t and suppose that correspondng pars of lne segents n total have been dentfed prevously, ncludng the collectons fro dfferent atched groups. Moreover, let ( xn, yn ) denotes the nth edge pont of the th atched lne segent n the reference age, where( xn, yn ), =,,,, n=,,, n. In age reconstructon, each regstered pxel can be obtaned n a backward transforaton fro the test age usng the nverse of the estated appng functon. Slar deas can be used to solve for the transforaton paraeters. Each lne segent n the test age can be backward transfored nto the reference age to overlay the counterparts by usng rotaton angle Δ and the relatve translaton ( tx, ty). In atheatcal ters, ( x tx)cos( Δ ) + ( y ty)sn( Δ ) = ρ () Hence the edge ponts ( xn, y n ) n the reference age should satsfy () and the followng least-square proble s forulated for accurate regstraton n ( xn tx)cos( Δ ) + ( yn ty)sn( Δ) ρ () Δ, tx, ty n = n= Apparently, the above nzaton proble () s nonlnear n the transforaton paraeters Δ and ( tx, t y), and t requres a coputatonally ntensve optzaton soluton. In the followng we wll decouple the nonlnear nzaton proble () nto two lnear parts: rotaton and translaton, respectvely. Furtherore, closed-for solutons wll be analytcally derved. Notng fro (), the change of the orentaton s copletely orgnated fro the relatve rotaton ntroduced n a rgd oton. Hence, the relatve rotaton angle Δ can be estated fro backward regstraton of those atched lne segents va the followng lnear least-square proble n Δ (3) = ( ) Δ It can easly be shown that the analytcal soluton to the above proble s ( ) ˆ = Δ = (4) 35

5 Internatonal Journal of Electrcal and Electroncs Engneerng 3:3 009 Next, substtutng Δ ˆ back nto the least-square forulaton n (), the orgnal nonlnear least-square proble reduces to n ( xn tx) cos + ( yn ty )sn ρ (5) tx, ty n = n= where Δˆ. The above nzaton proble now s lnear n t x and t. Then t s easy to verfy that the analytcal y soluton to (5) be tˆ x = ( ab ab )/( aa aa), tˆ y = ( ab + ab )/( aa aa) where n = n cos + n sn cos ρ cos = n= n = n sn cos + n sn ρ sn = n= = cos, = sn cos = = = a, a = nsn = b x y b x y a n a n a Please notce that the above estatons of transforaton paraeters are explct and effcent once the correspondng pars of lne segent are dentfed. V. EXPERIMENTAL RESULTS In ths secton the proposed regstraton ethod and ts usefulness n defect detecton are frst deonstrated. Then extensve experents are carred out to quanttatvely evaluate the atchng accuracy. We also copare ts effcency wth Hough transfor ethod n fndng straght lne segents. Consder the two gray ages shown n Fg. 3a and Fg. 3b, the sze of whch s 3 pxels. Both are taken fro an AOI applcaton n LCD panel anufacturng, and the test age contans a ouse-bte defect. After extractng straght lne segents, we get 0 and 8 canddates for the reference and test ages, respectvely, as shown n Fg. 3c and Fg. 3d. Note that soe parallel lne segents wth very close relatve dstance are otted fro canddate lne segents. After lne atchng, we obtan 8 correspondng pars of lne segents: 4 are close to the vertcal drecton and the other 4 are close to horzontal drecton. The rotaton and translaton paraeters are then calculated accordng to (4) and (6) as lsted n Table III. TABLE III REGISTRATION RESULTS IN THE DEFECT DETECTION EXAMPLE Real paraeters Sub-pxel results Pxel-level results Rotaton Translatons (-0.,-0.) pxels (6) (7) (-0.,-0.3) pxels (-0.04,-0.) pxels Next, dfference ages are constructed by coparng regstered ages. To pont out defects, we transfor the reference age and subtract t fro the test age. Usng gray level value 30 as a threshold, two bnary ages are obtaned as dsplayed n Fg. 3e and 3f. It s noted that, though the ouse-bte affect the extracton of canddate lne segents, the proposed ethod stll correctly locates t. The coparson of Fg. 3e and 3f also suggests the present sub-pxel based regstraton ethod s superor to that based on pxel level detecton. Here we quanttatvely easure the atchng accuracy of our ethod by perforng extensve experents. Frst we consder a reference age of sze 56 8 pxels as shown n Fg. 4. A rando sall rgd oton ncludng a sall rotaton angle wthn ± 5 and a sall translaton wthn ± 0 pxels n both drectons s eployed to transfor t nto an unregstered test age. Then the proposed regstraton ethod s appled to fnd the regstraton paraeters. In total,000 experents have been carred out and the results are gven n Table IV, whch shows that the present approach s relable and accurate. The nubers wthn parentheses are for pxel-level regstraton, whch are nferor to sub-pxel results. Besdes, the coputaton te for extractng straght lne segents and for copletng an age regstraton n each experent are recorded to be seconds and 0.95 seconds, respectvely, whch shows extractng straght lne segents occupes about 94% of the coputatonal cost. To evaluate the effcency of the present approach for lne segent extracton, t s copared wth the Hough transfor. Two step szes n the paraeter space of Hough transfor are used. Besdes, Fg. 3a s adopted as another exaple for the case wth uch ore edge pxels. The results are copared n Table V, whch shows that our approach s uch faster than Hough transfor wth fne paraeter resoluton n 0. and 0. pxel. All above coparsons are based on codng n the MATLAB envronent runnng on a Pentu 4-.8GHz PC. TABLE IV QUANTITATIVE MEASUREMENT OF REGISTRATION ACCURACY OF THE PROPOSED METHOD (THE NUMBERS WITHIN PARENTHESES ARE FOR PIXEL-LEVEL REGISTRATION) Max (absolute) Mean (absolute) Standard (absolute) devaton devaton devaton rotaton angle ( Degrees) (0.803) (0.7) (0.3) X-translaton ( Pxels) (.094) (0.9) (0.07) Y-translaton ( Pxels) (.56) 0.59 (0.503) 0.0 (0.38) TABLE V COMPARISON OF EFFICIENCY IN FINDING STRAIGHT LINE SEGMENTS BETWEEN OUR METHOD AND HOUGH TRANSFORM METHOD The present result HT wth steps / pxel HT wth steps 0. / 0. pxel Averaged te for Fg sec.684 sec 46.0 sec Averaged te for Fg. 3a.4 sec.6 sec 68.7 sec 36

6 Internatonal Journal of Electrcal and Electroncs Engneerng 3:3 009 the proposed ethod s accurate to regster ages and s sutable for defect detecton. To the knowledge of the authors, the work presented n ths paper s the frst one n the lterature whch utlzes the relatve dstance between parallel lne segents as atchng features. In coparson wth other pont-lke features or lnear features relyng on length, center and/or endponts, the present approach s ore relable, robust and results n ore precse regstraton. (a) Reference age (c) Matched lne segents n a (e) Sub-pxel regstraton (b) Test age (d) Matched lne segents n b (f) Pxel level regstraton Fg. 3 Coparson of defect detecton between sub-pxel based regstraton and pxel level based regstraton a & b: AOI ages for regstraton; c & d : atched lne segents; e & f: bnary dfference ages for gray level threshold value 30 REFERENCES [] Alhchr, H. S., Kael, M.: Mult-resoluton age regstraton usng ult-class Hausdorff fracton. Pattern Recognton Letters. 3, (00). [] Burns, J.B., Hanson, A.R.: Extractng straght lnes. IEEE Trans. Pattern Anal. Mach. Intell. 4, (986) [3] Canny, J.F.: A coputatonal approach to edge detecton. IEEE Trans. Pattern Anal. Mach. Intell. 8(6), (986) [4] Chen, Q., Defrse, M., Deconnck, F.: Syetrc phase-only atched flterng of Fourer-Melln transfors for age regstraton and recognton. IEEE Trans. Pattern Anal. Mach. Intell. 6(), (994) [5] Ghosal, S., Mehrotra, R.: Orthogonal oent operators for subpxel edge detecton. Pattern Recognton. 6(), (993). [6] Hseh, J.W., Lao, H.Y.M., Fan, K.C., Ko, M.T., Hung, Y.P.: Iage regstraton usng a new edge-based approach. Coputer Vson and Iage Understandng. 67(), -30 (997) [7] Jan, R., Kastur, R., Schunck B. G.: Machne Vson. McRraw-Hll (995 [8] Keller, Y., Averbuch A., Israel M.: Pseudopolar-based estaton of large translatons, rotatons, and scalngs n ages. IEEE Trans. Iage Progress. 4(), (005) [9] Kugln, C. D., Hnes, D. C.: The phase correlaton age algnent ethod. In: IEEE 975 Conf. Cybernetcs and Socety. pp Septeber (975) [0] L, H. L., Chakrabart, C.: Moton estaton of two-densonal obects based on the straght lne Hough transfor: a new approach. Pattern Recognton. 9(8), (996) [] Nevata, R., Babu, K.R.: Lnear feature extracton and descrpton. Coput. Graphcs Iage Process. 3, (980) [] Qu, Y. D., Cu, C. S., Chen, S. B., L, J. Q.: A fast subpxel edge detecton ethod usng Sobel-Zernke oents operator. Iage and Vson Coputng, 3(), -7 (005). [3] Sh, W., Shaker, A.: The lne-based transforaton odel (LBTM) for age-to-age regstraton of hgh-resoluton satellte age data. Int. J. [4] Reote Sensng. 7(4), (006) [5] Stockan, G. C., Kopsten, S., Benett, S.:Matchng ages to odels for regstraton and obect detecton va clusterng. IEEE Trans. Pattern Anal. Mach. Intell. 4, 9-4 (98) [6] Y, X., Caps, O. I.: Lne-based recognton usng a ultdensonal Hausdorff dstance. IEEE Trans. Pattern Anal. Mach. Intell. (8), (999) [7] Ztovà, B., Flusser, J.: Iage regstraton ethods: a survey. Iage and Vson Coputng., (003). Fg. 4 Synthetc age for evaluatng accuracy VI. CONCLUSION A practcal sub-pxel age regstraton ethod usng lne segents and sub-pxel edge detector has been proposed n ths paper. The present approach s coputatonally effcent, and can be appled to varous felds where fast regstraton wth sub-pxel accuracy s requred. Nuercal exaple shows that 37