• Aucun résultat trouvé

An Iterative Template Matching Algorithm Using the Chirp-Z Transform for Digital Image Watermarking

N/A
N/A
Protected

Academic year: 2022

Partager "An Iterative Template Matching Algorithm Using the Chirp-Z Transform for Digital Image Watermarking"

Copied!
4
0
0

Texte intégral

(1)

Article

Reference

An Iterative Template Matching Algorithm Using the Chirp-Z Transform for Digital Image Watermarking

PEREIRA, Shelby, PUN, Thierry

Abstract

Digital watermarks have been proposed as a method for discouraging illicit copying and distribution of copyrighted material. This paper describes a method for the secure and robust copyright protection of digital images. The key contribution lies in the development of a fast iterative template matching algorithm based on log-log or log-polar maps. The algorithm exploits the properties of the Chirp-Z transform to obtain the accuracy needed in the detection of transformations in realistic watermarking applications. Test results verify the robustness of the method.

PEREIRA, Shelby, PUN, Thierry. An Iterative Template Matching Algorithm Using the Chirp-Z Transform for Digital Image Watermarking. Pattern Recognition , 2000, vol. 33, no. 1, p.

173-175

DOI : 10.1016/S0031-3203(99)00106-5

Available at:

http://archive-ouverte.unige.ch/unige:47478

Disclaimer: layout of this document may differ from the published version.

1 / 1

(2)

56*879'( 79'(:+#;<=>#(@? , AB2"$#

CEDGF"HJILKNM F"OPF"QJOSR$RUTGVNWDGQXFYOZOZKNM\[GT

]_^a`cb6dAegf(hji!k5d`Yfb

l,mon prq"posotvuwyx{z}| q~Lzymon gqwytv€=x€ongnƒ‚mru„†…ƒt‡nPuwyt‡|ˆ€9nZ‰ q"Š‹„ŒzwŽucznP€ zmon…q"‰ˆ‰ nZwy…ƒxut‹pUqzynƒŠYzxvutUq~Lzymon €9x‘x‡zyutr‰’sot‡zx‰ nP€9xvu

‰uwy“nƒzZ”•Šo~–qwzsoŠ‹uznZt‡|5moqc—>nƒ˜"nƒwP™‹€9x‘x‡zyutEŠonz}—>qwy“9„uŠr€(‰šsot‡zx‰ˆnZ€9xvuut„quc›œqwŽ€5˜x‡wzsrutt‡|<soŠopowynZ…ƒnZ€9nZŠYznZ€5q"popUqwzsoŠox‡zxnZ„

zq;pox‡wŽuczyn…q"pY|wyx‡‘"mYznZ€a‰uczynƒwyxutX”<ž„šu5wynZ„sot‡zZ™G€9x‘x‡zyut†x‡‰u‘"n—>uznZw‰uwy“x‡Š‹‘Am‹u"„\‚UnZ…q"‰ˆnu(uŠju…zx˜nuwnPu5q~,wnP„ŒnPuwŽ…Žm_”

lEnZ…ŽmoŠoxvŸYsonZ„4~–qw8mox€ox‡Šo‘š—>uznƒwy‰uwy“9„m‹uS˜n‘"wqc—Š„ŒznPu€9xt‡| ‰ˆqwyn„Œq"pomoxv„}zyx…ZuczynZ€uŠr€ˆx‡Š‹…ƒwnPu„x‡Š‹‘t|šwyq‚os‹„Œz4zyqš„}zŽuŠ‹€‹uwŽ€ˆx‡‰u‘"n

powyq9…nZ„y„x‡Šo‘5zynZ…ŽmoŠ‹xŸYsonP„ƒ”a 8sowywynƒŠYz\znP…ŽmoŠoxvŸ"s‹nZ„¡nZ‰š‚UnZ€j—,uczynƒwy‰uwy“„‚|g‰ˆnZuŠr„¡q~u"€o€9xŠo‘;u„powynZu€¢„prnP…£zywso‰¥¤J¦o¦o§¡„x‘Š‹ut

xŠ2zm‹n<„p‹uczyxut>€oq‰uxŠ2qwˆu(zywyuŠ‹„Œ~–qwy‰¨€oq‰uxŠ$„s‹…Žm6u"„¡zymon<©\ >l™© ªGl™Gqw ¢uS˜nƒtnz’zwŽuŠ‹„Œ~–qwy‰5”a«¬Š6qwŽ€9nƒwšzqgwnZŠ‹€9nZw

zm‹nut‘qwyx‡zmo‰­wynZ„x„ŒzyuŠYz zyq5…ƒwq"popoxŠo‘‹™E„…Zutx‡Šo‘5uŠr€;wyqzŽuczxqŠ®™Lzmonˆxv€9nZu<q~>s‹„xŠo‘(uŠgx‡Š˜x„x‚ot‡n zynƒ‰ˆpotvucznˆnZ‰š‚UnZ€o€9nP€gx‡Šgzm‹n

©¯ª°l±€9q‰ux‡Šam‹u„¯utv„ŒqA‚rnZnƒŠ¢u€9q"p9znP€L”³²´l,mon’znƒ‰ˆpotvuczyn…qŠYzŽuxŠ‹„Š‹qAxŠ9~–qwy‰uczyx‡q"Š‚os9z\xv„ ‰ˆnZwnZt‡|uzqqtGs‹„nZ€zq5wnP…qc˜"nƒw

pUq"„y„Œx‚otnšzywyuŠ‹„}~–q"w‰uzxqŠ‹„ x‡Š;zmonˆx‰u‘n"”š•t‡zx‰uczynƒt|™Lzymon’wynZ…ƒqc˜nZw|<q~4zymonˆ—>uznZw‰uwy“5x„uz}—8q5„Œzyu‘"nšpowyq9…nP„„Z”¡ª°x‡wŽ„}z—>n

uczznZ‰ poz\zq(€9nzynƒwy‰ˆx‡Šon zymon zwŽuŠ‹„Œ~–qwy‰uczxqŠ6¤–x‡~,uŠY|o§ soŠ‹€onƒwy‘qŠ‹n’‚|5zm‹nx‡‰u‘"n™œzymonƒŠ¢—>n’xŠ˜nƒwz¯zmonˆzywyuŠ‹„}~–q"w‰uzxqŠ;uŠ‹€

€9nP…q9€9nzm‹nš„Œp‹wnPu€5„ŒpUnZ…zwyso‰µ„ŒnPŸ"s‹nƒŠ‹…ƒn”, 8q"Š‹„nZŸYsonƒŠYzyt‡|zmonš©¯ªGl¶x„ upopowyqp‹wxvuczyn~–q"wnƒ‰’‚rnP€o€9xŠo‘u znZ‰ˆpotuznš„xŠ‹…n¡txŠonZuw

zwŽuŠr„}~–q"w‰uczyx‡q"Š‹„>x‡Š<zymon¡„Œpruczxvut_€oq‰uxŠAx‰ˆpot|tx‡ŠonPuw>zwŽuŠr„}~–q"w‰uczyx‡q"Š‹„>x‡Š<zymon¡© ªGl¶€9q‰ux‡Š_”·

¸nP…nƒŠYz¡ut‘q"wx‡zm‹‰ˆ„mruS˜n s‹„ŒnP€gt‡q"‘¹ºprq"tuw ‰upr„~–qtt‡qc—>nZ€a‚|;…wyq"„y„Œ¹º…ƒqwywnZtuzxqŠ(‚Unz}—>nƒnƒŠju<“Šoqc—Šgwnƒ~–nƒwynƒŠ‹…ƒn’zynƒ‰ˆpotvuczyn

uŠr€!zmonawnP…qc˜nZwnP€$x‰u‘"n(zq2wynZ…ƒqc˜nZw…Žm‹uŠo‘"nZ„xŠ»„y…ƒut‡nuŠ‹€=wyqzyuzxqŠ_”³²y¼½ ¸nP…nƒŠYzyt‡|"™moqc—8nZ˜nZwZ™,¾Gnzyx{zŽ…qtvu„¿powynZ„nƒŠYzynZ€

u(‚UnƒŠ‹…Žm‹‰ˆuw“¢u‘YuxŠ‹„Œzš—moxv…Žmj—>uznƒwy‰uwy“x‡Šo‘ut‡‘"qwyx{zymo‰„¡…ƒuŠ2‚Unq‚oÀ}nZ…£zyx‡˜"nƒt|;nZ˜Sut‡srucznP€L”;¸nP„Œs‹t{zŽ„šxŠ‹€9xv…ƒuznzym‹uczˆ…sowywynƒŠYz

ut‘q"wx‡zm‹‰ˆ„8pUnƒw~–qwy‰Áprqqwyt|u‘"ux‡Šr„}z,…q‰’‚oxŠ‹uczyx‡q"Š‹„†q~°„‰uttUwyqzŽuczyx‡q"Š‹„ƒ™„y…ƒutn…Žm‹uŠo‘"nZ„>uŠ‹€A…wyqpop‹x‡Šo‘r”E«¬Š<qwŽ€9nZw†zyq’x‰ˆpowqc˜"n

zm‹n<pUnƒw~–qwy‰uŠ‹…ƒnq~zmonAznZ‰ˆpotuzn5‰uczŽ…Žmox‡Š‹‘‹™4—>npowyqpUq"„nAuaŠonZ—Âut‘q"wx‡zmo‰¨—moxv…Žm$xv„ ‰ˆqwyn<u"…ƒ…s‹wyuznuŠ‹€j~Ãu"„}zynƒw zm‹uŠ

…s‹wwynƒŠYz,znP…ŽmoŠoxvŸ"s‹nZ„Z”

Ä^adÅÆÈÇɏÊdÅËƵÊdkAÌ$`cbNÍ

Î

Š‹…ƒnzm‹n —,uczynƒwy‰ˆuw“ m‹u"„†‚UnƒnZŠnƒ‰’‚rnP€o€9nP€xŠ"zyq¡zymon x‰u‘"n™u\znZ‰ˆpotuzn…q"Š‹„Œxv„ŒzxŠo‘šq~®upopowyqSÏ9x‡‰uznƒt|ÐÑ\pUqxŠYzy„8soŠox‡~–qwy‰ˆt‡|

€9xv„}zywx‚os9zynZ€ax‡Šazm‹nˆ©¯ªGlÒxv„\u€‹€9nZ€zq<zmonˆx‰u‘n"”² l,monˆ‰u‘"Šox{zys‹€9nˆxv„¯…Žm‹q"„nƒŠa„qAzm‹uz¯zymonpUqxŠ"z\xv„¯t‡q9…ƒut‡t|u<prnPu“uŠ‹€

zm‹n¡pom‹u"„Œn\xv„„nzzqAÓo”8l,m‹n\powq"‚otnƒ‰„€9sowyxŠo‘€9nzynZ…zxqŠ(uwynzq€9nƒznZw‰ˆxŠon\x{~Gzymon¡x‰ˆu‘n\m‹u"„,soŠ‹€9nZw‘"qŠon¡u zywyuŠ‹„Œ~–qwy‰ˆuzxqŠ

uŠr€;zymonƒŠgzyq(x‡Š˜nZwŒzzymonˆzwŽuŠ‹„Œ~–qwy‰uczyx‡q"Ša‚Un~–q"wn€9nP…q9€9xŠo‘5zmon—,uczynƒwy‰uwy“U”Ônƒwyn—8nˆtx‡‰ˆx‡zšqsowŽ„nƒt˜nZ„ zyq(wqzyuczyx‡q"Š‹„Z™®„…Zutn

…Žm‹uŠo‘nP„°uŠ‹€ …wyqpopoxŠo‘r”®gn,Ջwy„Œz4…q"Š‹„Œxv€9nZwEzymonpowyqpUnƒwzxnZ„°q~œtq‘¹ºpUqtvuw°‰ˆup‹„G—moxv…Žm’—xtto‚rn,s‹„nZ€ xŠšzymon,znZ‰ˆpotuzn‰uczŽ…ŽmoxŠo‘

ut‘q"wx‡zm‹‰<”°gnzymonƒŠApownP„ŒnZŠYz>u¡Š‹nƒ—»ut‡‘"qwyx{zymo‰Ò~–q"w>€onznP…£zyx‡Šo‘’zm‹nzynƒ‰ˆpotvuczn¯xŠ„Œp‹x{zyn q~_zmon„yu‰ˆpotx‡Šo‘’powyq‚otnƒ‰„†u"„„q9…xvuczynZ€

—x‡zm<zmon\tq‘Yuwyx{zymo‰ˆx…¯„y…ƒutn”

 8qŠr„Œxv€9nƒwuˆpUqxŠYzš¤–ÖE׌Øo§Ù;Ú,·\uŠ‹€5€9nÕ‹Š‹nۆÖ5Ü»ÝSÞ>…qY„9ßoàŒØÜáÝSÞ8„x‡Šß—m‹nƒwyn¯âjÙÚáuŠ‹€(ӈãßä=Ðcå” Î Šon¡…ƒuŠ5wnPu€9xt‡|

„nƒnˆzmrucz\~–qw\nZ˜nZw|pUqxŠYz¤–ÖE׌Øo§¯zm‹nƒwynx„¡u<pUqxŠYzA¤–â׍ß"§ zm‹uzšsoŠoxvŸYsonƒt|a…ƒqwywnP„ŒpUqŠr€o„ zq(x‡zZ”l,monŠ‹nƒ—慐qqwŽ€9xŠ‹uczynˆ„|9„}zynƒ‰

m‹u"„¯zmonˆpowyqpUnƒwzxnZ„¯zym‹ucz\wyqzyuzxqŠ‹„uŠ‹€a„y…ƒut‡nP„uwyn …ƒqŠ˜nZwŒzynZ€(zyq<zwŽuŠ‹„tuzxqŠ‹„u"„~–q"t‡tqc—„Zۈ¤Ãç"ÖE׌çYØo§¯è@¤–â5é!t‡q"‘†çU׌ß"§¯uŠ‹€

(3)

…Žm‹uŠo‘nP„ uŠ‹€$zmonZŠ!xŠ˜nZwŒzˆzm‹nƒ‰5”«¬Š6zymon„nZ…q"Š‹€2pruwzˆ—>n5wnP…qc˜"nƒw’zmon5zywyuŠ‹„Œtvuczyx‡q"Š$q›œ„nzwynZŸYsoxwnP€2zyq¢„|Š‹…ŽmowyqŠoxîƒnAzm‹n

€9nP…q9€9xŠo‘’q~®zymon—>uznƒwy‰uwy“ˆ—x{zymzymon\nƒŠ‹…ƒq9€9x‡Š‹‘‹”l,moxv„„ŒnP…qŠr€„Œznƒp<xv„8Š‹nZ…nP„„yuwy|ˆx‡Š(„x{zys‹uczyx‡q"Š‹„>—monƒwyn zmonx‰ˆu‘n¯m‹u„,‚UnƒnZŠ

…wyqp‹prnP€;„x‡Š‹…ƒn’—>n ‰šs‹„Œz¡u…ƒ…ƒqsoŠYz ~–qw¯zmon ~Ãu"…£z¯zm‹uzpUqxŠYzy„¯xŠ;zymonˆx‡‰u‘"n’uwn ‰ˆx„y„ŒxŠo‘r”’ 8qŠ‹„nZŸYsonZŠ"zyt‡|"™_…q"wwynZ…zt|<tq9…ƒuzxŠo‘

zm‹n¡„}zŽuwzxŠo‘ˆprq"x‡ŠYzx„nZ„y„ŒnZŠ"zyxutœzq zm‹n\wnP…qc˜nZw|ˆq~Ezymon\—>uznZw‰uwy“œ”

«¬Š5zm‹n\ՋwŽ„}zpruwzq~Gzmon¡znƒ‰ˆpotvuczynš‰uczŽ…ŽmoxŠo‘powyq…ƒnZ„y„ƒ™ozmon¡wyqzŽuczyx‡q"Š5uŠ‹€(„y…ƒutn¡…q"‰ˆprnZŠ‹„uzxqŠ5xv„pUnƒw~–qwy‰ nP€(u„,~–q"t‡tqc—„ZÛ

¤ í

§Gx‡~Uzymonx‰u‘nxv„4wynZ…zyuŠo‘sotvuwP™cnÏzywyu"…£zzm‹ntvuwy‘nZ„Œz4uS˜cuxtu‚ot‡n„yŸYs‹uwyn,~–wq"‰ïzymonx‰ˆu‘n"àU¤JЧG…q"‰ˆpos9znzmon‰u‘Šox‡zs‹€onq~œzm‹n

©¯ª°l»q~_zymon¯—x‡Š‹€oqc—8nP€x‰ˆu‘n"àU¤Xð"§>…ƒut…ƒsotuznzmonpUq"„x{zyx‡q"Š‹„†q~_zm‹n¯tq9…ƒutrpUnZu“„>xŠzymon¯Õ‹t{zynƒwynZ€A© ªGl=s‹„xŠo‘ u „‰ˆut‡tœ—xŠ‹€9qc—

¤ í Ózyq

íZñ

—8q"w“9„—8nZt‡tò§uŠ‹€„Œzq"wnšzmonZ‰­x‡Šgu„p‹uwŽ„Œn’‰uczwyx‡Ïœà¤

ñ

§ …q‰ˆposozn’zmonˆ…q"wwynZ„prq"Š‹€9xŠo‘pUqxŠYzy„ x‡Šat‡q"‘pUqtvuw„Œp‹u"…n"à

¤XÑ"§…q"‰ˆpos9znzymon¡pUq"„x{zyx‡q"Š‹„q~Ezymon¡pUqxŠ"zŽ„xŠ(t‡q"‘ pUqtvuw „Œp‹u"…nq~Gzymon¡“Šoqc—ŠAznƒ‰ˆpotvuczynà°¤Ãó"§nÏ9m‹usr„}zyx‡˜"nƒt|„ŒnPuwŽ…Žmzymonš„p‹u…ƒn

q~_pUq"„y„x‡‚otn‰uzy…ŽmonP„†‚Unz}—>nƒnZŠzm‹n“Šoqc—Šzynƒ‰ˆpotvucznuŠr€ˆzmon¯nÏzywyu"…£znP€ˆprnPu“9„>uŠ‹€ˆzymonƒwynƒ‚|€9nP€9s‹…n zm‹n q"p9zx‰utUq›L„ŒnƒzZàL¤Jô§

s‹„nšzymon q›L„Œnƒz zyq<…ƒq‰ˆpos9zynšzymon„…Zutn’uŠr€wyqzyuzxqŠ…Žm‹uŠo‘n<¤ÃõY§xŠ˜nƒwz¯zmon wqzyuzxqŠ;uŠ‹€;„y…ƒut‡n"à4¤Ãö"§pUnƒw~–qwy‰÷zymon 8moxwp9¹Œø

zwŽuŠr„}~–q"w‰ù’q~>„xîƒnÑÓAúaÑÓAqŠazm‹n x‰u‘"n —x‡zmazm‹nˆ~–wnPŸ"s‹nƒŠ‹…ƒx‡nP„¯…ƒnƒŠYznZwnP€auz¡uA“Šoqc—Š;znZ‰ p‹tuznpUqxŠ"zPà8¤

í

Ó"§¯€9nƒznP…£z\zm‹n

tq…Zuczyx‡q"Šq~4zymon prnPu“¢à†¤

í"í

§x{~4zymonˆprnPu“5xv„ Š‹qz xŠzymonˆ…nƒŠYzynƒwq~zymonšzynƒ‰ˆpotvuczyn™L—>n’‰’s‹„}z¯~–sowzmonZw¯…ƒq‰ˆpUnƒŠ‹„yuczyn¡zm‹n’ÏuŠ‹€

|j„…ZutnZ„\q~zmonAx‡‰u‘n”;«º~ŠonZ…ƒnZ„y„uw|ax{zynƒwŽucznA„}zynƒp‹„’öc¹ íí

ucz qzymonƒw’prnPu“¢t‡q9…ZuczxqŠr„¡uŠ‹€$uS˜nƒwŽu‘"n zmonAwnP„Œsot‡zZ”;«¬Š2powŽu…£zyx…ƒn

uS˜nZwyu‘xŠo‘šqc˜"nƒwÑ prnPu“9„,|x‡nZt€‹„„Œs9û…ƒx‡nZŠ"zp‹wnP…xv„ŒxqŠ_”

l,mon‰ux‡Š2p‹wq"‚ot‡nZ‰ü—x‡zm6„}zynƒp‹„

í

¹¬õ(tx‡nP„¡xŠjzmon~Ãu…zšzmruczšzymonwynZ„qts9zyx‡q"Šjq~zm‹nA©¯ª°læxv„’t‡x‰ˆx{zynZ€j‚|gzmonAŠso‰š‚Unƒw’q~

„yu‰ˆpotnZ„\xŠgzmonx‰u‘"n”<¦znƒpr„šöc¹ íí

zm‹nƒwyn~–qwynwynƒpowynZ„nƒŠYzzmon“nƒ|aprq"x‡ŠYz¡q~>zymonut‘q"wx‡zm‹‰<”<l,moxv„\x{zynƒwŽuczyx‡q"ŠgxŠ‹…ƒwnPu„nZ„¯zm‹n

u…Z…sowŽu…ƒ|ˆ‚Y|uŠx‰ˆprq"wŒzŽuŠYz8~Ãu"…£zyqwP”°l,monš 8moxwyp9¹}ø<zwŽuŠ‹„Œ~–qwy‰ýutt‡qc—„†s‹„>zq’zx‘mYzyt‡|„yu‰ˆpotnzymon¯~–wnPŸYsonƒŠ‹…ƒ|€9q‰ux‡Š<…nƒŠYzynƒwynZ€

ucz4u¯pUqxŠ"zq~UxŠYznƒwynZ„ŒzG—x{zymˆu¯wynZ„qts9zxqŠ’x‡Šr€9nƒpUnƒŠ‹€onƒŠYz4q~rzmonŠso‰’‚rnZwq~U„yu‰ˆpotnZ„GxŠ’zmonx‰u‘n"”°¦x‰ˆpot|šwynƒpotvu…ƒx‡Šo‘ zm‹n,©¯ªGl

xŠ¢„ŒznZp¢ÐA—x‡zmju; 8moxwpo¹}ø¢zwŽuŠ‹„Œ~–qwy‰þxv„Šoqz\~–nPu„x‡‚otn„ŒxŠ‹…ƒn —>nˆ‰šs‹„Œz\zm‹nƒŠgzx‘mYzt|;„yu‰ˆpotn zmon—moq"t‡n ~–wynZŸYsonZŠ‹…|;€oq‰uxŠ

—moxv…Žmˆt‡nPu€o„Gzyq¡u¯powq"‚otnƒ‰Ò—m‹x…Žmˆxv„x‡ŠYzywyu"…£zyu‚otn”Gÿ8|šprnZwŒ~–q"w‰ˆxŠo‘zmonx‡znZwyuzxqŠˆxŠˆ„ŒznZp‹„¤Xö"§º¹£¤

í"í

§™—>n,…ZuŠˆtx‡‰ˆx‡z†qsowŽ„nƒt˜nZ„Ezyq

pUqxŠ"zŽ„,q~®xŠYznZwnP„}z,—moxv…Žm<uwnzmon\“Šoqc—Šzynƒ‰ˆpotvuczyn¯pUqxŠYzy„Z”4žŠoqzmonZw,“nƒ|pUqxŠYzx„8zmrucz,zmoxv„,x‡znƒwŽuczyx‡q"ŠAut‡tqc—„>s‹„8zqˆwnP…qc˜"nƒw

„‰ˆut‡tL…Žm‹uŠo‘nP„>x‡Š5u„prnP…£z,wyuzxq<¤XuŠ‹€AŠoqz,„qtnƒt|x‡Š<soŠox‡~–qwy‰Â„y…ƒut‡xŠo‘Y§™9„ŒxŠ‹…n¯—monZŠA—>nprnZwŒ~–q"w‰æzymonš 8mox‡wyp9¹Œø<zywyuŠ‹„}~–q"w‰5™Yzm‹n

ÏAuŠ‹€|q›L„Œnƒzy„,powyqc˜x€9n zm‹n¡„…Zutn¯…Žm‹uŠo‘nP„,utqŠo‘ nZu"…Žm<uϝxv„Z”¦9s‹…Žm<„‰utt_…Žm‹uŠ‹‘nZ„>xŠ<u"„ŒpUnZ…zwyuzxqˆuwn¯q~òzynƒŠ<x‡Šr…sowywnP€Au"„,u

wynZ„sot{zq~°wyqsoŠr€9x‡Š‹‘ nZwwyqwŽ„Z™Y„q zmonP„Œn¡…Žm‹uŠo‘nP„>‰šs‹„Œz‚rn¡€onznP…£zynZ€5uŠ‹€<…q"‰ˆprnZŠ‹„uznP€~–q"wZ”

gnˆut„qŠ‹qzn zym‹ucz¡„Œznƒp¢ó<…ƒuŠa‚rnˆwynƒŠ‹€onƒwynZ€‰ˆq"wn nû…xnƒŠYz\‚|„Œq"wŒzyx‡Š‹‘zymonˆprq"x‡ŠYzy„¯xŠ;zymon„ŒnPuwŽ…Žma„p‹u…ƒn uŠ‹€;€ox‡˜xv€9x‡Š‹‘

zm‹x„¡„p‹u"…nˆx‡ŠYzyquA‘"wxv€L”l,monZŠ_™Eq"Šot|prq"x‡ŠYzŽ„\t‡|xŠo‘5x‡Šgzymon„ŸYs‹uwnˆq~†zm‹nˆznƒ‰ˆpotvuczynpUqxŠ"zŽ„ŠonƒnP€azq(‚Un…qŠr„Œxv€9nƒwynZ€g€9sowyxŠo‘

zm‹n‰ˆuzy…ŽmoxŠo‘5powyq9…nZ„y„Z” l,moxv„xv„\x‡tts‹„}zywyuznP€;xŠ;Õr‘sowynZ„¤Xu"§¯uŠ‹€¤Ã‚r§¯—moxv…Žmg…ƒqŠYzyux‡Šazmon„nZuwy…Žmg„Œpru…n q~,wynZ…qc˜"nƒwynZ€(pUnZu“9„

—moxv…Žmx„†€9x‡˜xv€9nZ€ˆxŠYzqšu‘"wxv€L”Gl,monzynƒ‰ˆpotvucznprq"x‡ŠYzy„†uwynwnZpownP„ŒnZŠYznZ€’‚|\uŠ‹€ qŠot|šzymonpUnZu“„4x‡Šˆzymonu„y„q…ƒxuznP€’„yŸYs‹uwyn

ŠonZnZ€5zyq‚rn …q"Š‹„Œxv€9nZwnP€<€osowxŠo‘zymonšpUqxŠYz‰uczŽ…Žmox‡Š‹‘‹”«¬Š(zymonš„nZ…q"Š‹€5p‹uwŒzq~Gzmonšznƒ‰ˆpotvuczynš‰uczŽ…ŽmoxŠo‘powyq9…nZ„y„Z™‹—>n¡wnP…qc˜"nƒw

zm‹nzwŽuŠr„Œtvuczyx‡q"Šgq›œ„nz’wnPŸ"s‹x‡wynZ€azqa„Œ|Š‹…ŽmowyqŠ‹x‡îZnˆzmon<€9nZ…ƒq€ox‡Šo‘(q~zmon—>uznƒwy‰uwy“—x‡zmjzymonnZŠ‹…q9€9xŠo‘‹”(l,moxv„¡xv„š€oqŠon‚|

pUnƒw~–qwy‰ xŠo‘ˆu’~Ãu„Œz,…ƒqwywnZtuzxqŠ‚Unz}—>nƒnZŠzymon¯znƒ‰ˆpotvuczyn\uŠ‹€zmonx‰u‘n—moxv…Žmmru„utwynZu€o| ‚UnƒnZŠ<…ƒq‰ˆpUnƒŠ‹„yuczynZ€~–qw,wqzyuzxqŠ

uŠr€A„y…ƒut‡n…Žm‹uŠ‹‘nZ„Z”Gl,mox„„nZ…ƒqŠ‹€A„}zynƒp<x„,Š‹nZ…nP„„yuwy|ˆx‡Š5„x{zys‹uczyx‡q"Š‹„>—monƒwyn¯zmonx‰ˆu‘n¯m‹u„,ut„q’‚UnƒnZŠ<…ƒwq"popUnZ€<„ŒxŠ‹…n¯—>n¯‰’s‹„Œz

u…Z…q"soŠYz’~–q"wˆzmon<~Ãu…zˆzm‹uzprq"x‡ŠYzy„ˆxŠ6zmon5x‰ˆu‘n(uwyn<‰ xv„y„ŒxŠo‘‹™>uŠ‹€!…q"Š‹„nZŸYsonƒŠYzyt‡|2€9nƒznZw‰ˆxŠon<zmon(„ŒzyuwzxŠo‘gprq"x‡ŠYzq~zm‹n

nƒŠr…q9€9xŠo‘Ap‹wq9…nP„„¯xŠaq"wy€onƒw zq5…qwywynZ…£zyt‡|„|Š‹…ŽmowyqŠoxîƒnšzmon€9nP…q9€9xŠo‘<q~†zymonˆ—>uznZw‰uwy“œ”¡ªoq"w¯nƒÏou‰ˆpotn™Lx‡~†zm‹n —,uczynƒwy‰uwy“

(4)

. . .. . . .

. . . .. . . .

.

. . .. . . .

.

. . .. . . .

.

. . .. . . .

. . . .. . . .

.

. . .. . . .

. . . .. . . .

.

. . .. . . .

.

. . .. . . .

.

. . .. . . .

. . . .. . . .

. . .

.

. .

. . . . . . . . .. . .

. . .

. .. . . . . . .. . ..

. . . . . . . . . . . .. . . .. .

. . . . . . . . . . . . . . . .

. . .

. . . . . .. . . .. ..

. . . .. .. .

.. . . . .

. . . . . . . . . . .

. . . . . . .. .. . . .. . . . . . ...

. .

.. . . .

.. . .. . . .

. .

. . ..

.. .. .. .. . ..

.. . .. .. .. . .

. . . . . . .. . . . . .. . .

. .

..

. .. . . . .. . ..

.. ..

. . ..

. . . .. . .. .. . . .

. . .. . . . . . . . . . . . ..

. . . . . . . . . . . . . . . . . . . . . . . .

. .

.. .

. . . .

.

.. .

. . .

. .

.. .

. . .

. .

.. .

. . .

. .

.. .

. . .

. .

.. .

. . .

. .

.. .

. . . .

.

.. .

. . .

. .

.. .

. . .

. .

.. .

. . .

. .

.. .

. . .

. .

.. .

. .

. . .

. . .

. . . . .

. .

. ..

. . . .

. . ..

. . . . . .

. . ..

. . . . . . . . . . . . . . . . . . . . . . . . .

. . . . .

. .

.

. .

. . . . . . . . . .

. .. ..

. . . ..

. ..

.. . . .

. . . . . . . . . . . ..

. . . . . . . . . . . . . . . . . ... .

. .

..

. . .

.. . ..

. . .

. . . .

. . . . . ..

. . . . . . ..

.. . .. . . .

. . . . . . .

. ..

. .

. . . . .

.. ..

..

.. .. .

.. . .

.. . .

. . . . . . . . . . . . . ..

. . . . . . . . . . .

. . .

. . . . . . . .

. . .

.

. .

. . . . . . .

. . . . . . . .

x x

x x

x x x

x

x

—,u„nZ‰š‚UnZ€o€ox‡Šo‘<‚|5s‹„ŒxŠo‘A‚ot‡q9…Ž“9„ ¤

Î

l¶~–q"w nƒÏou‰ˆpotnZ·ƒ§zmonZŠ;x‡z¯xv„ nZ„y„ŒnZŠ"zyxut_zyq<€9nƒznZw‰ˆxŠon’uŠ;upop‹wq"powxvuczyn¡pUqxŠ"z zq5„}zŽuwz

zwŽuŠr„}~–q"w‰ˆxŠo‘zmon x‡‰u‘n”°«¬Šp‹uwŒzyx…ƒsotuwZ™"—8nwnPŸ"s‹x‡wynzmrucz†nƒÏ9u"…£zyt‡|’zmon¯„u‰ˆn‚otq…Ž“ tq…Zuczyx‡q"Š‹„‚Uns‹„nZ€€9s‹wxŠo‘¡nZŠ‹…q9€9xŠo‘šuŠ‹€

€9nP…q9€9xŠo‘‹”

^aegÅ"!GijÉd#!

Î sow\wynZ„sot‡zy„\xŠ‹€9xv…ƒuznˆzmrucz¡zymonpowyqpUq"„nZ€¢upop‹wqYu…Žmau"…ƒ…ƒsowyuznZt‡|wynZ…ƒqc˜nZwy„ wqzyuzxqŠ‹„¯zyq(—x{zymox‡Š2Ӌ”Ð<€9nZ‘wynƒnP„\uŠ‹€azm‹n„…Zutn

q~>uŠ;x‰u‘"n’—x‡zm¢„Œs‹‚9¹Jp‹x{Ï9nƒtu"…ƒ…s‹wyu"…|”«¬Šgp‹uwzxv…s‹tuwZ™œ—monZŠ;—>n’xŠ˜nƒwz¯zmon„y…ƒutn’uŠ‹€wyqzŽuczyx‡q"Š‹„xŠ‹…ƒsowwynZ€;‚|5zmonˆx‰ˆu‘n"™

—>n\wnP…qc˜nZw>zmon¡q"wx‘xŠ‹utLx‡‰u‘"n\„Œxîƒn"”>ª‹sowŒzymonƒwy‰ˆqwyn¯zmon¡p‹wq"prqY„ŒnP€Aupopowyq"u…Žm<pUnƒw~–qwy‰ˆ„,—>nƒtt®xŠ(…q"ŠcÀ}soŠ‹…zxqŠ(—x‡zm5zm‹n$ Î l

—,ucznZw‰uw“xŠo‘’„y…Žmonƒ‰ˆnP·\u„,nƒ˜cut‡s‹uznP€‚|zymon\—>uznZw‰uwy“x‡Š‹‘š‚UnƒŠ‹…Žmo‰uw“zynZ„Œzy„Z”

eaÅ&%¡Åˆegňb=kAÅ"!

í

”žtnÏouŠr€9nƒw4Ônƒwywx‘nZtX™('"qn Î ws‹uŠ‹uxv€9m_™"Ô¡”¾GnƒznƒwŽ„qŠ_™¾GnZwnZx‡wŽu¯¦L”‡™YuŠ‹€ ¾4soŠl”™)Ž¦nZ…ƒsowyn,…ƒqp|wx‘mYzGpowyqznP…£zyx‡q"ŠšzynZ…ŽmoŠoxvŸYsonZ„

~–qw€9x‘x‡zyut_x‰ˆu‘nP„ƒ™xŠ+*(,.-0/1,325461,.7298:,.7<;./1,>=:61?&7298:,A@B8-<8C,EDGFH:<6I<JK:MLœ™U¾Gq"wŒzytuŠ‹€L™ Î wynƒ‘q"Š_™9žpowyxt

í

ö"öõo”

Ð9”¦monZt‡‚|¾GnZwnZx‡wŽuo™E'qn

Î

wsruŠ‹ux€9m®™uŠ‹€<l,mox‡nZwwy|¾4s‹Š_™Ny¦nP…sowyn wyq‚‹s‹„}z€9x‘x‡zyutL—>uznƒwy‰uwy“x‡Šo‘’s‹„x‡Šo‘’zm‹n\tupoprnP€q"wŒzymoq‘¹

qŠ‹utGzwŽuŠ‹„Œ~–qwy‰5™Òx‡ŠPORQS/TVU(U2CKW,X,3YX7<;O3Z<?[L:<J18CYR?\:<,+T];^4_26:,X8_`/1?a7D(8C,bDbcaOd_84,._4e7,.-gfX4_KE,.:;^:MDZ"Th/Xij(j™G¦9uŠ

'qY„Œn"™r >utx{~–q"wŠ‹xu‹™E'YuŠs‹uw|

í

öö"öo”

ðo”lk¯nƒq›Uwynƒ|ÿ¯”Z¸moqYu€o„Z™Ž¦YznZ‘"uŠoq‘"wyupom|„Œ|9„Œznƒ‰„Z™¡x‡Š$/,X2m461,n7<28:<,.7;(Qo7<2m4,32oFpGjEqMrnsbqUbq<stQvu[frxwOnjbqrnyzqzqU({™E|qc˜nZ‰ ¹

‚rnZw

í

ö"öó‹”

ñ

”ª‹u‚ox‡nZŠž¡”¾G”‹¾Gnzyx{zŽ…q"tu"„ƒ™o¸qY„„žŠ‹€9nZwy„qŠ®™‹uŠ‹€A}uw“s‹„lk ”.~somoŠ_™0ž>zzyu…Ž“9„,q"Š…qp|wyx‡‘"m"z,‰uwy“x‡Šo‘„|9„}zynƒ‰„ƒ™jxŠ+*(,.-

/1,325461,.7298:,.7<;./1,>=:61?&7298:,A@B8-<8C,EDFH:<6I<JK:LU™r¾Gq"wŒzytuŠ‹€L™ Î wynƒ‘q"Š_™9žpowyxt

í

ö"öõo”

Ñ9”lk¯x‡q"w‘"x‡q(ÿ>qŠ‹‰ˆu"„„yuw¡uŠ‹€€4wyxv…ˆ¦o…ŽmY—,uwzî"™‚y¦p‹u"…nƒ¹J˜cuwyxvuŠYz ~–q"sowyx‡nZwšuŠ‹ut‡|9„x„Zۚl,monnÏ9prq"ŠonƒŠYzyxut†…Žmoxwp¢zywyuŠ‹„}~–q"w‰5™ýxŠ

/TSTxTƒf67<,XJ7z_28:<,XJ$:<,AQl7<225461,„W,.7;…Z†J18‡J07<,n-&ˆ‰7(_KE8C,n4v/,X2m4;C;Š8ŠDz4,._4ƒ™ Î …£zyq‚Unƒw

í

ööYô9”

Références

Documents relatifs

In this letter, we introduce a generalization of Fourier analysis developed by de Branges at the end of the sixties [4] and demonstrate its application to analysis of chirp-like

Qian [17], developed a graph based semi-supervised learning (SSL) scheme using deep convolutional neural net- work (CNN) for breast cancer diagnosis with a small portion of labeled

The standard ICP starts with two point clouds and an initial guess for their relative rigid-body transform, and iteratively refines the trans- form by repeatedly generating pairs

Dunkl, Hankel transforms associated to finite reflection groups inProceedings of Special Session on Hypergeometric Functions on Domains of Positivity, Jack Polynomials and

In this section, we study the characterization of the image of exponential type functions under the discrete Radon

When the tested watermarked image undergoes ''copy /past'' attack, a message containing the patient’s and diagnostic information data in addition to the

Figure 9 shows the quality of MRI watermarked image robustness of our watermarking schema against JPEG attacks with different rate compression.. Concerning the error correcting

We introduced the Partitioned Image Foresting Transform, an algorithm that computes minimum-cost path forests as a set of independent DIFTs [6, 9] in partitions of the input image..