29 3 2006 3 CHIN ESE J OU RNAL OF COMPU TERS Vol. 29 No. 3 Mar. 2006 Fourier2Mellin 1),2) 3) 1) 3) 1) ( 100081) 2) ( 030006) 3) ( 100080) Fourier2Mellin.,,,,,;,,,. ( ), Fourier2Mellin,., ( ). ; Fourier2Mellin ; ; ; TP391 An Image Registration Technique Based on Fourier 2Mellin Transf orm and Its Extended Applications L I Xiao2Ming 1),2) ZHAO Xun2Po 3) ZH EN G Lian 1) HU Zhan2Yi 3) 1) ( S chool of Mechat ronic Engineering, B ei j ing I nstitute of Technology, Bei j ing 100081) 2) ( Department of M athematics, S hanx i Universit y, Tai y uan 030006) 3) ( N ational L aboratory of Pattern Recognition, I nstitute of A utomation, Chinese A cadem y of Sciences, B ei j ing 100080) Abstract The image registration technique based on Fourier 2Mellin transform can be used to register images which are misaligned due to rotation, scaling and translation and find it s applica2 tions in many different fields t hanks to it s high accuracy, robust ness and low comp utational cost. In t his paper, t he technique is extended to two new application fields. The first one is panoramic mosaics. U nlike conventional methods, this technique is capable of successf ully building a coarse f ull view of a large scene wit hout eit her requiring special hardware to control camera motion or knowing camera s focus lengt h, or detecting image feat ures and their correspondences. The other extended application is of curve matching. In t he most traditional curve matching methods, t he correspondence of curve feat ures, such as corners, extrema of the curvat ure etc, should be at first established, and t hen t he matching parameters are comp uted. Here a new approach is pro2 posed, where the curves matched are at first converted into binary images and t hen t he matching of t hese binary images is carried o ut by t he Fo urier 2Mellin t ransform based regist ratio n tech2 :2004211202 ; :2005212201. (60121302) (20051032).,,1965,,, E2mail : lixm @sxu. edu. cn.,, 1974,,,,1942,,,.,,1961,,,,
3 : Fourier2Mellin 467 nique. Numerous experiment s show t hat for most of images capt ured by a hand2held camera, if t he projective distortions are not too severe, the registration result s are satisfactory. Keywords Fourier transform ; Fourier 2Mellin transform ; image registration ; image mosaics ; curve matching 1 1994 Chen [1 ] Fourier 2 Mellin., ( rotation) ( scaling) (translation) ( RST ). Fourier, 2 (Log2Polar), 2, RST. Chen [1 ] Reddy [2 ].,,, [3, 4 ],.,,. (1) RST,, (weak perspective), ;,., [5 8 ],,,,,,. (2) [9 11 ], ( )., RST,.,. 2 ; 3 4, ; 2 Fourier2Mellin [1, 2 ] 211 f 2 ( x, y) f 1 ( x, y) x y x 0 y0, f 2 ( x, y) = f 1 ( x - x0, y - y0 ) (1) f 1 f 2 F1 ( u, v) F2 ( u, v), : F2 ( u, v) = F1 ( u, v) e - j ( u x 0 + v y 0 ) (2) f 1 ( x, y) f 2 ( x, y) F1 ( u, v) F 3 2 ( u, v) F1 ( u, v) F 3 2 ( u, v) = e j ( u x 0 + v y 0 ) (3) F 3 2 F2.,. (3), ( x, y) ( x0, y0 ), x0 y0. 212 Fourier2Mellin s ( x, y) r ( x, y), s( x, y) r ( x, y) ( ), s( x, y) = r [ ( ( x cos + y sin ) - x0, ( - x sin + y cos ) - y0 ] (4) s( x, y) r( x, y) Fourier S ( u, v) R ( u, v) S ( u, v) = - 2 R [ - 1 ( ucos + v sin ), - 1 ( - u sin + vco s ) ] (5),. (5), x 0 y0
468 2006., ( x0, y0 ),,. rp1 (,log ) = rp (, ) (6) sp1 (,log ) = sp (, ) (7) rp s p r s (, ). sp1 (,log ) = rp1 ( -,log - log ) (8) sp1 (, ) = rp1 ( -, - ) (9) = log, = log.,, (9) (1), 2 (Log2Polar) Fourier, (2) (3),. e, = e (10). s ( x, y) s1 ( x, y), ( 2), ( 3) s1 ( x, y) r( x, y) x0 y0. (9) Fourier 2Mellin. 3, 311 ;, ( ).,,,,,, cannon PhotoStitch 311., ( )..., CCD, [12 ],,, 1 8 [6 ]., Sun [8 ] 2. I ( x, y) I ( x, y ) m11 x + m12 y + m13 x = m31 x + m32 y + 1, y m21 x + m22 y + m23 = m31 x + m32 y + 1., Sawhney [5 ], mi j ( i = 1, 2, 3 ; j = 1,2, 3). ( x i, y i ) ( x i, y i) ( i = 1,2,, n), n E = min [ I ( x, y ) - I ( x, y) ] 2 i = 1 Levenberg2Marquardt mi j,,,, ;,,,,., ; Levenberg2Marquardt,,. 2 [6,7 ].., P = ( x, y, z, w) 2D, (, v), [ -, ] : = tan - 1 ( x/ z), v = y/ x 2 + z 2., (, v),,,,,, ;,,,,, 1, [5,8 ],
3 : Fourier2Mellin 469 312 2, Fourier 2Mellin,, RST., RST.,,,. 1.,, 1024 1024, 1 (a). ( ), RST, RST,, 1 (b). 1,.,,,, RST,. cannon Photo Stitch 311, 311 2,, 1 (c). 2..,, 1,,, ( 2 (b) ), ( ),,,. 2 (c) cannon PhotoStitch 311., http :/ / nl2 pr2web. ia. ac. cn/ english/ rv/ mainpage. html. 313 (1),,, 1175 118,. (2), RST.,.,,.,. (3),
470 2006 2, 2., RST (4),.,, (5),,. 4 411,., ( sensed curve) ( reference curve).,. Freeman [9 ],,,. Ayache Faugeras [10 ],,.,, Wolf son [11 ],,,. 412 RST,, 1, 0 ; RST,,,Fourier 2Mellin., 1, 0,
3 : Fourier2Mellin 471 413, ( ) ( ) RST, http :/ / nlpr 2web. ia. ac. cn/ english/ rv/ mainpage. html., : (1), RST., 2 ( ), ; (2) ( ),, ; (3) ; (4),,,,.,.,,.,,,,, : ( ),,, 3., (a) ; (b) (a) ; (c) ;, ( b) (c) (d) ; (e). 3,,. 5 Fourier 2Mellin, RST,.,, ;,,
472 2006,,,,.,,,,,.,,,,., :,,, Fourier 2Mellin,, 1 Chen Q. S., Defrise M., Deconinck F.. Symmetric phase2only matched filtering of Fourier2Mellin transforms for image regis2 tration and recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1994, 16 (12) : 1156 1168 2 Reddy B. S., Chatterji B. N.. An FFT2based technique for translation, rotation, and scale2invariant image registration. IEEE Transactions on Image Processing, 1996, 5 (8) : 1266 1271 3 Brown L. G.. A survey of image registration techniques. ACM Computing Surveys, 1992, 24 (4) : 325 376 4 Zitov B., Flusser J.. Image registration methods : A survey. Imaging and Vision Computing, 2003, 21 (11) : 977 1000 5 Sawhney H. S., Kumar R.. True multi2image alignment and its application to mosaicing and lens distortion correction. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1999, 21 (3) : 225 243 6 Szeliski R.. Video mosaics for virtual environment s. IEEE Computer Graphics and Applications, 1996, 16 (2) : 22 30 7 Chen S. E.. Quick Time VR An image based approach to virtual environment navigation. In : Proceedings of the Com2 puter Graphics(SIGGRAP H 95), New York, 1995, 29 38 8 Sun X. Y., Dubois E.. A novel algorit hm to stitching multiple views in image mosaics. In : Proceedings of the IEEE Interna2 tional Conference on Acoustics, Speech, and Signal Processing, Montreal, Quebec, Canada, 2004, 3 : 481 484 9 Freeman H., Garder L.. Apictorial jigsaw puzzles : The com2 puter solution of a problem in pattern recognition. IEEE Trans2 actions on Electronic Computers, 1964, EC213 : 118 127 10 Ayache N. J., Faugeras O. D.. H YPER : A new approach for t he recognition and positioning of two2dimensional object s. IEEE Transactions on Pattern Analysis and Machine Intelli2 gence, 1986, 8 (1) : 44 54 11 Wolfson H. J.. On curve matching. IEEE Transactions on Pat2 tern Analysis and Machine Intelligence, 1990, 12 (5) : 483 489 12 Shum H. Y., Szeliski R.. Construction of panoramic image mosaics wit h global and local alignment. International Journal of Computer Vision, 2000, 36 (2) : 101 130 LI Xiao2Ming, born in 1965, Ph. D. candidate, associate professor. His re2 search interest s include image registra2 tion, computer vision and pattern recog2 nition. ZHAO Xun2Po, born in 1974, Ph. D.. His research in2 terests include computer vision and image processing. ZHENGLian, born in 1942, professor, Ph. D. supervi2 sor. His research interest s include neural network and pat2 tern recognition. HU Zhan2Yi, born in 1961, Ph. D., professor, Ph. D. supervisor. His research interest s include computer vision and pattern recognition. Background The group has been working on computer vision applica2 tions, such as camera calibration, 3D reconstruction, robot navigation and behavior understanding. Several peer 2re2 viewed papers have been published in major international journals, such as IEEE Transactions on PAMI, Pattern Rec2 ognition. This work focuses on image registration that is a funda2 mental problem in computer vision. This work was supported by the National Natural Science Foundation of China under grant No1 60121302.