1 45 ?1 1 2009 c 2 ?=?g,? Journal of Lanzhou University (Natural Sciences)Vol. 45 No. 1 Feb. 2009?: 0455-2059(2008)06-0115-05uuu111?CurveletCCC?nnn?1,?U1, ?2, oyc2(1. I? C?n?, = 730000;2. =? ; B; ?U?a?: TP399zI: AAlgorithm of fingerprint preprocessing based onthe second generation curvelet transformGU Ke-wei1, ZHANG Wei1, MA Yi-de2, LI Bo-nian2(1. Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China2. School of Information Science and Engineering, Lanzhou University, Lanzhou 730000, China;)Abstract: An algorithm for the enhancement of fingerprints was presented; an algorithm for realizing theforeground/background segmentation was also discussed, based on a new mathematical transform, namely,the second generation curvelet transform. The result shows that the algorithm is effective and the transformis attractive.Key words: automatic fingerprint identification; curvelet; ridgelet; directional energyg?OE?n?. ?p, ?1A?J?A?:. ?Or?kGabor?! ?C?! DFDFB ?.Gabor?OB?“1, D(?/B?“?O?)?, ?d?B?“?O?A?O?Gabor?n?, ?)Jb?. ?C?u:?(?3u?)k?Z?%C?J, ?u?%C?J?Z, ?B?. ?C?vk|? 2, 3, 4=?cCurveletC?; 15?p“, ?y. ?X(?XL111.2.3CurveletCCC?XXXNNN?CurveletC?XN?8?D(. 1 1 ?, ?: u1?CurveletC?n?117L 1CurveletC?X(?Tab. 1Structure of Curvelet transform?g ”?X ?/“$“C1132 32C232(4 8)16 12 12 16 16 12 12 16“C332(4 8)32 22 22 32 32 22 22 32C464(4 16)64 22 22 64 64 22 22 64p“C51256 256?D(?k?5, ?5?.l?U?u, D(U?5?( ? ? ? 5 f), ? ? ? ? 5 r, =CurveletC?X?(?)?D(?. ud, 3?”?eO?X? c2j(?U?)?X?j(j ?”?), 3z?”?eO?oU?Ej, l, O?T”?oU?3?Ej. -s = Ej/Ej, l. s?,?oU?(d? s 0,j = 2, 3;(11)cj, l, k=( 0,c2j, l, k c2jsj,j = 4; (12)cj, l, k= 0, j = 5.(13)?u?D(?D12?k?. D(?, ?D(?D(U?, u?D5?. ?lJ?.?D(?/?, ?k?, Uk?/J? ?D(?, ?F“?n?, ?. ?8?K?, JpA?J?.?3? ,?2?u?K?1?, ?JkJp, c?uXx?J?uz13.u?K?13Xe:1) ?Or?yp?U?M M ?, KkM(m, n) =1 M2MXi=1MXj=1I(i, j),(14)V (m, n) =1 M2MXi=1MXj=1(I(i, j) M(m, n)2. (15)?: I(i, j)L?:(i, j)?; M(m, n)?V (m, n)OL(m, n)?. -V (m, n)maxL?.2) ?K?T, 1Lc?, 0L?, KUe“?:m(m, n) =( 1,V (m, n)/V (m, n)max T,0,?.(16)?!Or?U?, T ?0.1(2). 2 ?(JFig. 2 Experimental result of segmentationd?(J?, T?Jp?z13?J, Or?J?1?k?/?.5(?0?1?CurveletC?iy, 3CurveletC?:?Or?. l?A:(?5r)?D(?59CurveletC?5?n?k?. l?U?u, 3?“?K?3CurveletC?X, k?/?P?&E, ?D(. u?3?Or?1?,?J. ?Jy, ?n?U?vS?Or?I?.?zzz1?l, ?, ?R, ?. ?Or?#?J. ?: ?, 2005, 35(6):55-58.2Candes E J, Donoho D L. Curvelets: a surpris-ingly effective nonadaptive representation for ob-jects with edgesM/Rabut C, Cohen A, Schu-maker L L. Curves and Surfaces Fitting. Nashville,TN: Vanderbilt University Press, 2000: 105-120.1 1 ?, ?: u1?CurveletC?n?1193Zhang Wei-peng, Wang Qing-ren, Tang Yuan-yuan. A wavelet-based method for fingerprint imageenhancementC/Machine Learning and Cybernet-ics. Beijing: Proceedings of 2002 International Con-ference on China, 2002: 1973-1977. 4Meng Ling-feng,Ma Yi-de,Dun Jian-zheng.A new fingerprint image enhancement based ondecimation-free directional filter bankC. Dubai,United Arab Emirates:IEEE International Con-ferenceonSignal Processingand Communica-tions(ICSPC07), 2007. 5Candes E J. Harmonic analysis of neural net-worksJ. Applied and Computational HarmonicAnalysis, 1999, 6: 197-218. 6Candes EJ. Ridgelets:theory and applica-tionsDPalo Alto, California:Department ofStatistics, Stanford University, 1998. 7Candes E J, Donoho D L. New tight framesof curvelets and optimal representations of objectswith C2singularitiesJ. Commun on Pure and ApplMath, 2004, 57(2): 219-266.8Candes E J, Demanet L, Donoho D L, et al.Fast discrete curvelet transforms: applied and com-putational mathematicsR. California Institute ofTechnology, 2005: 1-43.9Candes E J, Guo F. New multiscale transforms,minimum total variation synthesis: applications toedge-preserving image reconstruction:image andvideo coding beyond standarsJ. Signal Process,2002, 82(11): 1519-1543.10Lin Hong, Wan Yi-fei, Jain A. Fingerprint imageenhancement: algorithms and performance evalua-tionJ. IEEE Transactions on PAMI, 1998, 20(2):777-789.11?v. CurveletC?9?3?n?A?D. ?S: ?Sn?&E?, 2007.12?, o, /o?. u?C?K?J. =?: g,?, 2006,42(2): 81-85.13?, ”?. ?gO?J. ?.MA, 1999, 15(12): 20-22.