ࠦࡦࡇࡘ࡯࠲ᡰេ↹௝⸻ᢿቇળ⺰ᢥ⹹ Vol.8 No.1-2Nov.2004⎇ⓥ⺰ᢥႺ⇇ᒻ⁁䈱․ᓽ᛽಴䈍䉋䈶㩷േᓘၮᐩ㑐ᢙ䈮䉋䉎ᒻ⁁ౣ᭴ᚑ䈮ၮ䈨䈒㩷㪯 ✢ 㪚㪫 ௝䈮䈍䈔䉎⢄⤳㗔ၞ䈱⥄േ᛽಴䈫ᒻ⁁䊝䊂䊥䊮䉫Ⴧ⼱૫ቁ ᧁ᧛ᢥᒾ̐ ૒ਭ㑆৻㇢̐̐ⷐᣦ㧦න⋧ߩㅧᓇ : ✢ %6 ௝ߦ߅ߌࠆ⢄⤳ߩ㗔ၞ᛽಴‫ޔ‬ᒻ⁁ࡕ࠺࡝ࡦࠣߦ߅޿ߡ‫ޔ‬᛽಴ኻ⽎ߩႺ⇇᛽಴߅ࠃ߮േᓘၮᐩ㑐ᢙ㧔4CFKCN$CUKU(WPEVKQP4$( ߦࠃࠆᒻ⁁ౣ᭴ᚑߦၮߠߊᚻᴺࠍ㐿⊒ߒߚ‫ᧄޕ‬ᚻᴺߢߪ‫޿߈ߒޔ‬୯ಣℂߥߤߢᓧࠄࠇߚೋᦼᒻ⁁ߩ⴫㕙ࡏࠢ࠮࡞ࠍ᛽಴ᓟ‫ߩ࡞࠮ࠢࡏߩߘޔ‬૏⟎ߦ߅ߌࠆర↹௝ߩାภ୯߿ᦛ₸ߥߤߩ․ᓽ㊂ࠍ೑↪ߒߡ⢄⴫㕙ߩࡏࠢ࠮࡞ߩߺࠍㆬᛯߒ‫ߩ࡞࠮ࠢࡏߩߘޔ‬૏⟎߅ࠃ
߮ᴺ✢ᣇะࠍਛ㑆࠺࡯࠲ߣߔࠆ‫ᦨޕ‬ᓟߦਛ㑆࠺࡯࠲ࠍ 4$( ߦࠃࠅᄙ୯ࡏ࡝ࡘ࡯ࡓ࠺࡯࠲ߦᄌ឵ߒߡ⢄ᒻ⁁ࠍౣ᭴ᚑߔࠆᣇᴺߢ޽ࠆ‫ᧄޕ‬Ⓜߢߪ‫⥃ޔ‬ᐥ࠺࡯࠲ᢙ଀ࠍ↪޿ߚ⹏ଔታ㛎ߦࠃߞߡ‫ޔ‬㗔ၞ᛽಴ߦ㑐ߔࠆ․ᕈ߿ᕈ⢻ࠍ⹏ଔߒߚ⚿ᨐࠍ␜ߔ‫ޕ‬
Keywords: 3D medical images, radial basis functions, liver segmentation, and shapefeatures㧝㧚߹߃߇߈⥃ᐥߦ߅ߌࠆᖚ⠪࠺࡯࠲ࠍ↪޿ߚࠦࡦࡇࡘ࡯࠲⸻ᢿᡰេ߿ᚻⴚᡰេ‫߫߃଀ޔ‬⢄≸ߩ⥄േᬌ಴߿ᚻⴚࠪࡒࡘ࡟࡯࡚ࠪࡦ߅ࠃ߮࠽ࡆࠥ࡯࡚ࠪࡦߥߤߢߪ‫ߩེ⤳߫ߒ߫ߒޔ‬㗔ၞ᛽಴߅ࠃ߮ᒻ⁁ࡕ࠺࡝ࡦࠣ߇ⷐ᳞ߐࠇࠆ‫ޔߚ߹ޕ‬ᄙߊߩ႐ว‫ޔ‬ኻ⹤⊛ᠲ૞ࠍᷫࠄߒ‫ޔ‬ቴⷰᕈߩะ਄߿⥄േൻ߇㊀ⷐⷞߐࠇࠆ‫ޕ‬⢄⤳ߦ㑐ߒߡ߽‫࡞ࠞ࡝ࡋޔ‬㧯㨀ߦࠃࠆ‫╬߷߶ޔ‬ᣇ⊛ߥⓨ㑆⸃௝ᐲߩ↹௝࠺࡯࠲߇ᓧࠄࠇࠆએ೨߆ࠄ⥄േ᛽಴ߩ⹜ߺ[Bae93] [Gao96]ߪߐࠇߡ߅ࠅ‫ޔ‬․ߦㄭᐕ‫ᧄޔ‬ቇળߦࠃࠆࠦࡦ࠹ࠬ࠻[ᷡ᳓ 02]ࠍᄾ
ᯏߦ‫ޔ‬ᄙߊߩᚻᴺߦ㑐ߔࠆႎ๔߇ߥߐࠇߡ޿ࠆ㧔଀߃߫‫ ᧖৻[ޔ‬02] [᪊ᧄ 02] [ᮮጊ 02] [ᷰㄝ 02] [ਛᎹ03]ߥߤ㧕‫ޕ‬ᚒ‫ߩࠄࠇߎޔߪޘ‬ᚻⴚ߅ࠃ߮⸻ᢿߩᡰេࠍ⋡⊛ߣߒߡ‫ེ⤳ߦߢ߹ࠇߎޔ‬ᒻ⁁߅ࠃ߮ᒻ⁁ᄌᒻࡄ࠲࡯ࡦߦ㑐ߔࠆࡕ࠺࡝ࡦࠣߦ㑐ߔࠆ⎇ⓥࠍⴕߥߞߡ
߅ࠅ‫৻ߩߘޔ‬Ⅳߣߒߡ᛽಴ኻ⽎ߩႺ⇇᛽಴߅ࠃ߮േᓘၮᐩ㑐ᢙ㧔4CFKCN$CUKU(WPEVKQPએਅ 4$(㧕ߦࠃࠆᒻ⁁ౣ᭴ᚑߦၮߠߊ⤳ེ㗔ၞߩ⥄േ᛽಴ᚻᴺߩน⢻ᕈ߿᦭ലᕈߦߟ޿ߡᬌ⸽ߒߡ߈ߚ[Ⴧ⼱01] [Ⴧ⼱ 02]‫ᧄޕ‬ᚻᴺߩ೑ὐߪ‫ޔ‬นᄌᒻࡕ࠺࡞ࠍ↪
޿ߚ㗔ၞ᛽಴ᴺߣห᭽ߦ‫ޔ‬ᒻ⁁ߩႺ⇇ߩ৻ㇱಽ߇ᰳߌߡ޿ߡ߽‫⴫ޔ‬㕙ᒻ⁁ߩṖࠄ߆ߐࠍ೨㚟⍮⼂ߣߒߡ‫ޔ‬ᒻ⁁ߩផቯ‫ޔ‬ౣ᭴ᚑ߇ߢ߈ࠆὐߢ޽ࠆ‫ޕ‬ᧄⓂߢߪ‫ߩߘޔ‬ၮᧄේℂ‫ ߮ࠃ߅ޔ‬: ✢ %6 ௝ߦ߅ߌࠆ⢄⤳ߩ⥄േ㗔ၞ᛽಴ࠍ଀ߣߒߡ‫ߩߘޔ‬ᚻᴺߩ⹦⚦ࠍㅀߴࠆ‫ޕ‬㧞㧚ᣇᴺ
4$( ࠍ૶↪ߒߚᒻ⁁ౣ᭴ᚑᚻᴺߦၮߠߊᧄ㗔ၞ᛽಴ᚻᴺߦ߅ߌࠆಣℂᚻ㗅ߪ‫ࠍࡓ࡜ࠣ࠻ࠬࡅޔ‬ขᓧߔࠆߥߤ‫ޔ‬೨ಣℂߩᓟߪ‫ޔ‬᭎ߨએਅߩ㧠ߟߩࠬ࠹࠶ࡊߦಽߌࠄࠇࠆ‫ޕ‬㧝㧕๟ㄝ㗔ၞߩ㒰෰㧞㧕ೋᦼᒻ⁁ߩขᓧ㧟㧕⢄⴫㕙ࡏࠢ࠮࡞ߩ᛽಴
㧠㧕4$( ߦࠃࠆ⢄ᒻ⁁ౣ᭴ᚑᦨೋߦ‫ޔ‬⢖㗔ၞߥߤ‫ޔ‬Ყセ⊛᛽಴ߩኈᤃߥ๟ㄝ
⤳ེߩ᛽಴ࠍⴕ޿‫╙ޔ‬㧞ࠬ࠹࠶ࡊߩೋᦼᒻ⁁ขᓧᤨߩㆊ᛽಴ࠍᛥ೙ߔࠆ‫ޕ‬ᰴߩೋᦼᒻ⁁ߩขᓧߢߪ‫ޔ‬๟ㄝ⤳ེㇱಽࠍᶖ෰ߒߚ࠺࡯࠲ߦ߅޿ߡ‫ޔ‬න⚐ߒ߈޿୯ಣℂ‫ޔ‬ធ⛯ⷐ⚛⸃ᨆ㧔࡜ࡌ࡝ࡦࠣ㧕‫ࡈ࡞ࡕޔ‬ࠜࡠࠫಣℂߦࠃࠆᒻ⁁ᐔṖൻߥߤߦࠃࠅⴕ޿‫ޔ‬ᄢ߹߆ߥ⢄ᒻ⁁ߩขᓧࠍⴕߥ߁‫ޕ‬ᰴߦ‫ޔ‬ೋᦼᒻ⁁ߩ⴫㕙ߩࡏࠢ࠮࡞ߩߺࠍ᛽಴ߒߚᓟ‫ޔ‬⢄⴫㕙ࠍ޿ߊߟ߆ߩㇱಽߦಽ⸃ߒߚࡕ࠺࡞ߣߩ․ᓽ㊂ߩ৻⥌ᐲ᧲੩ᄢቇᄢቇ㒮කቇ♽⎇ⓥ⑼[‫ޥ‬113-8655 ᧲੩ㇺᢥ੩඙ᧄㇹ 7-3-1]
̐᧲੩ᄢቇᄢቇᎿቇ♽⎇ⓥ⑼̐̐᧲੩ᄢቇᄢቇᣂ㗔ၞഃᚑ⑼ቇ⎇ⓥ⑼ᛩⓂฃઃ㧦2004 ᐕ 6 ᦬ 3 ᣣᦨ⚳Ⓜฃઃ㧦2004 ᐕ 7 ᦬ 23 ᣣណ↪᳿ቯᣣ㧦2004 ᐕ 8 ᦬ 9 ᣣߦࠃࠅ‫ޔ‬⢄⴫㕙ࡏࠢ࠮࡞ߩߺࠍㆬᛯߔࠆ‫ᦨޕ‬ᓟߦ‫ޔ‬⢄⴫㕙ࡏࠢ࠮࡞ߩ૏⟎ߣᴺ✢ᣇะࠍ↪޿ߡ‫ޔ‬4$(ߦࠃࠅ⢄ᒻ⁁ࠍᄙ୯ࡏ࡝ࡘ࡯ࡓ࠺࡯࠲ߣߒߡౣ᭴
ᚑߔࠆ߇‫ߩ▚⸘ޔ‬㜞ㅦൻߩߚ߼‫ߩߡߴߔޔ‬⢄⴫㕙ࡏࠢ࠮࡞ߢߪߥߊ‫ޔ‬㑆ᒁ߈ࠍⴕ޿‫৻ߩߘޔ‬ㇱࠍ೑

- 10 -

Journal of Computer Aided Diagnosis of Medical Images Vol.8 No.1-2

Nov.2004

ࠆ 4$( ߦࠃࠆᒻ⁁ౣ᭴ᚑᴺߦߟ޿ߡㅀߴ‫ޔ‬㧚 ▵㧟ߟߩ೙ᓮὐࠍ↢ᚑߒߚ‫ޔߚ߹ޕ‬᭴ᚑߒߚ㒶㑐ᢙߦ߅޿ߡ‫ޔ‬Ⴚ⇇ౝߩ㗔ၞߢ㑐ᢙ୯߇㜞ߊߥࠆࠃ߁ߦ‫ޔ‬೙ᓮὐߩାภ୯߇ᒻ⁁ߩౝ஥ߢߪ 1‫ޔ‬Ⴚ⇇ߢ 0‫ޔ‬ᄖ஥ߢߪ-1 ߣߒ㧔࿑㧝㧕‫ޔ‬2 ୯ᒻ⁁ߩ᛽಴ߪႺ⇇ߩ୯ߢ޽ࠆ 0 ߢߒ߈޿୯ಣℂߔࠆߎߣߦࠃࠅᓧࠆ
[Masutani02]‫ޕ‬ࠃࠅ⢄ᒻ⁁᛽಴ࠕ࡞ࠧ࡝࠭ࡓߩ⹦⚦ࠍㅀߴࠆ‫ޕ‬↪ߔࠆ‫ޕ‬ᧄᚻᴺߩኻ⽎ߣߥࠆ࠺࡯࠲ߪ‫ޔ‬න⚐ : ✢ %6 ௝ࠍ฽߻ㅧᓇ : ✢ %6 ௝ߩන⋧࠺࡯࠲ߢ޽ࠆ‫ޕ‬ᧄ▵ߩએਅߩㇱಽߢߪ‫ޔ‬⢄ᒻ⁁ߩౣ᭴ᚑߦട߃
ߡ‫ޔ‬๟ㄝ⤳ེᒻ⁁ߩࡑࠬࠢᒻ⁁ߩ૞ᚑߦ૶↪ߐࠇ㧞㧚㧝㧚4$( ߦࠃࠆᒻ⁁ౣ᭴ᚑᴺᄖ(x+n,-1)

4$( ߪᒻ⁁㧔ାภߩỚᐲࡄ࠲࡯ࡦ㧕ߩߺߥࠄߕ‫ޔ‬ᄌᒻߥߤߩࡌࠢ࠻࡞႐ߥߤ‫ޔ‬ᄙᰴర࠺࡯࠲ߩ⵬㑆߅ ࠃ ߮ ⵬ ᄖ ߥ ߤ ߦ ࠃ ߊ ↪ ޿ ࠄ ࠇ ࠆ ‫ ޕ‬%CTT ࠄ[Carr01]ߪ‫  ߩߤߥࠨࡦ࠮ࠫࡦ࡟ޔ‬ᰴరᒻ⁁᷹ቯⵝ⟎߆ࠄᓧࠄࠇࠆ⸘᷹ὐ⟲ࠃࠅࡏ࡝ࡘ࡯ࡓ࠺࡯࠲ࠍ

Ⴚ⇇(x, 0)ౝ(x-n,+1)4$( ߦࠃࠅౣ᭴ᚑߔࠆᣇᴺ‫ߩߘ߮ࠃ߅ޔ‬㜞ㅦൻߦ࿑㧝 Ⴚ⇇ὐ߆ࠄ↢ᚑߐࠇࠆ㧟ߟߩ೙ᓮὐߟ޿ߡႎ๔ࠍⴕߥߞߡ޿ࠆ‫⎇ᧄޕ‬ⓥ߽‫ޔ‬ᔅⷐߣߔࠆ⴫㕙ᒻ⁁ߩὐ⟲߅ࠃ߮ߘߩᴺ✢ࡌࠢ࠻࡞ࠍ೑↪

4$( ߦࠃࠆᒻ⁁ౣ᭴ᚑߪ‫ޔ‬ᰴ▵ߦ␜ߔࠃ߁ߦ‫ޔ‬⢄ߒߡࡏ࡝ࡘ࡯ࡓ࠺࡯࠲ࠍౣ᭴ᚑߔࠆὐߢ㘃ૃߒߡ⤳ߩߺߥࠄߕ೨ಣℂߦ߅޿ߡ㒰෰ߩኻ⽎ߣߥࠆ๟޿ࠆ‫ޕ‬એਅߦ 4$( ߦࠃࠆᒻ⁁ౣ᭴ᚑߦߟ޿ߡㅀߴㄝ㗔ၞߩ᛽಴ߦ߽↪޿ࠄࠇࠆ‫ޕ‬ࠆ‫ޕ‬

ౣ᭴ᚑኻ⽎ߣߥࠆ  ᰴరⓨ㑆(xЩR3)ߦ߅ߌࠆ㒶㑐ᢙ s(x)ߪ‫ޔ‬એਅߩࠃ߁ߦ␜ߐࠇࠆ‫ޕ‬Ns (x) p (x)  ¦ OiI ( x  x i )i 1
ߎߎߢ p(x)ߪ p(x)=c1+ c2x+ c3y+ c4z ߢ⴫ߐࠇࠆ৻ᰴᄙ㗄ᑼ‫ޔ‬xi=(xi,yi,zi)T ߇೙ᓮὐᐳᮡ‫ ߪ| |ޔ‬3 ᰴరⓨ㑆ߦ߅ߌࠆ࡙࡯ࠢ࡝࠶࠼〒㔌‫ޔ‬N ߇೙ᓮὐߩᢙ‫ޔ‬O i ߇೙ᓮὐߦኻߔࠆ㊀ߺઃߌଥᢙ‫ޔ‬I(r)߇ၮᐩ㑐ᢙߢ޽ࠆ‫ޕ‬ၮᐩ㑐ᢙߪࠬࡊ࡜ࠗࡦ㑐ᢙߩਛ߆ࠄㆬ߫ࠇࠆ߇‫⎇ᧄޔ‬ⓥߢߪએਅߦ␜ߔ biharmonic ࠬࡊ࡜ࠗࡦ㑐ᢙࠍ૶↪ߒߚ‫ޕ‬I (r ) rߎࠇࠄࠍ↪޿ߡ㊀ߺઃߌଥᢙ߅ࠃ߮৻ᰴᄙ㗄ᑼߦ߅ߌࠆቯᢙ c1㨪c4 ࠍ᳿ቯߒᒻ⁁ࠍ⴫⃻ߔࠆ㒶㑐ᢙࠍ᭴ᚑߔࠆ‫ޔߢߎߎޕ‬਄⸥ߩᑼߢߪ⥄↱ᐲ߇ᄙ޿ߚ߼એਅߩ᜔᧤᧦ઙࠍㅊടߒߡㅪ┙৻ᰴᣇ⒟ᑼࠍ⸃ߊ‫ޕ‬NNNN¦O ¦O x ¦O y ¦O zi 1ii 1i ii 1iii 1i i0ᧄ⎇ⓥߢߪ‫ޔ‬㧝ߟߩႺ⇇ὐߦኻߒߡ㧟ߟߩ೙ᓮὐࠍ↢ᚑߒߚ‫ޔߜࠊߥߔޕ‬Ⴚ⇇਄ߩὐߦട߃ߡ‫ޔ‬ᴺ✢ᣇะ߅ࠃ߮ߘߩㅒᣇะߩᒻ⁁ౝᄖߩὐߣߥࠆ㧞ߟߩὐࠍㅊടߒ‫ޔ‬Ⴚ⇇ὐㄭறߦᴺ✢ᣇะߦਗ߱㧞㧚㧞㧚๟ㄝ㗔ၞߩ㒰෰ᧄ⎇ⓥߢಣℂ↹௝߆ࠄߩ㒰෰ߩኻ⽎ߣߒߡ᛽಴ߐࠇࠆߩߪ‫ޔ‬⢖‫ޔ‬ᔃ⤳‫ޔ‬⡻㛽ࠍ฽߻⣻⣧ᄖ㗔ၞ‫ޔ‬ⴊ▤ߣ⣢⤳ߢ޽ࠆ‫ޕ‬ૉߒ‫ޔ‬ㅧᓇ⋧ߦᔕߓߡ૶޿ಽߌࠆߎߣߦࠃࠅ‫ޔ‬ಣℂߩ㜞ㅦൻࠍ࿑ࠆ‫ޔ߫߃଀ޕ‬⢄⤳ߦኻߒߡචಽߥࠦࡦ࠻࡜ࠬ࠻߇޽ࠆࠃ߁ߥㅧᓇ⋧ߢߪ‫ޕ޿ߥߒ↪૶ޔ‬߹ߕ‫ᦨޔ‬ೋߩಣℂߣߒߡ‫ࠍࡓ࡜ࠣ࠻ࠬࡅޔ‬⢄⤳㗔ၞઃㄭߦ߅޿ߡขᓧߒ‫࠼࡯ࡕߩߘޔ‬୯ࠍ⢄⤳࡟ࡌ࡞ .. ߣቯ⟵ߒ‫ޔ‬ᓟߩߒ߈޿୯᳿ቯߦ↪޿ࠆ‫ޕ‬Ԙ ⢖㗔ၞߩ᛽಴ߦࠃࠆ⢖࡮ᔃ⤳㗔ၞߩ㒰෰ߎߎߢߪ‫ޔ‬⢖㗔ၞߩ᛽಴߅ࠃ߮‫ޔ‬᛽಴ߒߚ⢖ߩᒻ⁁ࠍ೑↪ߒߡ‫ޔ‬⢄⤳ߣធߒߡ޿ࠆᔃ⤳㗔ၞࠍ฽߼ߡ᛽಴ߒ‫ޔ‬⢄⤳ߦធߒߡ޿ࠆ਄ㇱߩ㗔ၞࠍߔߴߡ㒰෰ߔࠆࠃ߁ߥࡑࠬࠢࠍ↢ᚑߔࠆ‫ޕ‬⢖㗔ၞߩ᛽಴ߪ‫ޔ‬න⚐ߒ߈޿୯ಣℂ㧔㨪*7㧕‫ޔ‬ ㄭறߩធ⛯ⷐ⚛⸃ᨆ‫ߩߘޔ‬ᓟߩᦨᄢ૕Ⓧⷐ⚛ߩ᛽಴ߦࠃࠅⴕߥࠊࠇࠆ‫ޕ‬᛽಴ߐࠇߚ⢖ᒻ⁁ߩ⴫㕙ࡏࠢ࠮࡞ߩ߁ߜ‫ޔ‬ᴺ✢ࡌࠢ࠻࡞߇ਅᣇߦะ޿ߡ޿ࠆ߽ߩߩߺࠍ᛽಴ߒ‫ޔ‬ౣ߮  ㄭறߩធ⛯ⷐ⚛⸃ᨆࠍⴕ޿‫ᦨޔ‬ᄢ߅ࠃ߮  ⇟⋡ߩ૕Ⓧߩᄢ߈ߐࠍᜬߟ
ⷐ⚛ࠍ᛽಴ߔࠆ‫ߦ⚛ⷐߩࠄࠇߎޕ‬฽߹ࠇࠆࡏࠢ࠮࡞ߩ૏⟎ࠍႺ⇇ὐߣߒߡ೙ᓮὐࠍ↢ᚑߒ‫ޔ‬4$( ߦࠃࠆౣ᭴ᚑ߅ࠃ߮ߒ߈޿୯ಣℂߢ‫ޔ‬⢖㗔ၞߣᔃ⤳㗔ၞࠍ฽߻⢄⤳਄ㇱߩߚ߼ߩࡑࠬࠢᒻ⁁ࠍ↢ᚑߔࠆ‫ޕ‬࿑㧞ߦ␜ߔࠃ߁ߦ‫ޔ‬⢖ߩਅㇱࠍṖࠄ߆ߦ❬޿ߛࠃ߁ߥᦛ㕙ࠍ↢ᚑߔࠆߎߣߦࠃࠅ‫ޔ‬⢄⤳਄ㇱߦធߒ‫ޔ‬ାภ୯ߩૃߚᔃ⤳㗔ၞߩㆊ᛽಴ࠍ㒐ᱛߔࠆ‫ޕ‬- 11 -ࠦࡦࡇࡘ࡯࠲ᡰេ↹௝⸻ᢿቇળ⺰ᢥ⹹ Vol.8 No.1-2

Nov.2004࿑㧟 ⣻⣧ᄖ㗔ၞߩࡑࠬࠢ㧔╬୯㕙㧕㧦#ZKCN ᢿ㕙ߣߩ  ᰴరหᤨ⴫␜ᄖㇱࠃࠅⷰኤ㧔Ꮐ㧕‫ޔ‬ౝㇱࠃࠅⷰኤ㧔ฝ㧕એ਄ߢᓧࠄࠇߚ⢄⤳ᄖ㗔ၞߩࡑࠬࠢᒻ⁁ㇱಽߦ߅޿ߡ‫ޔ‬ర࠺࡯࠲ߩାภ୯ࠍ*7 ߣߒ‫ޔ‬⢄⤳ߩೋᦼᒻ⁁᛽಴ߦ೑↪ߔࠆ‫ޕ‬࿑㧞 ⢖㗔ၞߣᔃ⤳㗔ၞߩࡑࠬࠢ㧔╬୯㕙㧕㧦㧞㧚㧟㧚ೋᦼᒻ⁁ߩขᓧ%QTQPCN ᢿ㕙ߣߩ  ᰴరหᤨ⴫␜೨▵ߢ೨ಣℂߐࠇߚ࠺࡯࠲ߦ߅޿ߡ‫ޔ‬⢄⤳㗔ၞ਄ㇱࠃࠅⷰኤ㧔਄㧦ඨㅘ᣿㧕‫ޔ‬ઃㄭߦ߅޿ߡขᓧߐࠇߚࡅࠬ࠻ࠣ࡜ࡓߩࡕ࡯࠼୯ਅㇱࠃࠅⷰኤ㧔ਅ㧕ࠍ⢄⤳࡟ࡌ࡞ .. ߣߒ‫ޔ‬.. ࠍၮḰߣߒߚߒ߈޿୯᳿ቯࠍⴕ޿‫ޔ‬න⚐ߒ߈޿୯ಣℂࠍⴕߥ߁㧔⴫㧝ࠍෳԙ ⣻⣧ᄖ㗔ၞ㒰෰ᾖ㧕‫ޕ‬ᰴߦ‫ޔ‬ធ⛯ⷐ⚛⸃ᨆߦࠃࠆᦨᄢ૕Ⓧⷐ⚛ߩ᛽⣻⣧ᄖߩ㗔ၞߩ㒰෰ߪ‫ޔ‬න⚐⋧࠺࡯࠲ߦ߅޿ߡ‫ ޔ‬಴ߢೋᦼᒻ⁁ࠍᓧࠆ‫ޕ‬ඨᓘ XQZGN ߩ᭴ㅧⷐ⚛ࠍ⢄⤳ߣ⡻㑆ߥߤߩ๟ㄝ㗔ၞߩࠦࡦ࠻࡜ࠬ࠻߇ᓧࠄ ↪޿ߚ  ୯ࡕ࡞ࡈࠜࡠࠫߩ %NQUKPI ಣℂ‫߮ࠃ߅ޔ‬ࠇߥ޿႐วߦ↪޿ࠆ‫ߩߎޕ‬㗔ၞߦኻߒߡߪ‫ޔ‬⡻㛽 ⓨᵢ㒰෰ಣℂࠍⴕߥ߁‫ޕ‬߅ࠃ߮⣄ᬁ㗔ၞߩ᛽಴ߦࠃࠅࡑࠬࠢᒻ⁁ࠍ↢ᚑߔߎߩೋᦼᒻ⁁ߩᲑ㓏ߢߪ‫ߞߥⴕࠍࠣࡦࠠࠬࡑޔ‬ࠆ‫ޕ‬㛽⚵❱ࠍන⚐ߒ߈޿୯ಣℂ㧔*7㨪㧕߅ࠃ ߚㇱಽࠍ㒰߈‫ޔ‬⢄⤳ਅㇱߥߤߢㆊ᛽಴߇ⴕߥࠊࠇ߮  ㄭறߩធ⛯ⷐ⚛⸃ᨆߦࠃࠆᦨᄢ૕Ⓧⷐ⚛ߩ ߡ޿ࠆ႐ว߇ᄙ޿߇‫ޔ‬ᰴߩಣℂߢ⢄⴫㕙ࡏࠢ࠮࡞᛽಴ߢⴕ޿‫⴫ޔ‬㕙ࡏࠢ࠮࡞ࠍ᛽಴ߔࠆ‫ߩߘޕ‬ᓟ‫ࠍߺߩ ޔ‬᛽಴ߔࠆ‫ޕ‬ฦࡏࠢ࠮࡞ߦ߅޿ߡ‫ߩߘޔ‬૏⟎ߩ૕ゲ߹ࠊࠅߩⷺᐲࠍ⸘▚ߒ‫ޔ‬૕⴫ࠍ౞╴⴫㕙ߢㄭૃߒߚ႐วߩߘ 㧞㧚㧠㧚⢄⴫㕙ࡏࠢ࠮࡞ߩ᛽಴ߩⷺᐲߦ߅ߌࠆᴺ✢ࡌࠢ࠻࡞ߣⷺᐲߩౝⓍ߇ ೋᦼᒻ⁁ߩ⴫㕙ࡏࠢ࠮࡞ߩ߁ߜ‫ߩߘޔ‬ᴺ✢ᣇะએ਄ߣߥࠆࡏࠢ࠮࡞ߩߺࠍࠍ᛽಴ߒߡႺ⇇ὐߣߒ‫ߦ ޔ‬ၮߠ޿ߡ‫ޔ‬㧠ߟߩㅪ⚿ߒߚࠣ࡞࡯ࡊࠍ↢ᚑߔࠆ‫ޕ‬ᴺ✢ࡌࠢ࠻࡞ᖱႎߣߣ߽ߦ 4$( ౣ᭴ᚑࠍⴕߥ߁‫ ޕ‬ᴺ✢ᣇะߦࠃࠅㅪ⚿ߒߚṖࠄ߆ߥᒻ⁁ࠍ๒ߔࠆ⴫ߎࠇߢᓧߚࡏ࡝ࡘ࡯ࡓ࠺࡯࠲ࠍߒ߈޿୯ಣℂߔࠆ 㕙ࡏࠢ࠮࡞߇᛽಴ߐࠇࠆ‫ޕ‬ߎߣߦࠃࠅࡑࠬࠢᒻ⁁ࠍౣ᭴ᚑߔࠆ㧔࿑㧟㧕‫ޕ‬๟ㄝ⤳ེߣធߒߡ޿ࠆ႐วߥߤ‫ޔ‬ర࠺࡯࠲ߩ൨㈩ࠍ↪޿ࠆߣᱜߒ޿ᴺ✢ᣇะࠍផቯߔࠆߎߣߪߢԚⴊ▤࡮⣢⤳㗔ၞߩ㒰෰߈ߥ޿ߚ߼‫ޔ‬ೋᦼ᛽಴  ୯ᒻ⁁ࠍᐔṖൻߒߚࡏ࡝ⴊ▤㗔ၞ߇⢄⤳㗔ၞࠃࠅ㜞ାภࠍ๒ߔࠆ‫ޔ‬㐷⣂ ࡘ࡯ࡓ࠺࡯࠲߆ࠄ൨㈩ࠍขᓧߒ‫ߩߘޔ‬ㅒᣇะࠍᴺ⋧‫߮ࠃ߅ޔ‬ㅧᓇᓟᦼߩ࠺࡯࠲ߩ႐ว‫⴫▤ⴊޔ‬㕙ߦ ✢ᣇะߣߒߚ‫ޕ‬⢄⤳㗔ၞߣ㘃ૃߒߚࡏࠢ࠮࡞߇ሽ࿷ߔࠆߚ߼‫ޔ‬නએਅߦ㧠ߟߩࠣ࡞࡯ࡊߩ᛽಴᧦ઙࠍ␜ߔ‫↪૶ޕ‬⚐ߒ߈޿୯ಣℂ㧔.. *7㨪㧕‫ᦨ߮ࠃ߅ޔ‬ᄢ૕Ⓧߩ ߐࠇࠆ᧦ઙߪ‫ࠆߥߣ࡞࠺ࡕޔ‬ᴺ✢ࡌࠢ࠻࡞ PO‫߹ޔ‬ធ⛯ⷐ⚛ߩ᛽಴ᓟ‫ޔ‬XQZGN ಽߩ  ୯ࡕ࡞ࡈࠜࡠ ߚᴺ✢ᣇะߩ PO ߦኻߔࠆ⸵ኈⷺᐲǰV‫᧦ߩ₸ᦛޔ‬ࠫߩ⤘ᒛಣℂߦࠃࠅᓧߚᒻ⁁ࠍࡑࠬࠢᒻ⁁ߣߒߡ ઙ㧔ᐔဋᦛ₸ H ࠍ↪޿ߡಽ㘃㧕‫߮ࠃ߅ޔ‬᛽಴ߐࠇ૶↪ߔࠆ‫ޕ‬ࠆធ⛯ⷐ⚛ߩ᧦ઙߢ޽ࠆ‫ޕ‬- 12 -

Journal of Computer Aided Diagnosis of Medical Images Vol.8 No.1-2Ԙ ⢄਄㕙PO  6ǰV FGI ᦛ₸㧦*ኻ⽎㧦ᦨᄢ૕Ⓧߩㅪ⚿ᚑಽԙ ⢄ฝ㕙PO  6ǰV FGI ᦛ₸㧦*ኻ⽎㧦ᦨᄢ૕Ⓧߩㅪ⚿ᚑಽԚ ⢄೨㕙PO  6ǰV FGI ᦛ₸㧦*ኻ⽎㧦ᦨᄢ૕Ⓧߩㅪ⚿ᚑಽԛ ⢄ਅ㕙PO  6ǰV FGI ᦛ₸㧦㧔೙㒢ߥߒ㧕ኻ⽎㧦ᦨᄢ૕Ⓧߩㅪ⚿ᚑಽ㧗 ⇟⋡ߦᄢ߈޿૕Ⓧߩㅪ⚿ᚑಽ㧔૕Ⓧᦨᄢߩᚑಽ߇ో૕ߩ 㧑એਅߩ႐ว㧕⢄ਅ㕙ߢߪ‫ޔ‬⢙ྙઃㄭ߿ⴊ▤ߩዉ౉ㇱߢⶄ㔀ߥᦛ㕙ࠍ๒ߔࠆߎߣ߇ᄙ޿ߚ߼‫ߦ₸ᦛޔ‬㑐ߔࠆ೙㒢ߪ૶↪ߒߥ޿‫ⶄޔߚ߹ޕ‬㔀ߥᒻ⁁ߩߚ߼‫ߟߊ޿ޔ‬߆ߩⷐ⚛ߦಽഀߐࠇࠆߎߣ߇ೋᦼታ㛎ߢ᣿ࠄ߆ߦߥߞߚ‫ߩߎޕ‬ታ㛎⚿ᨐߦࠃࠆಽഀߐࠇߚ૕ⓍᲧࠍరߦ‫ᦨޔ‬ᄢ૕Ⓧߩㅪ⚿ᚑಽ߇ࡕ࠺࡞ߦㆡวߒߚࡏࠢ࠮࡞ో૕ߩ߁ߜ‫ޔ‬㧑એਅߥࠄ‫ࠍ⋡⇟ ޔ‬ㅊടߔࠆ‫ޕ‬ߎߎ߹ߢߩಣℂߢ‫ޔ‬⢄⴫㕙ߩᄢㇱಽߩᒻ⁁߇ಽഀߐࠇߡ᛽಴ߐࠇࠆߎߣߦߥࠆ㧔࿑㧡㧕‫ޕ‬ฦࠣ࡞࡯ࡊ㑆ߦ㊀ⶄߔࠆㇱಽ߽޽ࠆ߇‫⴫ޔ‬㕙ߩ⚦߆ߥಳಲߥߤߩ⚦ㇱࠍ㒰޿ߡ⢄⴫㕙ᒻ⁁ߩߺ߇᛽಴ߐࠇߡ޿ࠆߎߣ߇ࠊ߆ࠆ‫ޕ‬ᦨ⚳⊛ߦ‫  ߩࡊ࡯࡞ࠣ࡞࠮ࠢࡏߩࠄࠇߎޔ‬୯ࡏ࡝ࡘ࡯ࡓ࠺࡯࠲ߣߒߡߩ๺ߩ㓸วࠍߣࠅ‫ޔ‬⢄⴫㕙ࡏࠢ࠮࡞ߣߔࠆ‫ޕ‬㧞㧚㧡㧚4$( ߦࠃࠆ⢄ᒻ⁁ౣ᭴ᚑᦨᓟߦ‫ޔ‬⢄⴫㕙ࡏࠢ࠮࡞ߣߒߡ᳿ቯߐࠇߚࡏࠢ࠮࡞߅ࠃ߮ߘߩ૏⟎ߩᴺ✢ᣇะߦࠃࠅ‫ޔ‬4$( ࠍ↪
޿ߡࡏ࡝ࡘ࡯ࡓ࠺࡯࠲ߩౣ᭴ᚑࠍⴕߥ߁‫ޕ‬ᴺ✢ᣇะߪ‫ޔ‬⢄⴫㕙ߩࡏࠢ࠮࡞ߩ᛽಴ᤨߣห᭽‫ޔ‬ೋᦼᒻ⁁ࠃࠅ᳿ቯߔࠆ‫ߩߎޕ‬㓙‫⴫ޔ‬㕙ࡏࠢ࠮࡞ߩᢙ߇ᄙ޿႐ว‫ޔ‬㑆ᒁ޿ߡౣ᭴ᚑࠍⴕߥ߁ߎߣߢ㜞ㅦൻࠍ࿑ࠆ‫⴫ޕ‬㕙ࡏࠢ࠮࡞૏⟎ߩ :;< ฦⷐ⚛ߦ㑐ߒߡࠬ࠹࠶ࡊ᏷ࠍ㧟ߣߒߡࠨࡦࡊ࡝ࡦࠣࠍⴕߥߞߚ‫ޕ‬એ਄߇㗔ၞ᛽಴ߩ୘‫ߩޘ‬ᚻ㗅ߢ޽ࠆ߇‫౉ޔ‬ജߔࠆ࠺࡯࠲ߩㅧᓇ⋧ߦࠃߞߡ‫޿߈ߒࠆߔ↪૶ޔ‬୯ߥߤߩࡄ࡜ࡔ࡯࠲‫ࠆߔ↪૶ߦࠣࡦࠠࠬࡑ߮ࠃ߅ޔ‬㗔ၞߥߤ߇‫⧯ޔ‬ᐓ⇣ߥࠆ‫⴫ޕ‬㧝‫߮ࠃ߅ޔ‬࿑㧢ߦ‫ޔ‬ฦ⋧ߦኻߔࠆߒ߈޿୯‫߮ࠃ߅ޔ‬ಣℂᚻ㗅ࠍ߹ߣ߼ࠆ‫ޕ‬⴫ਛߩ +㨪+8 ߪ‫ޔ‬ㅧᓇ⋧ࠍ⴫ߒߡ߅ࠅ‫ޔ‬+ ߇න⚐⋧㧔ㅧᓇലᨐߥߒ㧕‫ޔ‬++ ߇ᣧᦼ⋧‫ޔ‬+8 ߇᥅ᦼ⋧ߢ޽ࠆ‫ޕ‬

Nov.2004࿑㧡 ⢄⴫㕙ࡏࠢ࠮࡞᛽಴Ꮐ㧦೨ᣇ߆ࠄߩⷰኤ‫ޔ‬ฝ㧦ᓟᣇ߆ࠄߩⷰኤ਄ࠃࠅ‫ޔ‬਄㕙‫ޔ‬ฝ㕙‫ޔ‬೨㕙‫ޔ‬ਅ㕙⴫㧝 ૶↪ߔࠆߒ߈޿୯㧔න૏㧦㧴㨁㧕ᦨዊ୯ᦨᄢ୯

+

+++8+++

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- 14 -Nov.2004⴫㧞 ᛽಴⚿ᨐߩ⹏ଔ
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࿑㧣 㗔ၞ᛽಴⚿ᨐ଀਄㧦㧰㧮㧙㧜㧞㧔⹏ଔ㧭㧕ਅ㧦㧰㧮㧙㧝㧟㧔⹏ଔ㧮㧕

Journal of Computer Aided Diagnosis of Medical Images Vol.8 No.1-2㧠㧚⠨ኤᧄᚻᴺߩ․ᓽߪ‫ޔ‬ㇱಽ⊛ߥ⴫㕙ᒻ⁁ߩߺ߆ࠄో૕ᒻ⁁ࠍ㧾㧮㧲ߦࠃࠅౣ᭴ᚑߔࠆߎߣߢ޽ࠅ‫ޔ‬ೋᦼᒻ⁁ߢᓧࠄࠇࠆᰳ៊ㇱಽߩᄢ߈ߐ߇ߤߩ⒟ᐲߢ
޽ࠆ߆ߦࠃߞߡ‫⚿ޔ‬ᨐ߇ᄢ߈ߊ⇣ߥࠆߎߣ߇␜ߐࠇߚ‫ޔߚ߹ޕ‬⢄ᒻ⁁ߩ․ᓽ⊛ߥㇱಽߦ∛ᄌ߇޽ࠅ‫ޔ‬ೋᦼ᛽಴ᒻ⁁ߢᰳ⪭ߒߚ႐ว߽‫․ߩߘޔ‬ᓽᒻ⁁߇ౣ⃻ߐࠇߕ‫ޔ‬Ṗࠄ߆ߥᒻ⁁߇ᓧࠄࠇߚ႐ว߇޽ߞߚ‫⚿ߩࠄࠇߎޕ‬ᨐ߆ࠄ‫ޔ‬ೋᦼᒻ⁁ࠍ᛽಴ߔࠆᤨὐߢ‫ߩࠄࠇߎޔ‬ᰳ⪭ࠍ޿߆ߦዋߥߊߔࠆ߆߇⺖㗴ߢ޽ࠆߣ޿߃ࠆ‫ޕ‬߹ߚ‫⎇ᧄޔ‬ⓥߢㅀߴߚᚻᴺߪ‫ޔ‬50#-'5[Kass87]
߿ .GXGN5GV[Sethian99] [৻᧖ 03]ߥߤߩนᄌᒻ
ࡕ࠺࡞ߦၮߠߊᚻᴺߦኻߒߡ‫࠲࡯࠺ߦ⥸৻ޔ‬㚟േဳߣ๭߫ࠇࠆಣℂᚻᴺߩ⚵ߺวࠊߖߦၮߠ޿ߡ޿
ࠆὐߦ․ᓽ߇޽ࠆ‫ޕ‬೨㚟⍮⼂ߣߒߡⷙቯߐࠇߚ⢄⴫㕙ߩะ޿ߡ޿ࠆᣇะࡌࠢ࠻࡞ߥߤ‫৻ޔ‬ㇱߦߏߊන⚐ߥࡕ࠺࡞ࠍዉ౉ߒߡ޿ࠆ߇‫ࠅߊޔ‬㄰ߒߩᡷༀߦࠃࠆᄌᒻࠍⴕߥ߁ߩߢߥߊ‫⸵ޔ‬ኈ▸࿐ߩⷙቯߩߺߢኻ⽎ࠍ᛽಴ߒߡ޿ࠆߚ߼‫࠲࡯࠺ޔ‬㚟േߩߚ߼ߩ⵬ഥᖱႎߦㆊ߉ߥ޿‫ߣ࠴࡯ࡠࡊࠕߥ߁ࠃߩߎޕ‬ߒߡߩ೑ὐߪ‫ࠅߊޔ‬㄰ߒᡷༀߩㆊ⒟ࠍ฽߼ߥ޿ߚ
߼‫ޔ‬ಣℂ߇㜞ㅦߢ޽ࠆߎߣ߇᜼ߍࠄࠇ‫⎇ᧄޔ‬ⓥߢߪ‫ ޔ‬ಽ⒟ᐲߢಣℂ߇ቢੌߔࠆߎߣ߇␜ߐࠇߚ‫ޕ‬ߎࠇߪ⥃ᐥᔕ↪ᤨߦ㊀ⷐߥⷐ⚛ߢ޽ࠆ‫ޕ‬ૉߒ‫੹ޔ‬ᓟߩᚻᴺߩᡷༀߣߣ߽ߦಣℂᤨ㑆ߪ㐳ߊߥࠆߣ⠨߃ࠄࠇࠆ߇‫ⷐޔ‬᳞ߐࠇࠆಣℂ⚿ᨐߣಣℂᤨ㑆ߩ࠻࡟࡯࠼ࠝࡈߢ‫ޔ‬᳿ቯߔߴ߈੐㗄ߢ޽ࠆߣ⠨߃ࠄࠇࠆ‫ޕ‬ᧄᚻᴺߢߪ‫ޔ‬න⋧ߩ࠺࡯࠲ࠍኻ⽎ߣߒߚ߇‫ޔ‬ᣢߦႎ๔ߐࠇߡ޿ࠆⶄᢙ⋧࠺࡯࠲ࠍ૶↪ߔࠆᣇᴺ[᪊ᧄ 01]ߣห᭽‫ޔ‬ᄙ⋧࠺࡯࠲ࠍ૶↪ߔࠆߎߣߦࠃࠅ‫ࠅࠃޔ‬ᱜ⏕ߥ᛽಴⚿ᨐ߇ᓧࠄࠇࠆߣᦼᓙߐࠇࠆ‫ޕ‬ૉߒ‫⥃ޔ‬ᐥ࠺࡯࠲ߢߪ‫ߦ࠲࡯࠺ߩ⋧ߩߡߴߔޔ‬㑐ߒߡ૏⟎߇ߕࠇߡ޿ߥ޿଻⸽ߪߥߊ‫ޔ‬㕖೰૕ߩ૏⟎วࠊߖࠍⴕߥ߁ᔅⷐ߇޽ࠆ߇‫ᧄޔ‬ᣇᴺߢߪ‫ޔ‬ర↹௝ࠍ㕖೰૕ߩ૏⟎วࠊߖߔࠆᣇᴺߩઁߦ‫ޔ‬ೋᦼᒻ⁁߆ࠄᓧࠄࠇࠆ‫ޔ‬⢄⴫㕙ߩਛ㑆࠺࡯࠲‫ࠊߥߔޔ‬ߜ‫⴫ޔ‬㕙਄ߩὐߩ૏⟎ߣᴺ✢ᣇะߩ⚵ߺวࠊߖߩ࠺࡯࠲ࠍ૏⟎วࠊߖߔࠆᣇᴺ߇⠨߃ࠄࠇࠆ‫ߥߔޕ‬ࠊߜ‫ࠅࠃߦ &((ޔ‬㕖೰૕ߩ +%2 ࠕ࡞ࠧ࡝࠭ࡓࠍㆡ↪ߔࠆᣇᴺ[Masutani01]ࠍ↪޿ߡ‫ⶄޔ‬ᢙ⋧ߩ⴫㕙ߩὐ࠺࡯࠲߆ࠄ‫ޔ‬ᰳ៊ࠍ⵬ߞߚࠅ‫ޔ‬ㆊ᛽಴ㇱಽࠍ೥㒰ߒߚࠅߢ߈ࠆߣᦼᓙߐࠇࠆ‫ޕ‬㧡㧚߻ߔ߮න⋧ߩㅧᓇ : ✢ %6 ௝ߦ߅ߌࠆ⢄⤳ߩ㗔ၞ᛽಴‫ޔ‬ᒻ⁁ࡕ࠺࡝ࡦࠣᴺߦ߅޿ߡ‫⴫ޔ‬㕙ᒻ⁁᛽಴‫ࠃ߅ޔ‬߮േᓘၮᐩ㑐ᢙ㧔4CFKCN$CUKU(WPEVKQP4$(㧕ߦࠃࠆᒻ⁁ߩౣ᭴ᚑߦၮߠߊᚻᴺࠍឭ᩺ߒ‫⥃ޔ‬ᐥ↹௝ߢ⹏ଔࠍⴕߥߞߚ‫ޕ‬ᄢ߈ߥ∛ᄌࠍ᦭ߔࠆ⢄⤳ߩ࠺࡯࠲߳ߩኻಣ߇⺖㗴ߣߒߡᱷߐࠇߡ޿ࠆ߇‫ޔ‬

Nov.2004ᄙߊߩ႐วߢ⦟ᅢߥ⚿ᨐࠍᓧߚ‫੹ޕ‬ᓟߪ‫∛ޔ‬ᄌߩ㗔ၞߩᬌ಴ࠍ฽߼ߚᚻᴺߩᡷༀࠍⴕߥ߁੍ቯߢ޽ࠆ‫ޕ‬⻢ㄉ
CADM ࠺࡯࠲ࡌ࡯ࠬߣߒߡ⾆㊀ߥ⥃ᐥ࠺࡯࠲ࠍឭଏߒߡ޿ߚߛ޿ߚ࿖┙߇ࠎ࠮ࡦ࠲࡯᧲∛㒮✽㊁❥వ↢‫ߩࠬ࡯ࡌ࠲࡯࠺ߦ߮ࠄߥޔ‬ᢛ஻߅ࠃ߮㈩Ꮣߦዧജߐࠇߡ޿ࠆ᧲੩ㄘᎿᄢ ᷡ᳓ᤘિవ↢ߦᗵ⻢ߒ߹ߔ‫ޕ‬߹ߚᣣ㗃ࠃࠅ⥃ᐥ㕙ߢߩ⼏⺰߿⍮⼂ߩឭଏ‫߅ޔ‬
ࠃ߮ಣℂ⚿ᨐߩ⹏ଔߦ㑐ߒߡ‫᧲ޔ‬ᄢ∛㒮᡼኿✢⑼ߩవ↢ᣇߦᗵ⻢ߒ߹ߔ‫ޕ‬ᧄ⎇ⓥߪᣣᧄቇⴚᝄ⥝ળᧂ᧪㐿ᜏࡊࡠࠫࠚࠢ࠻
㧔ᄖ⑼ᚻⴚࡠࡏ࠶࠻ߩ㐿⊒㧕ߩ৻ㇱߢ޽ࠆ‫ޕ‬ෳ⠨ᢥ₂[Carr01]
Carr JC, Beatson RK, Cherrie JB, etal. : Reconstruction and Representationof 3D Objects with Radial Basis
Functions, ACM SIGGRAPH2001:67-76, 2001
[Bae93]Bae KT, Giger ML, Chen CT, et al. :Automatic segmentation of liver
structure in CT images, MedicalPhysics 20(1): 71-78, 1993
[Gao96]
Gao L, Heath DG, Kuszyk BS, et al. :Automaticliver
segmentation
techniqueforthree-dimensional
visualization of CT data, Radiology :201(2) 359-364, 1996
[Kass87]
Kass, M., Witkin, A., and Terzopoulos,
D : Snakes: Active contour models.
International Journal of Computer
Vision: 1(4) 321-331, 1987
[Masutani01] Masutani Y, Kimura F, and Sakuma I :A New modal representation of liver
deformation for non-rigid registrationin image-guided surgery, Proc. ofCARS 2001 : 19-24, 2001
[Masutani02] Masutani
Y:
RBF-based
Representation of Volumetric Data:
Application in Visualization andSegmentation, Proc. of MICCAI 2002,
300-307, 2002
[Sethian99] J.A. Sethian, Level Set Methods andFast Marching Methods Evolving
Interfaces in Computational Geometry,Fluid Mechanics, Computer Vision, andMaterials
Science,
Cambridge
University Press, 1999
[ᷡ᳓ 02]ᷡ᳓ᤘિ㧦㧟ᰴర CT ௝߆ࠄߩ⢄⤳㗔 ၞ ᛽ ಴ ࠦ ࡦ ࠹ ࠬ ࠻ ,http://www.tuat.ac.jp/~simizlab/CADM/index.html[ਛᎹ 03]ਛᎹẢ຦㧘ᷡ᳓ᤘિ㧘৻᧖೰㧘 ઁ㧦3 ᰴర⣻ㇱ CT ↹௝߆ࠄߩ⢄⣲≜ᓇ- 15 -ࠦࡦࡇࡘ࡯࠲ᡰេ↹௝⸻ᢿቇળ⺰ᢥ⹹ Vol.8 No.1-2[৻᧖ 02][৻᧖ 03][Ⴧ⼱ 01][Ⴧ⼱ 02][᪊ᧄ 01][᪊ᧄ 02][ᮮጊ 02][ᷰㄝ 02]ߩ⥄േ᛽಴ᚻᴺߩ㐿⊒㧨╙ 2 ႎ㧪㧘 ⪺⠪⚫੺ାቇᛛႎ㧦MI2002-95㧘89-94, 2003
৻᧖೰ᔒ㧘ᷡ᳓ᤘિ㧘ዊ⇌⑲ᢥ㧦LevelSet Method ࠍ↪޿ߚ⢄⤳㗔ၞߩ⥄
േ᛽಴ᚻᴺߩ㐿⊒㧚╙ 12 ࿁ CADMᄢળ⻠Ṷ⺰ᢥ㓸㧦221-222, 2002
৻᧖೰ᔒ, ᷡ᳓ᤘિ, ↰᧛ߺߐߣ,ઁ㧦Level set method ࠍ↪޿ߚ⢄⤳㗔
ၞ᛽಴ᚻᴺߩ㐿⊒ߣ⹏ଔ", ࠦࡦࡇࡘ࡯࠲ᡰេ↹௝⸻ᢿቇળ⺰ᢥ⹹㧦
7(4-2), 1-9, 2003Ⴧ⼱૫ቁ㧘ᧁ᧛ᢥᒾ㧘૒ਭ㑆৻㇢㧦ਃᰴరක↪↹௝ߦ߅ߌࠆᒻ⁁․ᓽߩ᛽಴ߣߘߩ⢄⤳ᒻ⁁ࡕ࠺࡝ࡦࠣ߳ߩᔕ↪ 㧨╙৻ႎ㧪㧙ᣢሽᚻᴺߩ໧㗴ὐߣ㗔ၞ᛽಴ߐࠇߚ⢄ᒻ⁁ߦ߅ߌࠆᒻ⁁․ᓽ᛽಴㧙, ╙ 11 ࿁ CADM ᄢળ⻠Ṷ⺰ᢥ㓸㧦201-202, 2001Ⴧ⼱૫ቁ㧘ᧁ᧛ᢥᒾ㧘૒ਭ㑆৻㇢㧦ਃᰴరක↪↹௝ߦ߅ߌࠆᒻ⁁․ᓽߩ᛽಴ߣߘߩ⢄⤳ᒻ⁁ࡕ࠺࡝ࡦࠣ߳ߩᔕ↪ 㧨╙ੑႎ㧪-Ⴚ⇇ᒻ⁁․ᓽὐߩ⼂೎ߣ Radial Basis Function ߦࠃࠆᒻ⁁ౣ᭴ᚑ-㧘╙ 12 ࿁ CADM ᄢળ⻠Ṷ⺰ᢥ㓸㧦223-224, 2002᪊ᧄẢ㧘ၳ㓷ᢅ㧘૒⮮ ཅિ㧘ઁ㧦ࡑ࡞࠴ࠬ࡜ࠗࠬ CT ↹௝߆ࠄߩ⢄⤳㗔ၞ⥄േ᛽಴㧚㔚ሶᖱႎㅢାቇળ⺰ᢥ⹹, J84-DII(9) 2150-2161, 2001᪊ᧄẢ㧘૒⮮ ཅિ㧘ၳ㓷ᢅ㧘ઁ㧦⇣ߥࠆᤨ⋧ߩ↹௝ᖱႎࠍ↪޿ߚ⢄⤳㗔 ၞ⥄േ᛽಴ᴺ㧚╙ 12 ࿁ CADM ᄢળ⻠Ṷ⺰ᢥ㓸㧦219-220, 2002ᮮጊ⠹৻㇢㧘ർဈቁᐘ㧘᫪ஜ╷㧘ઁ㧦CT ୯ߩಽᏓ․ᓽߦၮߠ޿ߚ㕖ㅧᓇ⣻ㇱ X ✢ CT ௝߆ࠄߩ⢄⤳㗔ၞߩ᛽಴㧘╙ 12 ࿁ CADM ᄢળ⻠Ṷ⺰ᢥ㓸㧦217-218, 2002ᷰㄝᕺੱ㧘㊁ᣇ౞㧘㐳⼱Ꮉ⚐৻㧘ઁ㧦⣻ㇱන⚐࡮ㅧᓇ X ✢ CT ௝߆ࠄߩ⢄⤳㗔ၞో⥄േ᛽಴ᴺߩ㐿⊒㧚╙ 12࿁ CADM ᄢળ⻠Ṷ⺰ᢥ㓸㧦215-216,2002- 16 -Nov.2004Ⴧ⼱૫ቁ㧔߹ߔߚߦࠃߒߚ߆㧕
1997 ᐕ ᧲ᄢ࡮㒮࡮Ꮏቇ♽㧔♖ኒ㧕ඳ჻⺖⒟ୃੌ㧘Ꮏቇඳ჻㧚⃻࿷㧘หᄢቇ㒝ዻ∛㒮᡼኿✢⑼࡮หᄢቇ
㒮කቇ♽⎇ⓥ⑼⻠Ꮷ㧚↹௝⸃ᨆ࡮ࠣ࡜ࡈࠖࠢࠬ࡮ࡆ࡚ࠫࡦߩ⸻ᢿ࡮ᴦ≮߳ߩᔕ↪ߦ㑐ߔࠆ⎇ⓥߦᓥ੐
ᧁ᧛ᢥᒾ㧔߈߻ࠄ߰ߺ߭ߎ㧕
1974 ᐕ ᧲ᄢ࡮㒮࡮Ꮏቇ♽㧔⥶ⓨ㧕ඳ჻⺖⒟ୃੌ㧘Ꮏቇඳ჻㧚⃻࿷㧘หᄢቇ㒮Ꮏቇ♽⎇ⓥ⑼ᢎ᝼㧚↢↥ࠪࠬ࠹ࡓᎿቇ㧘CAD/CAM㧘࡜ࠗࡈࠨࠗࠢ࡞࡮ࠛࡦࠫ࠾ࠕ࡝ࡦࠣ㧘ࡔࡦ࠹࠽ࡦࠬᎿቇߥߤߦ㑐ߔࠆ⎇ⓥߦᓥ੐㩷૒ਭ㑆৻㇢㧔ߐߊ߹޿ߜࠈ߁㧕ᐕ᧲ᄢ࡮㒮࡮Ꮏቇ♽㧔♖ኒ㧕ඳ჻⺖⒟ਛㅌ㧘Ꮏቇඳ჻㧔᧲੩ᄢቇᐕ㧕㧚⃻࿷㧘หᄢቇ㒮ᣂ㗔ၞഃ
ᚑ⑼ቇ⎇ⓥ⑼ᢎ᝼㧚ක↪↢૕⸘᷹㧘ක↪↹௝࡮ࡠࡏ࠹ࠖࠢࠬࠍ೑↪ߒߚᚻⴚᡰេߦ㑐ߔࠆ⎇ⓥߦᓥ੐Journal of Computer Aided Diagnosis of Medical Images Vol.8 No.1-2

Nov.2004

Automated liver segmentation in X-ray CT images and shape modelingbased on boundary shape feature extraction and shape reconstruction
by using radial basis function

Yoshitaka Masutani, Fumihiko Kimura+, and Ichiro Sakuma++
Graduate School of Medicine, The University of Tokyo+Graduate School of Engineering, The University of Tokyo++Graduate School of Frontier Sciences, The University of Tokyo
Abstract
We developed a new method for liver segmentation and modeling in single phase CT angiographic
images, which employs boundary feature extraction and shape reconstruction based on radial basis function(RBF).

In the method, segmentation is performed in several steps; initial shape definition, surface voxel

extraction based on voxel features such as curvature, and shape reconstruction by RBF.

In this paper, we

describe our method and present our experimental results for validation of our method regarding segmentation
performance by using several clinical dada sets.

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