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Homography Estimation - Computer Science

ComputerVisionICSE252A,Winter2007 DavidKriegmanHomography Estimation , wecanwritethetransformationofpointsin3 Dfromcamera1 tocamera2 as:X2=HX1X1;X22R3(1)Intheimageplanes,usi nghomogeneouscoordinates,wehave 1x1=X1; 2x2=X2;therefore 2x2=H 1x1(2)Thismeansthatx2is equaltoHx1uptoa scale(duetouniversalscaleambiguity).Note thatx2 Hx1is it is knownthatsomepointsalllieina planeinanimage1, theimagecanberecti EstimationTo estimateH, westartfromtheequationx2 Hx1. Writtenelementbyelement,inhomogenouscoor dinateswegetthefollowingconstraint:24x2y 2z235=24H11H12H13H21H22H23H31H32H333524x 1y1z135,x2=Hx1(3)Ininhomogenouscoordinat es(x02=x2=z2andy02=y2=z2),x02=H11x1+H12y 1+H13z1H31x1+H32y1+H33z1(4)y02=H21x1+H22 y1+H23z1H31x1+H32y1+H33z1(5)Withoutlosso fgeneralit

Computer Vision I CSE 252A, Winter 2007 David Kriegman Homography Estimation 1. From 3D to 2D Coordinates Under homography, we can write the transformation of points in 3D from camera 1 to camera 2 as: X2 = HX1 X1;X2 2 R 3 (1) In the image planes, using homogeneous coordinates, we have

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