B-SPLINE ACTIVE CONTOUR FOR FAST VIDEO SEGMENTATION F

the computation of the contours curvature at any point using an analytic ... represents the Background domain, Ωп,iп(t) represents the Object, and Гп(t) the frontier ...
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‰_d|ka  › £beh_fc `a‡f_g_bf apbn|g_bf |c_fd h q|l_q ‚mcjn_fa _fgakjbnhg_bf –x ˆ¤ ˆw—z †ihfc gb gi_c _fgakjbnhg_bf gia c_…a bo `hgh _f gia hnm dbk_gie _c o|nn} qbfgkbna` hf` i_din} ka`|qa`z œibbc_fd q|l_q ‚mcjn_fa _fgakjbnhg_bf hnnb~ gb jkacakpa h ¥¦ kad|m nhk_g} _f ahqi jb_fg bo gia qbfgb|kz „afqa gakec `ajaf`m _fd bf gia qbfgb|k§c q|kphg|ka qhf la qbej|ga`z †ia jk_fq_jna bo cjhg_bmgaejbkhn cadeafghg_bf eagib` _c h phk_hg_bfhn hjjkbhqi _f bk`ak gb e_f_e_…a gia obnnb~_fd qk_gak_bf › ¨© rªy « ¬­®¯°±²³´µ ¶·¸ ´¹º » ¬­®¯¼®³´µ ¶½© ¹º » ¾ ¬¿®³´µ ¹À ryÁ f gi_c a€jkacc_bfˆg _c gia jhkheagak obk qbfgb|k§c apbm n|g_bf ˆ f _c gia f|elak bo gia q|kkafg okheaˆ ©÷¸´ rªy kajkacafgc gia ‚hqdkb|f` `beh_fˆ ©ý©rªy kajkacafgc gia ”l’aqgˆ hf` Ä©rªy gia okbfg_ak lag~aaf giaca `bm eh_fczrÅÆÇȌyz ¶·¸ ´ _c h lhqdkb|f` `acqk_jgbk hf` ¶½© _c h ebp_fd bl’aqg `acqk_jgbkz Ša q|kkafgn} |ca h gaejbkhn dkh`_afg ¶·¸ ´ « rÉ© ÊÉ©ËÌy¦ ~_gi É© gia okhea f _f gia ca‹|afqa hf` ¶½© « ÍÎ ~_gi ÍÎ h qbfcghfgz ‚} `_cgk_l|g_bfc `_•akafg_hg_bf bf gia qk_gak_bf ryˆ ~a blgh_f h ÏÐÑÒÓÔÓÕÖ Ñ×ØÏÙÚ kajkacafg_fd gia qbfgb|k apbn|g_bf›Û Ü ¿®³´µ Ü´ Ê Ê «¢ Ý Þß « Þà r˜ yÁ Ä©r y « Ä©Ãá

‰_d|ka ˜ › œbfgb|k upbn|g_bf ‰kbe hf _f_g_hn q|kpa Ä©r¢ y d_pafˆ gia qbfgb|k Ä©rªy apbnpa gihfc gb panbq_g} `a‡f_g_bf › ÞÊà « Ý ÞÊß ˆ obnnb~m _fd gia fbkehn `_kaqg_bf bo gia qbfgb|kz †ia a€jkacc_bf bo gia obkqa _c `a`|qa` okbe gia qk_gam k_bf ry –Ÿ ˆŸ—› ´ » ¾â Ý « ¶½© ¶·¸ rŸyÁ Ê â ~_gi gia qbfgb|k q|kphg|ka bo gia qbfgb|k rÅÆÇÈãyz ”fa e_dig _ejnaeafg hqg_pa qbfgb|k apbn|g_bf obnnb~m _fd g~b `_•akafg ~h}c› Ê ejn_q_g _ejnaeafghg_bf › ä kahnn} a“q_afg ånapan cagåmlhca` eagib` hnkah`} a€_cg gb– _ejnaeafg p_`ab cadm eafghg_bf okbe gi_c qk_gak_bf r y Ÿ ˆŸ—z gc eh_f h`phfm ghda _c gb jkbp_`a hf _ejn_q_g ehfhdaeafg bo gbjbnbd_qhn qihfdacz ”f gia bgiak ihf` qbej|ghg_bf qbcg bo gi_c hjjkbhqi _c _ejbkghfgz Ê u€jn_q_g _ejnaeafghg_bf › †ia j|kjbca bo gi_c jhm jak _c gb |ca jhkheagk_q hqg_pa qbfgb|kcz †~b cgkh_dig h`phfghdac qbea b|g› ä nb~ qbej|ghg_bf qbcg laqh|ca bo `hgh c_…a gb jkbqacc hf` h gbghn qbfgkbn bo gi_c qbem j|ghg_bf qbcg gihfc gb b|k fb~na`da bo gia f|elak bo apbn|g_bf jb_fgc gb ehf_j|nhgaz ä caqbf` h`phfghda bo gi_c eagib` n_ac _f ehf_j|nhg_fd hfhn}g_q a€jkacc_bfcz {c|hn jhkheagk_q hq_gpa qbfgb|k gaqif_qc `ahn ~_gi jbn}dbfcz „b~apak gihg _f` bo hjjkbhqi ka‹|acg nbg bo jb_fgc _f bk`ak gb aaj h chg_co}_fd kad|nhk_g}z ã æ\æXçX[Ž èé[ꏐ ãȌ æëÆìíÆîïð ñò óôð õðóôñö f gi_c jhjak ~a jkbjbca gb |ca ‚mƒjn_fa q|kpac rq|kpa qbejbca` l} capakhn ‡€a` `adkaa ‚ a÷…_ak q|kpacy laqh|ca giaca q|kpac hka ¥¦ kad|nhk _f ahqi jb_fg bo gia qbfgb|kz ”|k dbhn _c gb ka`|qa gia f|elak bo jb_fgc hf` gi|c gb ka`|qa qbej|ghg_bf qbcgz †ia jk_fq_jna _c lhca` bf hjjn}_fd gia obkqa rŸyˆ bpak oa~ qbfgb|k jb_fgcz †iaf qbfgb|k apbn|g_bf `ajaf`c bfn} bf gia apbn|g_bf bo giaca _fgakjbnhga` jb_fgc hf` fb ebka bf ahqi jb_fg bo gia qbfgb|kz {c_fd ‚mcjn_fac hnnb~ gb jkacakpa gia ¥¦ qbfg_f|_g}z †i|c gia gi_k` gake bo obkqa Ý rŸyˆ h kad|nhk_…hg_bf gake bpak gia qbfgb|k

‰_d|ka Ÿ› fgakjbnhga` tkbjhdhg_bf nafdgi r`ajaf`_fd bf gia q|kphg|ka â yˆ _c `a‡fa` _f ahqi jb_fgz ”|k hndbk_gie _c qbejbca` bo gikaa cgajc› m äqg_pa qbfgb|k _fgakjbnhg_bf m œ|kphg|ka qbej|ghg_bf â a‹zrxy m tkbjhdhg_bf a‹zr˜ y ãÈã XíóÆøð íñìóñùë ÆìóðëîñïúóÆñì Ša `agake_fhga h qbfgb|k rann_jcaˆ q_kqnaˆ zzzyz †iaf gi_c ûüýþ qbfgb|k _c _fgakjbnhga` kad|nhkn}z ÿ© kajkacafg qbfgb|k _fgakjbnhga` jb_fgc ~i_qi hka db_fd gb apbnpaz äogak qhnq|nhg_fd gia q|kphg|ka â _f ahqi jb_fg ÿ©ˆ gia apbn|g_bf obkqa rŸy _c `agake_fa` _f giaca jb_fgc gikb|di qk_gak_bf e_f_e_…hg_bf hf` aphn|hga` ~_gi gia fa~ q|km phg|kaˆ hf` ahqi `acqk_jgbk bo bl’aqgc hf` lhqdkb|f`z äogak h jkbjhdhg_bf cgajˆ ~a blgh_f jb_fgc ÿ okbe jb_fgc ÿ rhc cib~f bf ‡d|ka ÅÆÇÈ yz †ia qbfgb|k _fgakjbnhg_bf _c lhca` bf q|l_q {f_obke ‚mƒjn_fa q|kpacz †ia |f_obke_g} _c aejnb}a` iaka gb _ejkbpa qbej|ghg_bf a“q_afq} hc ~a hka db_fd gb caa lanb~z †i_k` `adkaa ‚mƒjn_fac hka |ca` laqh|ca ~a bfn} faa` caqbf` `ak_phg_bf gake _f gia q|kphg|ka a€jkacc_bf rxyz ä q|l_q ‚mƒjn_fa q|kpa _c d_paf l} h jbn}fbe_hn a€m jkacc_bf hc lanb~ –x—› ɽ rÀ y « »½ËÌ ¼ ¼ rÀ y À» » ½ ¼ r¼À y À ½ Ì r y ½ ¦ r yÁ rwyz À _c gia jhkheagak bo gia q|kpa r_f ohqg q|kp_n_fahk hlcq_cayˆ jb_fgc hka åhfqibkcå bo gia ‚mƒjn_fa rqhnna` |c|hnn}› œbfgkbn˜tb_fgcyˆ hf` ¼ rÀ y hka jbn}fbe_hn a€m jkacc_bfc r~_gi qbejbfafgcy `a‡f_fd lhc_q o|fqg_bfc bo gia ‚mƒjn_fariafqa å‚hc_qmƒjn_faåyˆ _g eahfc ~a_dig o|fqg_bfc bo ahqi jb_fg obk gia hkq ɽ rÀ yz g ihc gb la fbg_qa` gihg _f hnn giaca a€jkacc_bfc hf` ÿ kajkacafg˜ jb_fgc _f h okhea bo gia ca‹|afqaz ƒbÀ gia} lbgi ihpa qbejbfafgcz g§c gia chea ~_gi ɽr y ~i_qi _c gia jhkheagk_q a‹|hg_bf boÀ gia hkqÀ lag~aaf ÿ½ hf` ÿ½ Ìz †i|c ÿ½ kajkacafg r ½r y ½r yy ~_gi ÿ½ « 







 







  

 





  





 









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ãÈ æëñîúÇúóÆñì ƒb ~a ihpa ÿ á jb_fgc l} _f_g_hn_…_fd rcgaj ¢ y hnbfd h `am gake_fa` qbfgb|kzräc gia qbfgb|k _c hnkah`} `agake_fa` ~a `b fbg faa` gb |ca hfqibkcˆ cb ~a `b fbg faa` gb qbfgkbn jb_fgc obk fb~yz äogak hjjn}_fd gia obkqa bf ahqi jb_fgˆ ~a ihpa fa~ jb_fgc ÿ rcgaj yzÌ ‰kbe giaca jb_fgc ~a `agake_fa ‡kcg qbfgkbn jb_fgc rcgaj yz 7









äg ahqi _gakhg_bf ~a qbej|ga qba“q_afgc bo ahqi hkq bo gia {f_obke ‚mƒjn_fa _fgakjbnhg_fd gia hqg_pa qbfm gb|kz †iaca hkqc hka `a‡fa` ~_gi q|l_q jbn}fbe_hn a€m jkacc_bfcz †iakaobka kac|ngc hka g~b hfhn}g_q a€jkacc_bfc obk ahqi hkq rbfa jak qbejbfafgy hf` bfn} qba“q_afgc bo giaca a€jkacc_bfc ihpa gb la cgbka`z †ia fa~ obkqa Ý phn|a _c qbej|ga` _f ahqi jb_fg bo ÿ Ì |c_fd gia q|kphg|ka phn|a rxy rcgaj Ÿy z†i_c qbej|ghm g_bf _c lhca` bf hfhn}g_q a€jkacc_bfc bo hkqc qbejbc_fd gia qbfgb|kz †i_c kac|ngc _f h ohcgak hf` ahc_ak gihf |c_fd gia napan cag eagib`z Ša qbfc_`ak _fgakjbnhga` jb_fgc tˆ apafn} chejna` hnbfd gia q|kpaz †i_c hjjkb€_ehg_bf hnnb~c |c gb _fgakm jbnhga gia q|kpa |c_fd jb_fgc ÿ _fgb {f_obke ‚mƒjn_fa _fgakjbnhg_bfz äc ~a `anaga bk qkahga fa~ _fgakjbnhgm _fd jb_fgc–˜~_gi h gikaacibn` hc _f cbea jbn}dbf lhca` eagib`c —ˆ gia hjjkb€_ehg_bf bo kad|nhk chejn_fd _c fbg hlc|k`z sbkabpak a€jak_ehfghn kac|ngc qbf‡ke _gz †iaf ~a `agake_fa qbfgkbn jb_fgc rhfqibkc bo gia q|kpayˆ jb_fgc ˆ obk ahqi hkq n_f_fdÌ ÿ jkap_b|c jb_fgcz ”fqa ~a fb~ fa~ jbc_g_bfc bo ÿ jb_fgc ~a qhfâ _em ea`_hgn} gia a€jkacc_bf bo gia q|kphg|ka rcgaj ˜ y hnn hnbfdaphn|hga gia q|kpa hf` giaf gia fa~ phn|a obk gia obkqa Ý hg giaca jb_fgcz †i_c qbej|ghg_bf _c kajahga` |fg_n qbfpakdafqaz †ikb|di cg|`_ac bf gia qk_gak_bf ry –Ÿ ˆŸ—ˆ ~a fb~ gi_c apbnpa gb~hk`c ebp_fd bl’aqgcz ƒb ~a qbfc_`ak qbfpakm dafqa kahn_…a` ~_gi gia af` bo apbn|g_bf bo gia qbfgb|kz é æé\èéŽ[Z úìö ]èæX\ZŽ ÅÆÇÈ cib~c gia qbfgb|k _f_g_hn_…hg_bf obk cadeafghg_bf bo h ebp_fd cjahqiak _f h p_`ab ca‹|afqaz ÅÆÇÈ y _c gia kac|ng bo gia qbfpakdafqa bo b|k hndbk_giez Ša blm gh_f a“q_afg kac|ngc a€gkhqg_fd gia ebp_fd bl’aqg okbe h p_`ab ca‹|afqaz sbkabpak ~a qhf qbejhka b|k eagib` ~_gi qnhcc_qhn jbn}dbfmlhca` bfac› f b|k hndbk_gieˆ ~a |ca hf hfhn}g_q obke|nh gb qbem j|ga gia q|kphg|ka rxyz äc ~a hcc|ea _fgakjbnhga` jb_fgc t hka ¢apafn} cjhqa`ˆ gia jhkheagak g bo gia q|kpa apbnpa okbe gb bf ahqi q|l_q cadeafg qbejbc_fd gia q|kpaz „afqa gb qbej|ga gia a€hqg phn|a bo gia q|kphm g|ka hg gia jb_fg ÿ½ˆ ~a ’|cg |ca› â ½ « â ½r¢ y « ½ r¢ y ½ r¢ y Ê ½ r¢ y ½ r¢ y ½ r¢ y¦ » ½ r¢ y¦ ~iaka ahqi bo ½ r¢ y ˆ ½ r¢ y ˆ ½ r¢ y ˆ ½ Àr¢ y _c h bhgˆ¢ ohqgbk okbe gia jbn}fbe_hn a€jkacc_bf ɽr y ~_gi ª « z †i_c qhnq|n|c _c _f`ajaf`hfg bf gia jb_fg qbfc_`aka` r fb faa`c bo h cjaq_‡q ehfhdaeafg obk ‡kcg hf` nhcg _fgakjbnhga` jb_fgcyz äf bgiak h`phfghda _f |c_fd hfhn}g_q a€jkacc_bfc _c gb hnnb~ `_kaqg qbej|ghg_bf bo fbkehn paqgbkz f b|k 



‰_d|ka w› fgakjbnhga` œbfgb|k fg_hn_…hg_bf ; < = > ?@ A B C = D A