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A Brief Introduction Of PointCloud Registration MethodPoint Cloud Registration MethodPoint Cloud Registration With Target ControlQuaternion MethodIterative Closest Point(ICP) AlgorithmOutlineTwo point cloud sets of A andQ are conformations of the same points in different coordinate systemsRigid transformation:Objective function:F(T) = S + r-eJ2=min仪器科学与工程学疣(a ) Leica standard rotation plane target ( b ) Mensi plane target仪器科学与工程学枕(a ) Leica standard rotation plane target ( b ) Mensi plane target仪器科学与工程学枕(a ) Leica standard rotation plane target ( b ) Mensi plane target(d ) Mensi plane target(c) FARO standard plane targetFigure 1 Different kinds of plane target仪器科学与工程学枕06 spatial similarity transformation parameters 3 angle elements: x 3、3 translation elements: AXs ay. azAdjustment model:仪器科学与工程学枕0仪器科学与工程学枕0OrXYzba2a3 X Ay62b3y+AYc2c3zMBAZa仪器科学与工程学枕0仪器科学与工程学枕0 Y -AY, AZ,x,y,z)z = (0 匕 AX, AK, AZ, x, y. z)Rotation matrix:cos a sina01 cos PR = sin acos a1J Lsin 00 sin B卩 010 IO cos y0cos p 1L0 sinysinycosy(Ad2 c& coscosAT-sinsiivysinrb2 b3 =coswsirMrcl c2 c3 sincosAr+cossiiKysinr-cossi iw_sin0si ntocos*COStDCOSC-sinsinr+cosincxosr-sincoso_sitkCOSCOStt)仪器科学与工程学枕0X=(cos0cos*r_sin0$inQsin K)x_(cos0sin K+sin 0sin qcos 切一 (sin 0cosq)z+AYY=(cos & sin r)x+(cos o cos K)y - (sin qjI)z+Z=(sin 0COSK+8S 0sin兀+(-sin 0sin k+cos/sin ecos K)y+(8S0COS妙z+4Z仪器科学与工程学枕The expansion of Taylors formula:f =扎 + - dAy+d/SZ 诚 d& dK dX dY 5AZError Equation:卫L/AX+卫L/AY+西 dAZ+竺卯+e+色-45AX 3AY 5AZ 30 do) 泳vv 二空KAX + dY 十空NAZ + ddodK-l ySAXDAYSAZ诃deodKyv = cfAX + -Fsincos dKdfcdKSuppose that:lx=X-X、a a2 a3r Xl=r-AT_Ar，Yl=b b2 b3yl=Z_AZ-ZZz1 cl c2 c3 z 仪器科学与工程学疣XError equation matrix:dX如100-z0-厂XdZ=0100ZXVT001X、Y90 da)Jdie !yGravity-centra lize:dX 如 dAZdo) d/c仪器科学与工程学枕10仪器科学与工程学枕N pairs of corresponding points:100- Z0一乙7 JV/I0100如/刃0010JAZ “=dX 100- Z0-Y.d(pJ0100daI.001X0dK kJOrder:仪器科学与工程学枕 Vxl10 00 1 0叫】0 0 1,B =1 0 00 1 00 0 10-厂dtXJdhYJY0dhZJ,X =d人,L = 0dpJd(b0dK kJ仪器科学与工程学枕1. Point Cloud Registration With Target ControlError equation:V=BX-LAccording to Adjustment of indirect observations, vTpv = min(P is unit weight matrix)Solution of the normal eauation:x=(btb)bYor: X = d& d匕 dLZf g dwf dkT1. Point Cloud Registration With Target ControlNew approximate value:Iteration:AX严必+d% 人丫严乂+吗 AZ =AZo + dAZ 0i =0o+d0】K、= K+dK0 = (0o+d0)+ dc2)+ ); s =(吗 + ) + d)+ ); k = (r0 + dg)+ 加”);AX = (* + dAX J + JAY2 +);AY = (A/o + dAYJ + 时2 +)；AZ = (AZ。+ dAZ J + dZ2 +)；Finally we get the values of parameter:=Translation matrix:4丫 =比-盹,片Conclusions仪器科学与工程学疣18
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