Single View Based Measurement on Space Planes

The plane metrology using a single uncalibrated image is studied in thepaper, and three novel approaches are proposed. The first approach,namely key-line-based method, is an improvement over the widely usedkey-point-based method, which uses line correspondences directly tocompute homography between the world plane and its image so as toincrease the computational accuracy. The second and third approaches areboth based on a pair of vanishing points from two orthogonal sets ofparallel lines in the space plane together with two unparallelreferential distances, but the two methods deal with the problem indifferent ways. One is from the algebraic viewpoint whichfirst maps the image points to an affine space via a transformationconstructed from the vanishing points, and then computes the metricdistance according to the relationship between the affine space and theEuclidean space, while the other is from the geometrical viewpointbased on the invariance of cross ratios. The second and third methodsavoid the selection of control points and are widely applicable. Inaddition, a brief description on how to retrieve other geometricalentities on the space plane, such as distance from a point to a line,angle formed by two lines, etc., is also presented in the paper.Extensive experiments on simulated data as well as on real images showthat the first and the second approaches are of better precision andstronger robustness than the key-point-based one and the third one,since these two approaches are fundamentally based on line information.