Sceneplanesandhomographies現(xiàn)場(chǎng)平面的單應(yīng)性第1頁(yè)/共81頁(yè)P(yáng)roofofresult12.1第2頁(yè)/共81頁(yè)Example12.2Acalibrated

stereorig第3頁(yè)/共81頁(yè)Acalibratedstereorig2第4頁(yè)/共81頁(yè)Acalibratedstereorig3第5頁(yè)/共81頁(yè)ThehomographyinducedbyaplaneFig.12.1第6頁(yè)/共81頁(yè)Fig12.1Legend第7頁(yè)/共81頁(yè)HomographiescompatiblewithepipolarGeometry第8頁(yè)/共81頁(yè)Twosetsof4arbitrarypointsfrom2images第9頁(yè)/共81頁(yè)Epipolargeometrydefineconditionsonhomographies第10頁(yè)/共81頁(yè)Countingdegreesoffreedom第11頁(yè)/共81頁(yè)CompatibilityconstraintsFig.12.2a

e’=He第12頁(yè)/共81頁(yè)Compatibilityconstraints2

Fig.12.2bHTle’=le

第13頁(yè)/共81頁(yè)Compatibilityconstraints3

Fig.12.2c第14頁(yè)/共81頁(yè)Fig12.2Compatibilityconstraints第15頁(yè)/共81頁(yè)Result12.3第16頁(yè)/共81頁(yè)Homographiesarecompatiblewithfundamentalmatrix第17頁(yè)/共81頁(yè)Corollary12.4第18頁(yè)/共81頁(yè)Result12.5第19頁(yè)/共81頁(yè)13.6PlaneinducedhomographiesgivenFandimagecorrespondences:

(a)3points,(b)alineandapoint

第20頁(yè)/共81頁(yè)12.2.1Threepoints第21頁(yè)/共81頁(yè)Threepoints第22頁(yè)/共81頁(yè)Thefirst(explicit)methodispreferred第23頁(yè)/共81頁(yè)DegenerategeometryforanimplicitcomputationofthehomographyFig.12.3第24頁(yè)/共81頁(yè)Fig.12.3Legend第25頁(yè)/共81頁(yè)DeterminingthepointsXiisnotnecessaryinfirstmethodAllthatisimportant第26頁(yè)/共81頁(yè)Result12.6第27頁(yè)/共81頁(yè)P(yáng)roof第28頁(yè)/共81頁(yè)P(yáng)roof2第29頁(yè)/共81頁(yè)Consistencyconditions第30頁(yè)/共81頁(yè)Consistencyconditions2第31頁(yè)/共81頁(yè)Algorithms12.1Theoptimalestimateofhomographyinducedbyaplanedefinedby3points第32頁(yè)/共81頁(yè)12.2.2Apointandline第33頁(yè)/共81頁(yè)AoneparameterfamilyofhomographiesFig12.4(a),(b)第34頁(yè)/共81頁(yè)Fig12.4Legend第35頁(yè)/共81頁(yè)Result12.7第36頁(yè)/共81頁(yè)P(yáng)roofofresult12.7第37頁(yè)/共81頁(yè)P(yáng)roofofresult12.7(2)第38頁(yè)/共81頁(yè)P(yáng)roofofresult12.7(3)第39頁(yè)/共81頁(yè)Result12.8第40頁(yè)/共81頁(yè)Result12.82第41頁(yè)/共81頁(yè)GeometricinterpretationofthepointmapH(m)Explorethe第42頁(yè)/共81頁(yè)AhomographybetweencorrespondinglineimagesFig.12.5第43頁(yè)/共81頁(yè)Fig.12.5Legend第44頁(yè)/共81頁(yè)Degeneratehomographies第45頁(yè)/共81頁(yè)Degeneratehomographies2第46頁(yè)/共81頁(yè)AdegeneratehomographyFig.12.6第47頁(yè)/共81頁(yè)Fig.12.6Legend第48頁(yè)/共81頁(yè)12.3ComputingFgiventhehomographyinducedbyaplane第49頁(yè)/共81頁(yè)P(yáng)laneinducedparallax第50頁(yè)/共81頁(yè)P(yáng)laneinducedparallaxFig.12.7第51頁(yè)/共81頁(yè)Fig.12.7Legend第52頁(yè)/共81頁(yè)P(yáng)laneinducedparallax2Fig.12.8第53頁(yè)/共81頁(yè)Fig.12.8Legend第54頁(yè)/共81頁(yè)P(yáng)laneinducedparallax2第55頁(yè)/共81頁(yè)Algorithm12.2ComputingFgiventhecorrespondenceof6points,4ofwhicharecoplanar第56頁(yè)/共81頁(yè)Fundamentalmatrixfrom6pointsofwhich4arecoplanarFig.12.9第57頁(yè)/共81頁(yè)Fig.12.9Legend第58頁(yè)/共81頁(yè)P(yáng)rojectiveDepth第59頁(yè)/共81頁(yè)Example12.9第60頁(yè)/共81頁(yè)Binaryspacepartition:leftandrightimagesFig.12.10a,b第61頁(yè)/共81頁(yè)(c)Pointswithknowncorrespondence

(d)Atripletofpointsselectedfrom(c)andthistripletdefinesaplaneFig.12.10c,d第62頁(yè)/共81頁(yè)(e)Pointsononesideoftheplane

(f)Pointsontheotherside

Fig.12.10e,f第63頁(yè)/共81頁(yè)Fig12.10Legend第64頁(yè)/共81頁(yè)Twoplanes第65頁(yè)/共81頁(yè)Twoplanes2第66頁(yè)/共81頁(yè)TheactionofthemapH=H2-1H1onx

Fig.12.11第67頁(yè)/共81頁(yè)Fig.12.11Legend第68頁(yè)/共81頁(yè)Twoplanes3Uptothispoints,theresultsofthischapterhavebeenentirelyprojective第69頁(yè)/共81頁(yè)12.4TheinfinitehomographyHinf第70頁(yè)/共81頁(yè)TheinfinitehomographyHinf2第71頁(yè)/共81頁(yè)TheinfinitehomographyHinf3第72頁(yè)/共81頁(yè)Vanishingpointsandlines第73頁(yè)/共81頁(yè)TheinfinitehomographyHinfmapsvanishingpointsbetweenimagesFig.12.12第74頁(yè)/共81頁(yè)Affineandmetricreconstruction第75頁(yè)/共81頁(yè)Affineandmetricreconstruction2第76頁(yè)/共81頁(yè)