Scene planes ad homographies現(xiàn)場平面的單應(yīng)性

1、scene planes and homographieshomographies given the plane and vice versaproof of result 12.1example 12.2 a calibrated stereo riga calibrated stereo rig 2a calibrated stereo rig 3the homography induced by a plane fig.12.1fig 12.1 legendhomographies compatible with epipolar geometrytwo sets of 4 arbit

2、rary points from 2 imagesepipolar geometry define conditions on homographiescounting degrees of freedomcompatibility constraints fig.12.2 ae = h ecompatibility constraints 2 fig. 12.2 b ht le = le compatibility constraints 3 fig. 12.2 c x)h ( x x f ,elfig 12.2 compatibility constraintsresult 12.3hom

3、ographies are compatible with fundamental matrixcorollary 12.4result 12.513.6 plane induced homographies given f and image correspondences:(a) 3 points, (b) a line and a point12.2.1 three pointsthree pointsthe first (explicit) method is preferreddegenerate geometry for an implicit computation of the

4、 homography fig. 12.3fig. 12.3 legenddetermining the points xi is not necessary in first methodall that is importantresult 12.6proofproof 2consistency conditionsconsistency conditions 2algorithms 12.1 the optimal estimate of homography induced by a plane defined by 3 points12.2.2 a point and linea o

5、ne parameter family of homographiesfig 12.4 (a), (b)fig 12.4 legendresult 12.7proof of result 12.7proof of result 12.7 (2)proof of result 12.7 (3)result 12.8result 12.8 2geometric interpretation of the point map h(m) explore thea homography between corresponding line images fig. 12.5fig. 12.5 legend

6、degenerate homographiesdegenerate homographies 2a degenerate homography fig. 12.6fig. 12.6 legend12.3 computing f given the homography induced by a planeplane induced parallaxplane induced parallax fig. 12.7fig. 12.7 legendplane induced parallax 2 fig. 12.8fig. 12.8 legendplane induced parallax 2alg

7、orithm 12.2 computing f given the correspondence of 6 points, 4 of which are coplanarfundamental matrix from 6 points of which 4 are coplanar fig. 12.9fig. 12.9 legendprojective depthexample 12.9binary space partition: left and right imagesfig. 12.10 a,b(c ) points with known correspondence(d) a tri

8、plet of points selected from ( c ) and this triplet defines a plane fig. 12.10 c,d(e) points on one side of the plane (f) points on the other side fig. 12.10 e, ffig 12.10 legendtwo planestwo planes 2the action of the map h = h2-1 h1 on xfig. 12.11fig. 12.11 legendtwo planes 3up to this points, the results of this chapter have been entirely projective12.4 the infinite homography hinfthe infinite homography hinf 2the infinite homography hinf 3vanishing points and linesthe infinite homography hinf maps vanishing points between images fig. 12.12affine and metric reconstructionaffine and