視覚の幾何学3 カメラキャリブレーション

1 Rigid Body Motion Two views Xx 11 txRx 1122 Xx 22 babbaba 000;121323122131132332321321aaaaaabababa babababbbaaa 00 b)(abb)(aaba matrix form of cross product Geometric transformation ] with ]0| with t|[RE'pE'p'[IEEpptRpp' ] with ]0| with t|[RP'xP'x'[IPPxxtRxx' R : 3*3 rotation matrix t : 3*1 translation vector p p (Essential matrix ) p p ( ) TTyxyx)1,','(')1,,( with 0)](['ppRptpFrom geometry to algebra TRpp' TTRpTpT 'RpT RpTppTp '''0 Normal to the planeSlide credit: Kristen GraumanP2 R : 3*3 rotation matrix t : 3*1 translation vector p p (Essential matrix ) p p ( ) TTyxyx)1,','(')1,,( with 0)](['ppRptp RtEEpp'Rptp with 0)](['E (Essential matrix ) TTyxyx)1,','(')1,,( with 0)](['ppRptp RtEEpp' with 0 babba 000121323aaaaaa rank(E)=2 E t R

2 2カメラ間の姿勢と位置： • R : 3*3 rotation matrix • t : 3*1 translation vector pとp’が対応点同士なら： 即ち：同一平面内の三つのベクトルから二つのベクトルの外積と 残るもう一つのベクトルの内積は0となる エピポーラ方程式

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