Theory of aerial photogrammetry

The theme of aerial photogrammetry is to transform the central projection (aerial photograph) of the ground into the orthographic projection (topographic map). There are many ways to solve this problem. Graphic method, optical mechanics method (also known as simulation method) and analytical method. In each method, many specific methods can be subdivided, and each specific method has its own unique theory. Some of these concepts and theories are basic, and some have * * * characteristics, such as the internal and external orientation elements of a photo, the coordinate relationship between the image point and the ground point, the * * * line condition equation, the relative orientation of the image pair, the absolute orientation of the model and the principle of stereoscopic observation.

Internal orientation elements and external orientation elements of a photo.

The internal orientation element is used to determine the relative position between the rear node (image side) of the photographic objective and the photograph. It can be used to restore the photographic beam during photography. The internal orientation elements refer to the coordinate values (x0, у0) of the camera principal distance f and the orthogonal projection of the rear node of the camera objective in the frame coordinate system on the image plane. These values are obtained by identifying aerial cameras, so the internal orientation elements are always known. The data that determines the spatial position of the photographic beam during photography is called the external orientation element of the photograph or photography. The external orientation element has six numerical values, including three coordinate values Xs, Ys and Zs of the photography center S (Figure 2) in a certain spatial rectangular coordinate system and three angular orientation elements used to determine the spatial orientation of the photographic beam, such as φ, ω and K angles. These external orientation elements are defined for a model coordinate system O-XYZ. The X coordinate axis of the model coordinate system is roughly located in the direction of the photographic baseline, and the Z coordinate axis is roughly consistent with the elevation direction of the ground point. The three-dimensional model established in the model coordinate system must go through the process of absolute orientation to obtain the correct orientation of the three-dimensional model.

Image point coordinate conversion formula

In fig. 2, the coordinates of the image point ι with the shooting center S as the origin and the main shooting optical axis Z as the coordinate axis in the image space coordinate system (S-xуz) are x ι, у, z ι =-f, and then an auxiliary coordinate system (S-uvw) is established with S as the origin, in which the three coordinate axes U, V and W are respectively If the coordinates of a point in the auxiliary coordinate system are set to u, v and w, the transformation relationship is:

R is a rotation matrix, which consists of cosine of the angle between the corresponding coordinate axes of the image space coordinate system and the auxiliary coordinate system (called direction cosine), and these direction cosines are all functions of the three angular orientation elements of the photo. This is an important basic formula, because there are many theoretical formulas or operational formulas that are further evolved on this basis. For example, the "* * line condition equation" widely used in analytical photogrammetry is further evolved according to its inverse formula.

relative bearing

The process of determining the relationship between photo pairs. The simulation method of relative orientation is carried out on stereo mapping. Its theoretical basis is to make all lights with the same name intersect in pairs in space. When the lights with the same name do not intersect, the up-and-down parallax (generally expressed by Q) can be observed in the observation system of the instrument. The up-down parallax is the distance in the direction perpendicular to the photographic baseline when two rays with the same name do not intersect in space. At this time, this distance can be eliminated by slightly moving or rotating the projector in a straight line. Theoretically, as long as the up-and-down parallax can be eliminated at five properly distributed points at the same time, it is considered that the up-and-down parallax in this stereo image pair has been completely eliminated, thus completing the relative orientation and obtaining the stereo model. The analytical method of relative orientation is to measure the coordinates of each image point with the same name on the photo, for example, x 1 and у 1 on the left and x2 and у2 on the right. According to the * * * plane condition theory of the same name ray, the relationship between these measured values and relative orientation elements can be deduced. Theoretically, by measuring the coordinate values of five pairs of image points with the same name, five relative orientation elements of the pair of images can be solved. The vertical coordinate difference (у 1-у2) of the points with the same name on the left and right photos is also called up-down parallax, which is represented by the symbol Q.

Absolute direction of the model

In photogrammetry, the three-dimensional model established by relative orientation is often in the temporary or transitional model coordinate system, and the scale is arbitrary, so it must be converted into the ground survey coordinate system before mapping can be carried out. This transformation process is called absolute orientation. The mathematical basis of absolute orientation is three-dimensional linear similarity transformation, which has seven elements: three translation values of coordinate origin, three rotation values of three-dimensional model and 1 scale magnification.

Stereoscopic observation principle

The principle of stereoscopic observation is to establish artificial stereoscopic vision, that is, stereoscopic vision obtained by reflecting the parallax on the image pair as the physiological parallax of the human eye (Figure 3). There are three conditions for obtaining artificial stereo vision: ① taking two photos of the same scene from two different positions (two ends of a baseline) (called stereo image pair or image pair); ② Observe a photo in the image pair with both eyes; ③ When observing, the line connecting the image points with the same name on the image pair should be roughly parallel to the human eye baseline, and the distance between the same name points should generally be less than the eye baseline (or the expanded eye base distance). If two identical markers are placed on the same image point of the left and right photos respectively, a spatial scale can be added to the three-dimensional model during stereoscopic observation. In order to facilitate stereoscopic observation, some simple tools can be used, such as bridge stereoscope and reflective stereoscope. When two projectors are used to project the images of the left and right photos onto a bearing plane at the same time, the principle of complementary color or polarized light can be used for stereoscopic observation, and the measurement can be carried out through a mapping platform with a target.