ᚑくᄢቇℂᎿቇ⎇ⓥႎ๔
J. Fac. Sci. Tech., Seikei Univ.
Vol.47 No.2 (2010) pp.65-70
㧔․೎⎇ⓥ⾌ߦଥࠆ⺰ᢥ㧕ࠞࡔ࡜ࠍ↪޿ߚࠝࡦ࡜ࠗࡦ⟑ฬ⹺⸽㧙⟑ฬ࠺࡯࠲⵬ᱜߦࠃࠆ㜞♖ᐲൻ㧙᧛᧻ ᄢ๋ Camera-based Online Signature Verification-Modification of Signature DataDaigo Muramatsu㧖
ABSTRACT㧦 Several online signature verification systems that use cameras have been proposed.
These systems obtain online signature data from video images by tracking the pen tip. Such systems arevery useful because special devices such as pen-operated digital tablets are not necessary. One drawback,however, is that if the captured images are blurred, pen tip tracking may fail, which causes performancedegradation. To solve this problem, here we propose a scheme to detect such images and modify the pentip position associated with the blurred images. Preliminary experiments that use private database showthat the proposed algorithm improved performance in terms of verification accuracy.
Keywords㧦online signature verification, particle filter, change detection, tracking, biometrics
㧔Received September 22, 2010㧕߆ࠄᓧࠄࠇࠆേ⊛․ᓽࠍ⹺⸽ߦ↪޿ࠆᚻᴺ 3㨯4)㧔ᧄⓂߢߪ㧝㧚ߪߓ߼ߦએᓟ‫⟑ࡦࠗ࡜ࡦࠝޟ‬ฬ⹺⸽ᚻᴺ‫ߣޠ‬๭߱㧕߇ᦨ߽৻⥸⊛ࡅ࠻ߩり૕⊛․ᓽ߿ⴕേ⊛․ᓽࠍ↪޿ߡ⹺⸽ࠍⴕ߁ࡃߢ޽ࠅ㧘⋓ࠎߦ⎇ⓥߐࠇߡ޿ࠆ 5-8㧕‫৻ޕ‬ᣇ㧘ࡍࡦవ゠〔࠺ࠗࠝࡔ࠻࡝ࠢࠬߣ๭߫ࠇࠆᚻᴺ߇ㄭᐕ⋓ࠎߦ⎇ⓥߐࠇ㧘࡯࠲એᄖߦ߽ࡍࡦߩᜬߜᣇ߿ࡍࡦࠍីࠆᒝߐߦᵈ⋡ߒߚ1)

ᚻᴺߥߤ߽ႎ๔ߐࠇߡ޿ࠆ 9-14)‫߫߃଀ޕ‬ᢥ₂ 9)10㧕ߪ࠺৻ㇱታ↪ൻߐࠇߡ߈ߡ޿ࠆ 㨫ࡃࠗࠝࡔ࠻࡝ࠢࠬߦߪᜰ⚉߿Ⰲᓀ㧘㕒⣂㧘᝿ᒻߥߤߩ࡯࠲ࠣࡠ࡯ࡉࠍ↪޿ߡ╩⸥ߔࠆ㓙ߩᜰߩᦛߍᣇߦᵈ⋡ߒり૕⊛․ᓽࠍ↪޿ߚ߽ߩߣ㧘╩⸥േ૞㧔⟑ฬ㧕߿ᱠⴕേߡ⹺⸽ࠍⴕߞߡ߅ࠅ㧘ᢥ₂ 11-13㧕ߪࠞࡔ࡜ࠍ↪޿ߡࡍ૞㧘ࠠ࡯ࠬ࠻ࡠ࡯ࠢߥߤߩⴕേ⊛․ᓽࠍ↪޿ߚ߽ߩߣ߇ࡦߩᜬߜᣇ․ᓽࠍขᓧߒ⹺⸽ߦ↪޿ߡ޿ࠆ㧔એᓟࡍࡦᜬ޽ࠅ㧘ߘࠇࠄߪ୘೎ߦ⎇ⓥ࡮೑↪ߐࠇࠆߛߌߢߥߊ㧘ⶄߜᣇߦᵈ⋡ߒߚᚻᴺࠍ‫ࡦࡍޟ‬ᜬߜᣇ⹺⸽‫ߣޠ‬๭߱㧕‫ޕ‬ᢙߩ․ᓽࠍ⚵ߺวࠊߖߡ⹺⸽ࠍⴕߥ߁ࡑ࡞࠴ࡕ࡯࠳࡞ᚻ2)ࡍࡦᜬߜᣇ⹺⸽ߣࠝࡦ࡜ࠗࡦ⟑ฬ⹺⸽ࠍ⚵ߺวࠊߖࠆ㨫ࡑ࡞࠴ࡕ࡯࠳࡞ᚻᴺߪ⹺

ߎߣߦࠃࠅ㧘⟑ฬ╩⸥ߣ޿߁৻ߟߩേ૞߆ࠄหᤨߦขᓧ

⸽♖ᐲߩะ਄߇ᦼᓙߢ߈ࠆߛߌߢߥߊ㧘᡹᠄⠴ᕈࠍ㜞߼ߢ߈ࠆⶄᢙ․ᓽࠍ↪޿ߚࡑ࡞࠴ࡕ࡯࠳࡞ᚻᴺ߇น⢻ߦߥࠆߎߣ߇ߢ߈ࠆߥߤߩ೑ὐ߽޽ࠅ᦭ᦸߥᚻᴺߣ⠨߃ࠄࠇࠆ‫⟑ࡦࠗ࡜ࡦࠝࠄ߇ߥߒ߆ߒޕ‬ฬ⹺⸽↪࠺࡯࠲ߪ৻⥸ߦߡ޿ࠆ‫ࠄ߇ߥߒ߆ߒޕ‬㧘ࡑ࡞࠴ࡕ࡯࠳࡞ᚻᴺߩ೑ὐࠍᦨ

࠲ࡉ࡟࠶࠻ߣࡍࡦࠍ↪޿ߡขᓧߐࠇࠆߎߣ߇ᄙ޿ߩߦኻᄢ㒢ߦᵴ߆ߔߚ߼ߦߪ㧘ⶄᢙߩ⇣ߥࠆ․ᓽࠍหᤨߦ߆ߟ

ߒ㧘ࡍࡦᜬߜᣇ․ᓽߪ࠺࡯࠲ࠣࡠ࡯ࡉ߿ࠞࡔ࡜ࠍ↪޿ߡหߓ࠺ࡃࠗࠬߢขᓧߔࠆߎߣ߇ᦸ߹ߒ޿‫᧦ߩࠄࠇߘޕ‬ઙขᓧߐࠇߡ޿ࠆߚ߼㧘৻⥸⊛ߥᚻᴺࠍ⚵ߺวࠊߖࠆߛߌࠍḩߚߔᚻᴺߣߒߡᧄⓂߢߪ⟑ฬ╩⸥േ૞ࠍ↪޿ߚ⹺⸽ߢߪ৻ߟߩ࠺ࡃࠗࠬߢࠝࡦ࡜ࠗࡦ⟑ฬ⹺⸽↪࠺࡯࠲ߣࡍߦᵈ⋡ߔࠆ‫ޕ‬ࡦᜬߜᣇ⹺⸽↪࠺࡯࠲ࠍขᓧߔࠆߎߣߪ࿎㔍ߢ޽ࠆ‫ߘޕ‬ᴺ߽⋓ࠎߦ⎇ⓥߐࠇߡ޿ࠆ

⟑ฬ╩⸥േ૞ࠍ↪޿ߚ⹺⸽ߣߒߡߪ㧘⟑ฬ╩⸥ᤨߩࡍߎߢ㧘ᧄⓂߢߪࠝࡦ࡜ࠗࡦ⟑ฬ⹺⸽↪࠺࡯࠲ࠍ࠲ࡉ࡟࠶ࡦవ゠〔࠺࡯࠲ࠍขᓧߒ㧘╩⸥ᐔ㕙਄ߢߩ⟑ฬ↢ᚑㆊ⒟࠻ߢขᓧߔࠆߩߢߪߥߊ㧘ࠞࡔ࡜ࠍ↪޿ߡขᓧߔࠆᚻᴺ15㨯16)*

㧦ࠛ࡟ࠢ࠻ࡠࡔࠞ࠾ࠢࠬቇ⑼ഥᢎ

ߦᵈ⋡ߔࠆ‫ޕ‬ࠞࡔ࡜ࠍ↪޿ߡࠝࡦ࡜ࠗࡦ⟑ฬ⹺⸽↪࠺࡯࠲ࠍขᓧߔ㧙㧙ࠆ႐วߪ᠟ᓇߐࠇߚ↹௝ⓨ㑆ߦ߅޿ߡࡍࡦవࠍㅊ〔ߔࠆ‫ޕ‬ฬ࠺࡯࠲߇ขᓧߐࠇ㧘ขᓧߐࠇߚ࠺࡯࠲ߣ౉ജߐࠇߚ IDߒ߆ߒߥ߇ࠄ㧘ࡍࡦ߇ㅦߊേ߆ߐࠇࠆᤨೞߢߪ㧘᠟ᓇߐߦኻᔕߔࠆ࡝ࡈࠔ࡟ࡦࠬ࠺࡯࠲ࠍᲧセߔࠆߎߣߢ್ቯࠍࠇߚ↹௝ߦ߅޿ߡࡍࡦవ߇߷ߌߡߒ߹߁ߎߣ߇޽ࠅ㧘ߎⴕ߁‫ޕ‬೨ㅀߒߚߣ߅ࠅ㧘ࠞࡔ࡜ࠍ↪޿ߡࠝࡦ࡜ࠗࡦ⟑ฬࠇߦࠃࠅㅊ〔ᄬᢌ߇⿠ߎࠅ߃ࠆ 16)‫ߩߎޕ‬႐ว૞ᚑߐࠇߚ⹺⸽↪࠺࡯࠲ࠍขᓧߔࠆ႐วߦߪㅊ〔ᄬᢌߦࠃࠅ㧘৻ㇱࠝࡦ࡜ࠗࡦ⟑ฬ⹺⸽↪࠺࡯࠲ౝߦ߅߆ߒߥㇱಽ߇ሽ࿷ߔ߅߆ߒߥ࠺࡯࠲ࠍ฽ࠎߢ޿ࠆน⢻ᕈ߇޽ࠆߚ߼㧘ᧄⓂߢࠆߎߣߦߥࠅ㧘ࠞࡔ࡜ࠍ↪޿ߚࠝࡦ࡜ࠗࡦ⟑ฬ⹺⸽ߩ♖ߪ⊓㍳ࡈࠚ࡯࠭㧘⹺⸽ࡈࠚ࡯࠭ਔᣇߦ߅޿ߡ‫↹ߌ߷ޟ‬௝ᐲഠൻߦߟߥ߇ࠆ‫ߩߎޕ‬ㅊ〔ᄬᢌߪ↹௝⥄૕ߩ߷ߌߦ⿠ᬌ಴‫ୃ࠲࡯࠺ޟߣޠ‬ᱜ‫ୃߢߣߎ߁ⴕࠍޠ‬ᱜᓟࠝࡦ࡜ࠗࡦ࿃ߔࠆߚ߼㧘ㅊ〔ࠕ࡞ࠧ࡝࠭ࡓߩᡷ⦟ߛߌߢߪ⸃᳿ߔࠆ⟑ฬ࠺࡯࠲ࠍ૞ᚑߒ⹺⸽ߦ↪޿ࠆ‫ޕ‬ߎߣ߇࿎㔍ߢ޽ࠆ‫ޕ‬ᧄ┨ߩએ㒠ߩ▵ߢߪࡍࡦవㅊ〔ᚻᴺߩ᭎ⷐߣ߷ߌ↹௝

ߘߎߢᧄⓂߢߪ㧘ࡍࡦవㅊ〔ߦᄬᢌߒߚㇱಽ߇ࠝࡦ࡜ᬌ಴ᣇᴺ෸߮࠺࡯࠲ୃᱜᣇᴺࠍ⺑᣿ߔࠆ‫ޕ‬ࠗࡦ⟑ฬ⹺⸽↪࠺࡯࠲ߦ฽߹ࠇߡ޿ࠆ႐วߢ߽㧘⹺⸽♖ᐲߩഠൻࠍᛥ߃ࠆߎߣ߇ߢ߈ࠆᚻᴺࠍឭ᩺ߔࠆ‫ౕޕ‬૕⊛㧚 ࡍࡦవㅊ〔ߦߪ㧘ฦᤨೞߦ߅޿ߡㅊ〔ߦᚑഞߒߡ޿ࠆߩ߆ᄬᢌߒߡ޿ࠆߩ߆ࠍ⥄േ⊛ߦ್ቯߒ㧘ߘߩᖱႎࠍ⠨ᘦߒߡ࠺࡯࠲ࠍୃᱜߒ⹺⸽ߦ೑↪ߔࠆ‫ޕ‬13 ੱߩⵍ㛎⠪߆ࠄขᓧߒߚ1950 ୘ߩࠝࡦ࡜ࠗࡦ⟑ฬ⹺⸽↪࠺࡯࠲ࠍ↪޿ߚታ㛎ߢߪ㧘ឭ᩺ᚻᴺߦࠃࠅ⹺⸽♖ᐲ߇ᡷༀߔࠆ⚿ᨐ߇ᓧࠄࠇߚ‫ޕ‬㧞㧚ᚻ ᴺ⊓㍳䊐䉢䊷䉵⹺⸽䊐䉢䊷䉵╩⸥േ૞↹௝╩⸥േ૞↹௝䊕䊮వㅊ〔䊕䊮వㅊ〔䉥䊮䊤䉟䊮⟑ฬ䊂䊷䉺䉥䊮䊤䉟䊮⟑ฬ䊂䊷䉺

࿑&CVCCESWKUKVKQP䈿䈔↹௝ᬌ಴䈿䈔↹௝ᬌ಴䊂䊷䉺ୃᱜ䊂䊷䉺ୃᱜ࿕ቯߒ㧘࠺࡯࠲ࠍขᓧߔࠆ‫ޕ‬࿑ 2 ߢߪ╩⸥⠪߇ฝ೑߈ߩୃᱜᓟ䉥䊮䊤䉟䊮⟑ฬ䊂䊷䉺ୃᱜᓟ䉥䊮䊤䉟䊮⟑ฬ䊂䊷䉺ߚ߼╩⸥ߔࠆᚻࠍᏀ஥߆ࠄ᠟ᓇߒߡ޿ࠆ‫ߦ࡜ࡔࠞߩߎޕ‬೨ಣℂ೨ಣℂᧄ⹺⸽ࠪࠬ࠹ࡓߢߪ࿑ 2 ߦ␜ߔࠃ߁ߦᚻߩᮮߦࠞࡔ࡜ࠍࠃࠅ↹௝㧔㕒ᱛ↹㧕ߩᤨ♽೉࠺࡯࠲߇ขᓧߐࠇࠆ‫ᧄޕ‬Ⓜ
ߢߪฦ↹௝ࠍࠣ࡟࡯ࠬࠤ࡯࡞ൻߒߡ↪޿ࠆ‫ޕ‬․ᓽ᛽಴ᤨೞ t ߩ↹௝ࠍ Yt 㧘ขᓧߐࠇࠆ↹௝ᤨ♽೉࠺࡯࠲ࠍ Y․ᓽ᛽಴

Y = (Y1, , Y2 ,..., YT )ߣߔࠆߣ䊥䊐䉜䊧䊮䉴䊂䊷䉺㕖㘃ૃᐲ⸘▚

್ቯ

(1)

ߣߥࠆ‫ ߢߎߎޕ‬T ߪࡈ࡟࡯ࡓ㐳ߢ޽ࠆ‫ޕ‬ขᓧߐࠇߚ↹௝ᤨ♽೉࠺࡯࠲߆ࠄࡍࡦవࠍㅊ〔ߒ㧘ฦᤨೞߩ↹௝਄ߢߩࡍࡦవ૏⟎ᐳᮡࠍขᓧߔࠆߎߣߦࠃࠅ

࿑1XGTCNNCNIQTKVJO⟑ฬ࠺࡯࠲ࠍ૞ᚑߔࠆ‫ࡦࡍޕ‬వࠍਛᔃߣߒߚ⍱ᒻ㗔ၞ㧚 ᭎ ⷐ ឭ᩺ᚻᴺࠍ฽߻ࠝࡦ࡜ࠗࡦ⟑ฬ⹺⸽ࠪࠬ࠹ࡓߩో૕௝

ࠍ࿑ 1 ߦ␜ߔ‫⊓ߪߦࡓ࠹ࠬࠪ⸽⹺ߦ⥸৻ޕ‬㍳ࡈࠚ࡯࠭ߣ⹺⸽ࡈࠚ࡯࠭߇޽ࠆ‫⊓ޕ‬㍳ࡈࠚ࡯࠭ߢߪฦ࡙࡯ࠩߩෳᾖ㧔 h × w 㧕ࠍ࠹ࡦࡊ࡟࡯࠻㧔 tem 㧕ߣߒ㧘ฦᤨೞߢࡍࡦవࠍㅊ〔ߒߡ޿ߊ‫ᧄޕ‬Ⓜߢߪᤨೞ t ߩࡍࡦవ૏⟎ᐳᮡࠍ

ᤨೞ 1 ߆ࠄ t ߹ߢߩ↹௝ Y1:t ߇ਈ߃ࠄࠇߚ߽ߣߢផቯߔࠆ‫ޕ‬ផቯߐࠇࠆࡍࡦవ૏⟎ᐳᮡࠍ Xˆ t = ( xt , y t ) ߣߔࠆߣ࠺࡯࠲㧔࡝ࡈࠔ࡟ࡦࠬ࠺࡯࠲㧕ࠍ੐೨ߦขᓧߒ㧘࡙࡯ࠩID ߣߣ߽ߦ⊓㍳ߔࠆ‫ ߪߢ࠭࡯ࠚࡈ⸽⹺ޕ‬ID ߣߣ߽ߦ⟑㧙㧙Xˆ t = ∫ X t P( X t | Y1:t ) dX t(2)ߣߒߡ᳞߼ࠆ‫ ߢߎߎޕ‬P ( X t | Y1:t ) ߪᤨೞ t ߩࡍࡦవ૏⟎ߩ੐ᓟಽᏓߢ޽ࠅ X t ߪ⍱ᒻ㗔ၞ㧔 h × w [pixels]㧕ߩਛᔃ

P (Yt | Y1:t −1 ) ߩ㑐ଥࠍ␜ߒߚ߽ߩߢ޽ࠆ‫ᤨޕ‬ೞ t = 57 ߢ⚥Ⓧ⺋Ꮕ߇⓭ὼᄢ߈ߊߥߞߡ޿ࠆ‫ߩߘޕ‬ℂ↱ߪ↹௝ Yt ߩࡍࡦవ߇߷ߌߡ߅ࠅ㧘ㅊ〔ߦᄬᢌߒߡ޿ࠆߚ߼ߢ޽ࠆߣ⠨߃ࠄࠇࠆ߇㧘ߎߩหᤨೞߦ߅޿ߡㅙᰴ๟ㄝዕᐲ߇⓭ὼᷫᐳᮡߢ޽ࠆ‫ޕ‬ዋߒߡ޿ࠆߎߣ߽⏕⹺ߢ߈ࠆ‫ࠅࠃߣߎߩߎޕ‬ㅙᰴ๟ㄝዕࡌࠗ࠭ߩ౏ᑼࠍ↪޿ࠆߣ੐ᓟಽᏓߪ

P(Yt | X t ) P( X t | Y1:t −1 )P( X t | Y1:t ) =P(Yt | Y1:t −1 )(3)ߣᦠ߈឵߃ࠄࠇࠆ‫ޕ‬P (Yt | X t ) ߪዕᐲ㑐ᢙߢ޽ࠅ㧘ᧄⓂߢᐲ߇߷ߌ↹௝ᬌ಴ߦ᦭ലߢ޽ࠆߣ⠨߃ࠄࠇࠆ‫ᧄޕ‬Ⓜߢߪߎߩኻᢙㅙᰴ๟ㄝዕᐲࠍ೑↪ߒߡ㧘ᑼ㧔6㧕ߦࠃࠅ↹௝ Y = ߷ߌ↹௝ if log(P (Yt | Y1:t −1 ) ) < TRDlkߩ߷ߌ್ቯࠍⴕ߁‫ޕ‬tߪᰴߩࠃ߁ߦ⸳ቯߔࠆ‫ޕ‬ λλ 2
P(Yt | X t ) =  t  exp − t × dif  2 2π hw(6)㧚 ࠺࡯࠲ୃᱜ߷ߌ↹௝ᬌ಴ߢᤨೞ t ߩ↹௝ Yt ߇߷ߌ↹௝ߣ್ቯߐࠇ࠹ࡦࡊ ࡟࡯࠻ߣߩ 㕖 㘃ૃ ᐲߢ ޽ ࠅ 㧘 Sum of Square

Difference㧔SSD㧕ࠍ↪޿ߡ⸘▚ߐࠇࠆ‫ ߚ߹ޕ‬λt ߪࡂࠗotherwise

ߎߎߢ TRDlk ߪ߷ߌ↹௝ᬌ಴↪ߩߒ߈޿୯ߢ޽ࠆ‫ޕ‬(4)

ߎߎߢ dif ߪ↹௝ Yt ౝߩ X t ࠍਛᔃߣߔࠆ⍱ᒻ㗔ၞߣᱜᏱ↹௝ߚ႐ว㧘ᧄⓂߢߪߘߩᤨೞߢߩࡍࡦవផቯ૏⟎ߪᱜߒߊߥ޿ߣ⠨߃ࠆ‫ߢߎߘޕ‬㧘߷ߌ↹௝್ቯߩ⚿ᨐࠍ↪޿ߡࠝࡄࡄ࡜ࡔ࡯࠲ߢ޽ࠅࠝࡦ࡜ࠗࡦߢቇ⠌ߐࠇࠆ‫ޕ‬
ᧄⓂߢߪࡍࡦవߩផቯ෸߮ λt ߩቇ⠌ߦߪࡄ࡯࠹ࠖࠢࡦ࡜ࠗࡦ⟑ฬ࠺࡯࠲ࠍୃᱜߔࠆ‫ୃߩ࠲࡯࠺ޕ‬ᱜߦߪ⦡‫ޘ‬ߥᚻᴺ߇⠨߃ࠄࠇࠆ߇㧘ᧄⓂߢߪ߷ߌ↹௝ߣ್ቯߐࠇߚ࡞ࡈࠖ࡞࠲ࠍ↪޿ࠆ‫ࡦࡍޕ‬వㅊ〔ߩ⹦⚦ࠕ࡞ࠧ࡝࠭ࡓߦ
ߟ޿ߡߪᢥ₂ 16㧕ࠍෳᾖߐࠇߚߒ‫ޕ‬࠺࡯࠲ߪᰳ៊ߒߚߣ⠨߃㧘ᰳ៊ㇱಽߦኻߒ㧘⇣ߥࠆಣℂࠍᣉߔߎߣߢ࠺࡯࠲ࠍୃᱜߒ㧘ୃᱜᓟࠝࡦ࡜ࠗࡦ⟑ฬ࠺࡯࠲ࠍ૞ᚑߒ⹺⸽ߦ೑↪ߔࠆ‫ޕ‬㧚 ߷ߌ↹௝ᬌ಴㧟㧚ታ㛎㧚 ⟑ฬ⹺⸽ࠕ࡞ࠧ࡝࠭ࡓ㧚㧚 ೨ಣℂࡍࡦవㅊ〔෸߮࠺࡯࠲ୃᱜߦࠃࠅᓧࠄࠇߚࠝࡦ࡜ࠗࡦ࿑  %WOWNCVKXGGTTQTCPFUGSWGPVKCNOCTIKPCN

⟑ฬ࠺࡯࠲ Xˆˆ t = ( xˆˆ t , yˆˆ t ), t = 1,2,..., T ࠍᰴᑼߦࠃࠅ૏⟎࡮ࠨࠗ࠭⵬ᱜࠍⴕ߁‫ޕ‬NKMGNKJQQF

xt =↹௝ߩ߷ߌ್ቯߦߪᧄⓂߢߪᑼ㧔5㧕ߢቯ߼ࠆㅙᰴ๟P (Yt | Y1:t −1 ) = ∫ P (Yt | X t ) P ( X t | Y1:t −1 ) dX tㄝዕᐲࠍ↪޿ࠆ‫ޕ‬(5)

yt =xˆˆt − xgxmax − xminyˆˆ − yt(7)gymax − yminߎߩㅙᰴ๟ㄝዕᐲߪᑼ㧔3㧕ߩಽᲣߢ޽ࠅ㧘ᄌൻὐᬌ಴໧㗴 17)㧘ⅣႺᄌൻࠍ઻߁㗻ᬌ಴໧㗴ߢ᦭ലᕈ߇ႎ๔ߐߎߎߢ

ࠇߡ޿ࠆ 18)‫ޕ‬xg =ᑼ㧔5㧕ߪዕᐲ P(Yt | Xt ) ߩ੍᷹ಽᏓߦ߅ߌࠆᦼᓙ୯ࠍ⸘▚ߒߡ޿ࠆߣߺߥߖࠆ߇㧘↹௝߇߷ߌߡ޿ࠆ႐วߦߪᧄ

1 T ˆ
1 Txˆt , y g = ∑ yˆˆ t∑
T t =1T t =1(8)ߢ޽ࠅ㧘 xmin , xmax , y min , ymax ߪߘࠇߙࠇ⟑ฬߩ xˆˆ , yˆˆ ߩᦨ᧪ࡍࡦవ߇޽ࠆߣ੍ᗐߐࠇࠆ႐ᚲߢ߽↹௝ߩ߷ߌߦࠃࠅዊ୯෸߮ᦨᄢ୯ߢ޽ࠆ‫ޕ‬ዕᐲ߇ዊߐߊߥࠆߚ߼㧘ᑼ㧔5㧕ߩ୯߽ዊߐߊߥࠆߣ⠨߃ࠄࠇࠆ‫ޕ‬࿑ 3 ߪࡍࡦవㅊ〔ߩ⚥Ⓧ⺋Ꮕߣㅙᰴ๟ㄝዕᐲ㧙㧙ߎߎߢ㧘 Thߪ⹺⸽↪ߒ߈޿୯ߢ޽ࠆ‫ޕ‬㧚㧚 ․ᓽ᛽಴
ࠞࡔ࡜ࠍ࿑ 2 Data acquisition2 ߩࠃ߁ߦ⸳⟎ߒ╩⸥േ㧚 ታ㛎⸳ቯ૞ࠍ᠟ᓇߔࠆ႐วߦߪ㧘⟑ฬߩ Z ゲᣇะߩ࠺࡯࠲߇࿶❗

13 ੱߩⵍ㛎⠪ߦ 1 ࠮࠶࡚ࠪࡦ޽ߚࠅ⌀╩ 10 ୘ࠍ╩⸥ߐࠇߡߒ߹߁ߚ߼㧘Z ᣇะߩ․ᓽߪ޽߹ࠅ᦭ലߢߪߥ޿

ߒߡ߽ࠄ޿㧘ߘࠇࠍ 1 ㅳ㑆߅߈ߦ 3 ࠮࠶࡚ࠪࡦⴕߞߡ⌀‫ᧄߢߎߘޕ‬Ⓜߢߪ Z ᣇะߛߌߦଐሽߔࠆ․ᓽߪ⠨ᘦߖ╩࠺࡯࠲ࠍ෼㓸ߒߚ‫ޕ‬ᰴߦ⌀╩╩⸥⠪ߣߪ⇣ߥࠆ 4 ੱߩߕ㧘⟑ฬ․ᓽߣߒߡᑼ㧔㧕ߩ૏⟎࡮ࠨࠗ࠭⵬ᱜᓟߩ y ․

t =1
 0
Vyt =  yt − yt −1 otherwiseⵍ㛎⠪ߦ⌀╩ࠍ⌀ૃߒߚ⟑ฬߩ╩⸥ࠍଐ㗬ߒ㧘ன╩࠺࡯ᓽߦട߃㧘ᰴߩਃߟߩ․ᓽࠍ⸘▚ߒ⹺⸽ߦ↪޿ࠆ‫ޕ‬
(9)

0

t =1
θ t = tan −1  yt − yt −1
xt − xt −1  otherwise



(10)

V(11)

t0
t =0

=
2
2xxyy()()−+−otherwise
tt −1tt −1࠲ࠍ෼㓸ߒߚ‫ޕ‬ன╩╩⸥⠪ߦߪኻ⽎ߣߥࠆ⌀╩ߩ╩⸥ࡆ࠺ࠝࠍ⷗ߖ㧘✵⠌ߒߚᓟߦฦ⌀╩ߦኻߒ৻ੱᒰߚࠅ 30୘ߩன╩ࠍ╩⸥ߒߡ߽ࠄߞߚ‫⚿ߩߘޕ‬ᨐ㧘⌀╩࠺࡯࠲ 13

30=390 ୘㧘ன╩࠺࡯࠲ 13304=1560 ୘ࠍ෼㓸ߔࠆߎߣ߇ߢ߈ߚ‫ޕ‬ฦ╩⸥േ૞ߪ࠙ࠚࡉࠞࡔ࡜ߦࠃࠅ᠟ᓇߐࠇ㧘㕒ᱛ↹௝㧔320240[pixels]㧕ߩᤨ♽೉࠺࡯࠲ߣߒߡ଻ሽߒߚ‫ޕ‬㧚 ࠺࡯࠲ୃᱜ㧚㧚 㕖㘃ૃᐲ⸘▚
ᧄⓂߢߪ㧘ᰳ៊ㇱಽߩ࠺࡯࠲ୃᱜᣇᴺߣߒߡ㧘ᰴߩᣇੑߟߩ⟑ฬᤨ♽೉࠺࡯࠲㑆ߩ㕖㘃ૃᐲࠍ⸘▚ߔࠆ‫ᧄޕ‬ᴺࠍᬌ⸛ߒᲧセࠍⴕ߁‫ޕ‬Ⓜߢߪឭ᩺ᚻᴺߩ᦭ലᕈࠍ⏕⹺ߔࠆߚ߼ߦ㧘᛽಴ߐࠇߚ

ᚻᴺ㧝㧔✢ᒻ㧔Linear㧕㧕㧦✢ᒻ⵬㑆 19)․ᓽᤨ♽೉Ფߦ⁛┙ߦ dynamic time warping㧔DTW㧕20)

ࠍ↪޿ߡ〒㔌ࠍ⸘▚ߔࠆ‫ ࠍ࠲࡯࠺ࠬࡦ࡟ࠔࡈ࡝ޕ‬SigR 㧘ᚻᴺ㧞㧔ࠬࡊ࡜ࠗࡦ㧔Spline㧕㧕㧦3 ᰴࠬࡊ࡜ࠗࡦ⵬㑆⹺⸽ࡈࠚ࡯࠭ߢ౉ജߐࠇߚ⟑ฬ߆ࠄ᛽಴ߐࠇߚ⟑ฬ․ᓽ

ᚻᴺ㧟㧔ᰳ៊㧔Deletion㧕㧕㧦⵬㑆ߥߒ㧔ᰳ៊ߩ߹߹㧕ᤨ♽೉ࠍ SigV ߣߒߚߣ߈㧘ߎࠇࠄߩ⟑ฬ㑆㕖㘃ૃᐲࡌࠢ࠻࡞ D(SigR, SigV ) ࠍᰴߩࠃ߁ߦ⸳ቯߔࠆ‫ޕ‬D(SigR, SigV ) = ( D1 , D2 , D3 , D4 )

 dist ( SigRi , SigVi ) , i = 1,2,3,4
Di = TR㧚 ⹏ଔᣇᴺࡃࠗࠝࡔ࠻࡝࠶ࠢࠪࠬ࠹ࡓߩ♖ᐲࠍ⍮ࠆߚ߼ߦߪᧄੱ(12)ᜎุ₸㧔False Reject Rate㧔FRR㧕㧕ߣઁੱฃ౉₸㧔FalseAccept Rate㧔FAR㧕
㧕2 ߟߩᜰᮡߢ⹏ଔߔࠆᔅⷐ߇޽ࠆ߇㧘৻⥸⊛ߦߪߎࠇࠄߩ 2 ߟߩᜰᮡ߆ࠄ⸘▚ߐࠇࠆ╬⺋ࠅ₸

ߎߎߢ SigRi , SigVi ߪߘࠇߙࠇ⟑ฬ SigR, SigV ߩ i ⇟⋡ߩ․ᓽᤨ♽೉ߢ޽ࠅ㧘੹࿁ߩታ㛎ߢߪ․ᓽߪ ( y,Vy,V ,θ )ߦኻᔕߔࠆ‫ޕ‬TR ߪ࡝ࡈࠔ࡟ࡦࠬ⟑ฬߩ࠺࡯࠲㐳㧘 dist (, )ߪ DTW ࠍ↪޿ߡ⸘▚ߒߚ 2 ߟߩ․ᓽᤨ♽೉㑆ߩ〒㔌ߢ޽ࠆ‫〒ߥ⚦⹦ޕ‬㔌⸘▚ᣇᴺߪᢥ₂ 16)ࠍෳᾖߐࠇߚߒ‫ޕ‬㧔Equal Error Rate (EER)㧕ߦࠃࠅᲧセߐࠇࠆߎߣ߇ᄙ޿‫ޕ‬EER ߪ FAR㧩FRR ߣߥࠆߒ߈޿୯ߦ߅ߌࠆࠛ࡜࡯₸㧔FAR ߽ߒߊߪ FRR㧕ߢ޽ࠅߘߩ᳞߼ᣇߦߪੑㅢࠅߩᣇᴺ߇޽ࠆߣ⠨߃ࠄࠇࠆ‫ޕ‬
Global EER㧦ోⵍ㛎⠪ߦኻߒ౒ㅢߩߒ߈޿୯ࠍ⸳ቯߒߚ႐วߩ╬⺋ࠅ₸
Averaged EER㧦ⵍ㛎⠪Ფߦߒ߈޿୯ࠍ⸳ቯߒߡ᳞߼ߚ୘೎╬⺋ࠅ₸ߩᐔဋ୯㧚㧚 ್ ቯᑼ㧔12㧕ߢ⸘▚ߐࠇߚ㕖㘃ૃᐲࠍ⹺⸽↪ߒ߈޿୯ߣᲧ

Global EER ߪߒ߈޿୯⸳ቯᣇᴺࠍ฽߼⹺⸽ࠪࠬ࠹ࡓోセࠍⴕ߁ߎߣߢ㧘Accept/Reject ߩ್ቯࠍⴕ߁‫⟑ޕ‬ฬ߆ࠄ૕ߩ♖ᐲࠍ⹏ଔߔࠆᜰᮡߢ޽ࠆߚ߼㧘⹺⸽ࠕ࡞ࠧ࡝࠭ࡓⶄᢙߩ․ᓽࠍ᛽಴ߒߡ⹺⸽ࠍⴕ߁႐วߦߪⶄᢙߩ㕖㘃ૃࠍᲧセߔࠆߩߦㆡߒߚᜰᮡߢ޽ࠆߣ⠨߃ࠄࠇࠆ‫ߒ߆ߒޕ‬ᐲࠍ⸘▚ߒ㧘ߘࠇࠄࠍ⚵ߺวࠊߖߡ⹺⸽ߦ↪޿ࠆߩ߇৻ߥ߇ࠄ㧘ߎߩᜰᮡߪߒ߈޿୯ߩ⸳ቯᣇᴺߦᄢ߈ߊଐሽߒ21)‫ᧄߒ߆ߒޕ‬Ⓜߢߪ㧘߷ߌ↹௝ᬌ಴࡮࠺࡯࠲

ߡߒ߹߁ߚ߼㧘ฦ․ᓽߩ᦭ലᕈࠍ⹏ଔߔࠆ႐วߦߪ

ୃᱜߩ᦭ലᕈࠍ⏕⹺ߔࠆߚ߼ߦ㧘ฦ․ᓽߩ㕖㘃ૃᐲࠍ⁛

Averaged EER ߩ߶߁߇ㆡߒߡ޿ࠆߣ⠨߃ࠄࠇࠆ‫ߢߎߘޕ‬⥸⊛ߢ޽ࠆ┙ߦ㧘ߘࠇߙࠇߩ․ᓽ߆ࠄ⸘▚ߐࠇߚ㕖㘃ૃᐲᲤߦ್ቯ

Fi (Th) ࠍⴕ߁‫ޕ‬

Accept if Di < ThFi (Th) =  Reject OtherwiseᧄⓂߢߪ Averaged EER ࠍ᦭ലᕈߩ⹏ଔᜰᮡߣߒߡ↪޿
ࠆ‫ޕ‬

(13)

㧙㧙

㧚 ታ㛎⚿ᨐ߷ߌ↹௝್ቯߒ߈޿୯ TRDlk ࠍ − 19 ≤ TRDlk ≤ −10 ߣᄌᦝߒߚ႐วߦ߅ߌࠆ 3 ߟߩ⵬㑆ᣇᴺ㧔✢ᒻ㧘ࠬࡊ࡜ࠗࡦ㧘ᰳ៊㧕ߦࠃࠆ Averaged EER ࠍ⴫ 1㨪4 ߦ߹ߣ߼ࠆ‫ޕ‬

⴫#XGTCIGF''4ߒ߈޿୯-10-11Liner
7.0

7.1

6.9

6.0

Deletion

6.0

5.8

-14

7.5

7.3

7.0

-15
-16

8.2
9.8

-17

12.3

-19

12.7

-18

11.9

⵬ᱜߥߒ

6.1
8.7
9.3

11.6

11.1

12.5

10.0

ߒ߈޿୯
-10

5.9

5.6
6.4

Averaged EER ߽วࠊߖߡႎ๔ߔࠆ‫ޕ‬

6.8-12-13ߘߩ߹߹⹺⸽ߦ೑↪ߒߚ㧔⵬ᱜࠍⴕߞߡ޿ߥ޿㧕႐วߩ

⴫#XGTCIGF''4 V =?y =?

Spline߹ߚᲧセߩߚ߼ߦ㧘ฦ⴫ߩᦨ⚳ⴕߦࡍࡦవㅊ〔࠺࡯࠲ࠍ-11

5.9

-18

12.3

11.4

10.7

8.8

8.8

7.8

-17

11.0

8.9

8.8

-14
-16

11.5

Deletion

8.2

-15

8.9

Spline-12-13

8.1

Liner-197.0
7.6
8.5
9.5

9.7

10.4

⵬ᱜߥߒ
⴫#XGTCIGF''4 Vy =?ߒ߈޿୯
-10-11Liner
7.1

6.5

Spline8.3

7.8

Deletion
11.4

6.9

6.8

-14

6.2

6.2

5.5

-15
-16
-17-18
-19
⵬ᱜߥߒ

6.5
7.9
9.6

9.7
9.9

7.0
6.1
7.5
9.0

10.0
10.0
8.3

8.5
8.0
8.9
9.3

19.5

10.4
9.0

9.0
8.5
8.0
8.9
9.3

9.5

10.4

⴫#XGTCIGF''4 θ =?
ߒ߈޿୯
-10

7.9

5.3
5.2

9.8

13.7



-12-13

12.0

-11

6.2



3.7

4.6

-14

3.8

3.6

3.4

-189.6

4.4

5.1

3.2

-17

8.6

4.4

5.6

3.5

-16

8.4

Deletion

3.5

-15

6.3

Spline-12-13

5.4

Liner-19
⵬ᱜߥߒ

3.8
3.6
3.4
3.3
3.3
3.3

3.6
3.4
3.3
3.2
3.2
3.2

3.5

3.3
3.2
3.2
3.3
3.2
3.2

ᴺߪ⇣ߥࠆ߽ߩߩ㧘ฦ․ᓽߦ߅޿ߡߪ߷ߌ↹௝್ቯߒ߈㧠㧚߹ߣ߼޿୯ࠍ߁߹ߊ⸳ቯߢ߈ࠇ߫㧘⹺⸽♖ᐲ߇ᡷༀߐࠇࠆ⚿ᨐᧄታ㛎ߢߪㅙᰴ๟ㄝዕᐲࠍ↪޿ߡ߷ߌ↹௝ࠍᬌ಴ߒ㧘ߘߣߥߞߚ‫⚿ߩࠄࠇߎޕ‬ᨐࠃࠅ㧘߷ߌ↹௝ࠍᬌ಴ߒ㧘ୃᱜߩ⚿ᨐࠍ↪޿ߡࡍࡦవㅊ〔ߦࠃࠅขᓧߐࠇߚ⟑ฬ࠺࡯࠲ࠍⴕ߁ឭ᩺ᚻᴺߪ⹺⸽♖ᐲะ਄ߦ᦭ലߢ޽ࠆߣ⠨߃ࠄࠇࠍୃᱜߔࠆᚻᴺࠍ⠨߃㧘&69 ࠍ↪޿ߚࠝࡦ࡜ࠗࡦ⟑ฬ⹺ࠆ‫ޕ‬⸽ࠕ࡞ࠧ࡝࠭ࡓߦኻߒ㧘 ߟߩ࠺࡯࠲ୃᱜᣇᴺࠍㆡ↪ߒ⹏ଔࠍⴕߞߚ‫⚿ߩߘޕ‬ᨐᦨㆡߥߒ߈޿୯߅ࠃ߮ୃᱜᣇ㧙㧙̌ࡍࡦᜬ12) ᧛᧻ᄢ๋㧘㒙ㇱ⽸჻㧘ၳౝ ⠍㧘ዊᣇඳਯ㧘ෳ⠨ᢥ₂ߜᣇᖱႎࠍ↪޿ߚࡃࠗࠝࡔ࠻࡝࠶ࠢ୘ੱ⹺⸽̍㔚ሶ1) A.K.

Jain

andA.

Ross,

“Introductiontobiometrics, ” Handbook of Biometrics, eds. by A.K.
Jain, P. Flynn, and A.A. Ross, chapter1, Springerᖱႎㅢାቇળ⺰ᢥ⹹J92-A, No.5, pp.392-396, May.
2009.

13) Y.

verification, ”Handbook of Biometrics, eds. by A.K.

4) O. Henniger, D. Muramatsu, T. Matsumoto, I.
Yoshimura,recognition,”andM.

Encyclopedia

pp.1196-1205, 2009.

5) R.

Yoshimura,Plamondon

andG.

Biometrics,Lorette,“Automaticverification using gripping position and power,”
Proc. ISPACS2008, pp.647-650, 2008.

15) M.E. Munich and P. Perona, “Visual identification
by signature tracking,” IEEE Trans. PatternAnalysis and Machine Intelligence, vol.25, no.2,
pp.200-217, 2003.

16) K. Yasuda, D. Muramatsu, S. Shirato, and T.
Matsumoto,
Verification

signature verification and writer identification - the“Visual-Based

Using

Features

OnlineSignature

Extracted

FromVideo,” Journal of Network and Computer

state of the art,” Pattern Recognition, vol.22, no.2,
pp.107--131, 1989.

Ogata,

14) N. Wada and S. Hangai, “Online signature“SignatureofH.

SPIE, Vol. 7708㧘2010“Handbook of Multibiometrics,” Springer, 2006.

Science+Business Media, LLC., 2008.

Muramatsu,

features extracted from pen-holding style,” Proc.

2) A.A. Ross, K. Nandakumar, and A.K. Jain,Jain, P. Flynn, and A.A. Ross, chapter10, Springer

D.

“Biometric person authentication method using

Science+Business Media, LLC., 2008.

3) J. Fierrez and J. Ortega-Garcia, “On-line signature

Hashimoto,Applications, vol. 33, pp.333-341, 2010

“Automatic17) T. Matsumoto and K. Yosui. “Adaptation and1989-1993,” International Journal of Pattern

scheme,” IEEE Trans. on Systems, Man, and6) F.

LeclercandR.

Plamondon,

signature verification: The state of the art-change detection with a sequential monte carlo
Cybernetics part B:

Recognition and Artificial Intelligence, vol.8, no.3,
pp.643--660, 1994.

pp.592-606, 2007.

Cybernetics, Vol.37, No.3,

7) R. Plamondon and S.N. Srihari, “On-line and18) A. Matsui, S. Clippingdale, and T. Matsumoto,survey,” IEEE Trans. Pattern Analysis and Machine

re-initialization,” Proc. International Conference on

off-line handwriting recognition: A comprehensiveIntelligence, vol.22, no.1, pp.63--84, 2000.

8) D. Impedovo and G. Pirlo, “Automatic signature
verification: The state of the art,” IEEE Trans. onSystems,Applications

Man,andandpp.609-635, 2008.

Cybernetics

Reviews,

vol.38,“Bayesian sequential face detection with automatic

Pattern Recognition, 2008.

19) D. Muramatsu, K. Yasuda, S. Shirato and T.
Matsumoto,

PartC:

Changeno.5,9) N.S. Kamel, S. Sayeed, G.A. Ellis, “Glove-Based“Camera-Based

OnlineSignature

Verification with Sequential Marginal Likelihood
Detector,”

Proc.

13thInternational

Conference on Computer Analysis of Images andPatterns, pp. 229-236, 2009.

Approach to Online Signature Verification,” IEEE

20) L. Rabiner and B.-H. Juang, “Fundamentals ofIntelligence, Vol. 30, No. 6, pp.1109-1113, 2008.

21) D. Muramatsu and T. Matsumoto, “OnlineTrans.

On

PatternAnalysis

andMachine10) S. Hangai and T. Higuchi, “Writer Identification

speech recognition,” Prentice Hall, 1993.

Signature Verification Algorithm with a User
Specific Global Parameter Fusion Model,” Proc.

Using Finger-Bend in Writing Signature,” Proc.

IEEE International Conference on Systems, Man,BioAW2004, LNCS 3087, pp.229-237, 2004.

and Cybernetics, pp.492-497, 2009.

11) G. Gluhchev, M. Savov, O. Boumbarov and D.
Vasileva, “A New Approach to Signature-BasedAuthentication,”

pp.594-603, 2007.

Proc.

ICB2007,

LNCS4642,㧙㧙