The plane metrology using a single uncalibrated image is studied in the paper, and three novel approaches are proposed. The first approach, namely key-line-based method, is an improvement over the widely used key-poin...The plane metrology using a single uncalibrated image is studied in the paper, and three novel approaches are proposed. The first approach, namely key-line-based method, is an improvement over the widely used key-point-based method, which uses line correspondences directly to compute homography between the world plane and its image so as to increase the computational accuracy. The second and third approaches are both based on a pair of vanishing points from two orthogonal sets of parallel lines in the space plane together with two unparallel referential distances, but the two methods deal with the problem in different ways. One is from the algebraic viewpoint which first maps the image points to an affine space via a transformation constructed from the vanishing points, and then computes the metric distance according to the relationship between the affine space and the Euclidean space, while the other is from the geometrical viewpoint based on the invariance of cross ratios. The second and third methods avoid the selection of control points and are widely applicable. In addition, a brief description on how to retrieve other geometrical entities 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 show that the first and the second approaches are of better precision and stronger robustness than the key-point-based one and the third one, since these two approaches are fundamentally based on line information.展开更多
It is very powerful for constructing nearly saturated factorial designs to characterize fractional factorial (FF) designs through their consulting designs when the consulting designs are small. Mukerjee and Fang emplo...It is very powerful for constructing nearly saturated factorial designs to characterize fractional factorial (FF) designs through their consulting designs when the consulting designs are small. Mukerjee and Fang employed the projective geometry theory to find the secondary wordlength pattern of a regular symmetrical fractional factorial split-plot (FFSP) design in terms of its complementary subset, but not in a unified form. In this paper, based on the connection between factorial design theory and coding theory, we obtain some general and unified combinatorial identities that relate the secondary wordlength pattern of a regular symmetrical or mixed-level FFSP design to that of its consulting design. According to these identities, we further establish some general and unified rules for identifying minimum secondary aberration, symmetrical or mixed-level, FFSP designs through their consulting designs.展开更多
文摘The plane metrology using a single uncalibrated image is studied in the paper, and three novel approaches are proposed. The first approach, namely key-line-based method, is an improvement over the widely used key-point-based method, which uses line correspondences directly to compute homography between the world plane and its image so as to increase the computational accuracy. The second and third approaches are both based on a pair of vanishing points from two orthogonal sets of parallel lines in the space plane together with two unparallel referential distances, but the two methods deal with the problem in different ways. One is from the algebraic viewpoint which first maps the image points to an affine space via a transformation constructed from the vanishing points, and then computes the metric distance according to the relationship between the affine space and the Euclidean space, while the other is from the geometrical viewpoint based on the invariance of cross ratios. The second and third methods avoid the selection of control points and are widely applicable. In addition, a brief description on how to retrieve other geometrical entities 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 show that the first and the second approaches are of better precision and stronger robustness than the key-point-based one and the third one, since these two approaches are fundamentally based on line information.
基金supported by the National Natural Science Foundation of China(Grant Nos.10231030&10571093)Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20050055038).
文摘It is very powerful for constructing nearly saturated factorial designs to characterize fractional factorial (FF) designs through their consulting designs when the consulting designs are small. Mukerjee and Fang employed the projective geometry theory to find the secondary wordlength pattern of a regular symmetrical fractional factorial split-plot (FFSP) design in terms of its complementary subset, but not in a unified form. In this paper, based on the connection between factorial design theory and coding theory, we obtain some general and unified combinatorial identities that relate the secondary wordlength pattern of a regular symmetrical or mixed-level FFSP design to that of its consulting design. According to these identities, we further establish some general and unified rules for identifying minimum secondary aberration, symmetrical or mixed-level, FFSP designs through their consulting designs.
