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Published in Philip A. Laplante, Comprehensive Dictionary of Electrical Engineering, 2018
projective invariant projective invariant a measure that is independent of the distance and direction from which a particular class of object is viewed, under perspective projection. The cross-ratio is an important type of projective invariant, which is constant for four collinear points viewed under perspective projection from anywhere in space. Projective invariants are important in helping with egomotion (e.g., automatic guidance of a vehicle) and for initiating the process of object recognition in 3-D scenes. PROM See programmable read-only memory, Pockels readout optical modulator.
P
Published in Phillip A. Laplante, Dictionary of Computer Science, Engineering, and Technology, 2017
projective invariant a measure that is independent of the distance and direction from which a particular class of object is viewed, under perspective projection. The cross-ratio is an important type of projective invariant, which is constant for four collinear points viewed under perspective projection from anywhere in space. Projective invariants are important in helping with egomotion (e.g., automatic guidance of a vehicle) and for initiating the process of object recognition in 3D scenes.
Camera calibration method based on circular array calibration board
Published in Systems Science & Control Engineering, 2023
Haifeng Chen, Jinlei Zhuang, Bingyou Liu, Lichao Wang, Luxian Zhang
Particularly, when , the cross ratio is called the harmonic ratio, and the four collinear points, , , , and , are called harmonic conjugates. If point is the midpoint of and point among the four collinear points satisfying the harmonic ratio is an infinite point in the direction of the straight line where points and are located, then the four collinear points, , , , and , are harmonically conjugated. Thus, , and can be expressed as. If the four collinear points, , , , and , are harmonically conjugated, then there is . When the four collinear points , , , and are harmonically conjugated, there is .
A static and fast calibration method for line scan camera based on cross-ratio invariance
Published in Journal of Modern Optics, 2022
Shuaipeng Yuan, Dexue Bi, Zexiao Li, Ning Yan, Xiaodong Zhang
Cross-ratio invariance is a significant character in projection geometry. As illustrated in Figure 6, the X coordinates of pattern plane points Pi (i = 1, 3, 5, … , N−1) is known already. Their corresponding image point u can be obtained through image processing. According to cross-ratio invariance, the cross-ratio (CR) is expressed as, where xj, xj+1, xj+2, xj+4 (j = 1, 3, … , N−5) are X coordinates of intersection points Pj, Pj+2, Pj+4, and xj, xj+2, xj+4 are known, while uj, uj+1, uj+2, uj+4, are their corresponding image coordinates is established. Hence the X coordinate of point Pj+1 using Equations (9) and (10) can be calculated. Moreover, Pj+1 is the intersection point between line L and hypotenuse. Based on Equation (10), coordinate xj+1 of point Pj+1 is obtained by, where p = (xj+2−xj)/(xj+4−xj), then we substitute xj+1 into li: y = −k1(x−ia), we can obtain the coordinates (xj+1, yj+1) of point Pj+1 in pattern plane coordinate system (O'w-X'wY'wZ'w), as shown in Figure 7).