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A Quantum Computational Approach to Correspondence Problems on Point Sets
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peisuke
July 04, 2020
Technology
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630
A Quantum Computational Approach to Correspondence Problems on Point Sets
全日本CV勉強会
CVPR2020読み会発表資料
peisuke
July 04, 2020
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Transcript
"2VBOUVN$PNQVUBUJPOBM"QQSPBDIUP $PSSFTQPOEFODF1SPCMFNTPO1PJOU4FUT "VUIPST7(PMZBOJL $5IFPCBMU 1SFTFOUFS!QFJTVLF
荈䊹稱➜ せ谏劤 価➜ 䨽㾩"#&+" 灇瑔؝ٝؾُ٦ةؽآّٝծٗنحز 崞⹛ 5XJUUFS!QFJTVLF (JUIVC IUUQTHJUIVCDPNQFJTVLF 2JJUB
IUUQTRJJUBDPNQFJTVLF 4MJEF4IBSFIUUQTXXXTMJEFTIBSFOFU'VKJNPUP,FJTVLF
嚊銲 • ة؎زٕ • "2VBOUVN$PNQVUBUJPOBM"QQSPBDIUP$PSSFTQPOEFODF1SPCMFNT PO1PJOU4FUT • וז锷俑 • ꆀ㶨،ص٦ؚٔٝوءٝד挿纇窟さׅ倯岀חאְג
• 䊨㣗挿כ • 㔐鯄遤ך䱱稊26#0ד邌植׃鵚⡂涸ח鍑ְ !! ∈ 0, 1 26#0
ꆀ㶨،ص٦ؚٔٝوءٝך铡僇 • ⡦ָ⳿勻ַ • 2VBESBUJDVODPOTUSBJOFECJOBSZPQUJNJ[BUJPO剑黝⻉ • Rחꟼׅ穈さׇ剑黝⻉㉏겗 !! ∈ 0,
1 • 26#0ה׃ג鍑ֽ㉏겗ך⢽ • .BY$VU • ؚٓؿ䕙葿㉏겗 • 1BSUJUJPO1SPCMFN
ꆀ㶨،ص٦ؚٔٝوءٝך铡僇 • ⹛⡲⾱椚ך嚊銲 • ؎آٌؚٝرָٕ暟椚涸ח㹋鄲ׁגְ • 㛇䎿朐䡾חזהֹך朐䡾錁庠ׅה剑黝鍑䖤
ꆀ㶨،ص٦ؚٔٝوءٝך铡僇 • ꆀ㶨ؽحزהכ • אך朐䡾⢽ִלהָꅾזさֲ • ⢽ִלծ铣《הך然桦דָծ ך然桦דָ⳿⸂ׁ • ך朐䡾
⟩ |0 ծך朐䡾 ⟩ |1 ה邌׃ծ ـٗحم椔 ⟩ |# = ⟩ %|0 + ⟩ (|1 ך״ֲחꅾיさׇ邌ׅ %ծ &כ醱稆侧ծ % ! + & !弫ׅ • ـٗحم椔〸㔳כꆀ㶨ؽحزך朐䡾ך荈 歋䏝㔳爙׃ך
ꆀ㶨،ص٦ؚٔٝوءٝך铡僇 • ءُٖ٦ر؍ٝؖ٦倯玎䒭 • ꆀ㶨ؽحزך朐䡾ך儗涪㾜ך倯玎䒭 • 麊⹛倯玎䒭ךꆀ㶨غ٦آّٝך״ֲזךծ岚ך朐䡾䗍ⴓׅ✲ד実ת • 植㖈ך朐䡾חعىٕزص،ٝ)⡲欽ׇֿׁהד如ך朐䡾邌ׇ •
عىٕزص،ٝ • 朐䡾ךؒطؘٕ٦爙ׅ • 〢Ⱙ暟椚חֶֽ⸇鸞䏝ְז؎ً٦آ • 禸ָ㹀䌢朐䡾חזגְהծ)ď&ď弫׃朐䡾הז • عىٕزص،ٝך剑㼭㔿剣⦼ח㼎䘔ׅ㔿剣ꟼ侧ָꆀ㶨ؽحزך㛇䎿 朐䡾ծָֿꆀ㶨،ص٦ؚٔٝחֶֽ剑黝鍑ח㼎䘔
ꆀ㶨،ص٦ؚٔٝوءٝך铡僇 • ػؐٔ遤 • ꆀ㶨ؽحز怴皾ך剑㛇劤涸ז怴皾 • ػؐٔ遤穈さׇֿהדعىٕزص،ٝ圓眠 • " !
+ $ !弫׃תתד㢌䳔דֹ • ꆀ㶨،ص٦ؚٔٝوءٝחֶֽعىٕزص،ٝ • ꆀ㶨،ص٦ؚٔٝوءٝדכِ٦ؠָعىٕزص،ٝך⦼鏣㹀 • عىٕزص،ָٝ؎آٌؚٝرٕהז״ֲחׅ • 㹀䌢朐䡾⡲ֿהדծ؎آٌؚٝرٕך剑黝鍑ָ実ת
26#0ַ؎آٌؚٝرٕפך㢌䳔 • 鍑ְֹ26#0 • ؎آٌؚٝرٕ • ⟃♴ך״ֲח㢌侧㢌䳔
ꆀ㶨،ص٦ؚٔٝوءٝתה • ꆀ㶨،ص٦ؚٔٝوءٝחֶֽعىٕزص،ٝה׃גծ؎آ ٌؚٝرٕ♷ִ • ؎آٌؚٝرٕך㛇䎿朐䡾錁庠ׅ✲ד剑黝鍑ָ䖤 • ؎آٌؚٝرٕכ26#0ה瘝⣣ד֮ծ穈さׇ㉏겗ך剑黝 ⻉㉏겗鍑ֻֿהָ⳿勻
ꆀ㶨،ص٦ؚٔٝ欽ְ㔐鯄ך鎘皾% • 㔐鯄遤ծְֻאַך㛇䎿חⴓ鍑׃ծך穈さׇח״ ג邌植 • 如⯋ך㔐鯄遤40 כծ⟃♴ך״ֲח剅ֽ • 3כ*
.ךꅾ➰ֹㄤה鋅זׇծ⟃♴ך״ֲז㛇䎿2ך穈 さׇ㉏겗הׅ
ꆀ㶨،ص٦ؚٔٝ欽ְ㔐鯄ך鎘皾% • ⯓玎ך穈さׇ㉏겗⢪ְծ挿纇Y Zך騃ꨄ剑㼭⻉ & ' = ) − '+
% = ) − ,& + − ,% + − ⋯ − ,' + % ״
ꆀ㶨،ص٦ؚٔٝ欽ְ㔐鯄ך鎘皾% • %הず圫ח㔐鯄遤ⴓ鍑ׅ .ך⛦ך갪חꟼׅ㛇䎿 .חꟼׅ㛇䎿
㢳⡤㉏겗ⵃ欽׃ؚٗ٦غٕ挿纇窟さ • 㸘㸾ַ挿纇פ • 僤א鏣縧ׅהծ♰剣䒷⸂ד䒷ַさג遼瑱ׅ • 遼瑱ׅ澓ָծ䒷ַさֲؒطؘٕ٦ָ剑㣐הז • 湱㼎㪦ָ㔿㹀ׁ僤㔚ה僤㔚鏣縧׃ծ✼ְָ䒷䓸さֲ ؒطؘٕ٦ָ剑㣐ְֹ朐䡾⡲
• 僤㔚挿纇ה鋅甧גגծ剑㣐ؒطؘٕ٦ד遼瑱׃ծ挿纇ָ窟さׁ 朐䡾הז ؒطؘٕ٦㼭 ؒطؘٕ٦㣐 ؒطؘٕ٦㣐
㢳⡤㉏겗 • 湱✼⡲欽ׅ⡤⟃♳ך禸ַז麊⹛実㉏겗 • 㸘㸾ד僤ず㡦ָ♰剣䒷⸂ד䒷ֹさֲꥷך䞨僤麊遤זו ( . R ٥٥٥ꅾ⸂⸇鸞䏝 ٥٥٥颵ꆀ
٥٥٥⡘縧
㢳⡤㉏겗挿纇窟さח䘔欽 <7(PMZBOJL > • Ⰻגך挿ず㡦㼎䘔➰ֽծؒطؘٕ٦剑㣐⻉ • 挿ָ♧荜׃㜥さח♧荜׃挿ず㡦ךؒطؘٕ٦כ̺חזծ ➭ך铎㼎䘔湱㼎涸ח搀鋔דֹ • *$1،ٕ؞ٔؤيך״ֲז㼎䘔➰ֽ㉏겗涪欰ׇׁ׆חծؚ
ٗ٦غٕז窟さָ〳腉 ė ٥٥٥ⴓ嫡ָחזךּך㼭ׁז⦼
挿纇窟さ䩛岀ך何葺晛 <7(PMZBOJL > • 㢳⡤㉏겗ךתת鍑ֻה♶㸜㹀ծ尶㿊ך 勲鎘皾ָ䗳銲 • /FHBUJWFFMFNFOUXJTFSFDJQSPDBMUSBOTGPSNPQFSBUPSⵃ欽 ׃גؒطؘٕ٦ꟼ侧㢌䳔 • Ⰻגך挿ず㡦דؙٔٝ䓸湫䱸剑黝⻉
• (װNזוךػًٓ٦ةכד葺ְ
醱侧挿纇ؙٔٝ׃ג如䕎䒭ח㢌䳔 • ⚛鹌Uכ*$1ず圫ח⚕挿纇⚥䗰⻉׃גꤐ ( ) = + ",$ ," −
).$ ! = + ",$ ," − /% .$ − /! .$ − ⋯ − /& .$ ! ぐղךYחאְגծ鵚⩸,⦐ךZח㼎׃גךؙٔٝ鎘皾 㹋欽♳Ⰻגך挿חؙٔٝ顦הꅾְ ⰋגךYחאְגךؙٔٝ⚛ץ 如䕎䒭חׅكؙزٕRך銲稆כַ Rך穈さׇד3皾⳿
㹋꿀勴⟝ • 傀㶷ך鎘皾堣דءىُٖ٦ءّٝ㹋꿀 • %8BWFחכ➙㔐ך㉏겗鍑ֽ堣腉כזְהךֿה • 㔐鯄遤ך铎䊴הծ挿纇窟さ铎䊴חאְג㜠デ • ر٦ةإحز •
GJTI RVCJU LBOKJ DPNQPTFS %ⵃ欽 • זֶ%כ鎘皾♶〳腉ךד 㹋꿀ז׃
窟さ㹋꿀 • 㹋꿀勴⟝ • ر٦ةإحزכGJTI挿 • ؙٔٝח欽ְ挿侧\ ^
• ⴱ劍،ٓ؎ًٝز铎䊴< Ģ>ך眔㔲ד㔐㹋꿀 • أ؛٦ٕろ荈歋䏝ך窟さ • 㹋꿀穠卓 • 㼎䘔挿ח欽ְ侧ָ⟃ⰻד֮ל 勲 • 挿侧㟓װׅהوحثؚٝדֹזַ • أ؛٦ٕろ窟さדכTJOHVMBSJUZUIFPSFNח״ 挿纇ָ挿ח簭鷌ׅ
㹋꿀穠卓 • ⴱ劍،ٓ؎ًٝز铎䊴ך㹋꿀 • וך錬䏝חꟼ׃ג,ָ⟃♴ד֮ ל㸜㹀׃ג窟さ〳腉 • ؚٗ٦غٕז窟さָ〳腉דֿ֮ה 爙㇗׃גְ •
ظ؎ؤחꟼׅ㹋꿀 • ظ؎ؤꆀ圫ղח鏣㹀 • ,ָ㼭ֽׁלظ؎ؤח㼎׃גٗغ أزז窟さָ〳腉
㹋꿀穠卓 • ألؙزٍؘٕحفך锃叨 • 剑㼭㔿剣⦼ה殢ח㼭ְׁ㔿剣⦼ךٍؘحفחאְג㹀䚍涸ח锃叨 • 鸐䌢ٍؘحفָ㼭ְׁקו 勲ָ♶㸜㹀 • 㹋꿀ד涪欰ׅألؙزٍؘٕحفָוך玎䏝㣐ֹֽל״ְַך鍑匿כ ꨇ׃ְָծ窟さ荈⡤כ♳䩛ֻ遤גְךד⼧ⴓזٍؘحفָ䖤גְ
ה罋ִג葺ְ
תה • ꆀ㶨،ص٦ؚٔٝⵃ欽׃挿纇窟さ • 㔐鯄遤穈さׇ剑黝⻉㉏겗ד鵚⡂ • 㢳⡤㉏겗欽ְ挿纇窟さך䩛岀ك٦أחꆀ㶨،ص٦ؚٔٝ ד窟さ遤 • 鸐䌢ך鎘皾堣⢪ְծ%ך挿纇㼎韋ח窟さ㹋꿀遤ְծؚ
ٗ٦غַٕאظ؎ؤח䓼ְ窟さָ〳腉ד֮✲爙׃