Analytical relationship between image and relative orientation in photogrammetry

All the rays with the same name in the image pair must satisfy the intersecting condition equation, that is, the coplanar condition equation of the rays with the same name. Using this conditional equation, the relative orientation elements of the image pair can be solved, and then the spatial coordinates of each model point can be calculated, and a single three-dimensional digital model can be established analytically. The coplanar principle of light with the same name is shown in Figure 2. The coplanar condition is expressed by a vector as:

or

Where the vector B=S 1S2 is the photographic baseline; BX, BY and BZ are the three components of the baseline B in the spatial auxiliary coordinate system with S 1 as the origin; R 1 and R2 are vectors respectively, and X 1, Y 1 and Z 1 are the coordinate values of the image point ι 1 in the auxiliary coordinate system with S 1 as the origin; X2, Y2 and Z2 are image points ι 2.

Coordinate values in an auxiliary coordinate system with S2 as the origin, and the corresponding axes of these two coordinate systems are parallel to each other.