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1、第27卷第5期自動(dòng)化學(xué)報(bào)Vol.27,No.52001年9月ACTAAUTOMATICASINICASept.,20011)Kruppa方程與攝像機(jī)自標(biāo)定11,21雷成吳福朝胡占義1(中國科學(xué)院自動(dòng)化所模式識(shí)別國家重點(diǎn)實(shí)驗(yàn)室北京100080)2(安徽大學(xué)人工智能研究所合肥230039)(E-mail:leic@nlpr.ia.ac.cn)摘要首先研究探討了基于絕對二次曲線(theabsoluteconic)進(jìn)行攝像機(jī)自標(biāo)定魯棒性差的內(nèi)在原因.研究發(fā)現(xiàn),該類方法魯棒性不足的原因主要有三個(gè)方面:1)在目標(biāo)函數(shù)的全局最小點(diǎn)處存在大范圍的平坦區(qū)域,使得任何數(shù)值優(yōu)化算法難以達(dá)到全局最小
2、點(diǎn);2)當(dāng)存在噪聲時(shí),上述平坦區(qū)域內(nèi)會(huì)出現(xiàn)大量局部極小值,這樣數(shù)值優(yōu)化算法就非常容易收斂到靠近初值的局部極小值,使得算法對初始值的選取十分敏感;3)當(dāng)有噪聲時(shí),目標(biāo)函數(shù)的全局最小值極易偏離正確值.這樣,即使數(shù)值算法找到了全局最小值,該最小值也不再對應(yīng)正確的攝像機(jī)內(nèi)參數(shù)值.鑒于上述情況,探討了如何通過平面場景來確定內(nèi)參數(shù)矩陣的初始值,而后進(jìn)一步利用Kruppa方程的約束來精化內(nèi)參數(shù)矩陣的二步式方法.關(guān)鍵詞絕對二次曲線,Kruppa方程,攝像機(jī)自標(biāo)定.KRUPPAEQUATIONSANDCAMERASELF-CALIBRATION11,21LEIChengWUFu-ChaoHUZ
3、han-Yi1(NationalLaboratoryofPatternRecognition,InstituteofAutomationChineseAcademyofSciences,Beijing100080)2(InstituteofArtificialIntelligence,AnhuiUniversity,Hefei230039)(E-mail:leic@nlpr.ia.ac.cn)AbstractItiswellrecognizedthattheIAC(ImageoftheAbsoluteConic)basedcameracalibrationtechniques
4、arenotquiterobust,however,therearefewreportsonitsunderlyingreasonsintheliterature.Inthispaper,wefindthatthefollowingthreesourceslargelycontributetothenon-robustnessoftheIACbasedtechniques:1)Theglobalminimumofthecostfunctionliesonalargeflatarea,whichmakesanynumeri-caloptimizationmethodsdiffi
5、culttoreachit.2)Withnoise,manylocalminimumscouldappearintheaboveflatarea,whichmakesanynumericaloptimizationmethodsquitesensitivetothechoiceoftheinitialpointsincetheusedmethodcouldconvergeeasilytothelocalminimumclosetotheinitialpoint.3)Withnoise,thepointcorre-spondingtotheglobalminimumofthec
6、ostfunctioncoulddeviatesignificantlyfrom1)國家自然科學(xué)基金(69975021,60075004,60033010)、國家“973”計(jì)劃(G1998030502-3)、中國科學(xué)院機(jī)器人學(xué)開放實(shí)驗(yàn)室(RL200010)資助.收稿日期1999-12-23收修改稿日期2000-08-28622自動(dòng)化學(xué)報(bào)27卷theonesoughtfor,thusitisdifficulttogettherealcalibrationparametersbyminimiz-ingthecostfunction.Inaddition,weexploreatwo
7、-stepcalibrationtechnique.Inthisnewtechnique,firstlyaplane,whichisdistantfromtheorigin,isusedtoobtainaninitialsolution,thenKruppaequationsareusedtorefinethisinitialestimation.Theexperimentsonsimulateddataaswellasonrealimagesvalidateournewtechnique.Keywor
