Relative and absolute orientation

Two cameras record a scene. In the case of the subsequent orientation, the position of the images in relation to one another is restored as they were at the time they were taken.

The relative and the absolute orientation are part of a two-step process from photogrammetry , which is used to extract 3D information from images.

In order to determine 3D information from camera images, at least two images of an object or a scene must be available. These two images have a certain position and orientation to one another during the recording. To reconstruct the recorded object, the position and orientation must be subsequently restored during the evaluation. One possible approach is the mutual relative and subsequent absolute orientation of the images.

Relative orientation

With the relative orientation, the position of the two images in space is restored to one another. After the relative orientation, the rays of homologous image points intersect in space - these are the two image points that a single object point generates in the two camera images. The coordinates that can be reconstructed from this have no relation to a higher-level coordinate system. The scale is freely selectable, i. H. the object size is not determined. A so-called “photogrammetric model” is available, the coordinate system is called the model coordinate system.

Absolute orientation

In the case of absolute orientation, the relatively oriented model is transformed into a higher-level coordinate system. The relationship between a coordinate of the model system (x, y and z) and the corresponding object coordinate (X, Y and Z) can be expressed as follows:

${\displaystyle {\begin{pmatrix}X\\Y\\Z\end{pmatrix}}={\begin{pmatrix}X_{u}\\Y_{u}\\Z_{u}\end{pmatrix}}+\mathbf {m} \cdot \mathbf {R} \cdot {\begin{pmatrix}x\\y\\z\end{pmatrix}}}$

${\displaystyle \mathbf {m} }$is the scale number and the matrix of the spatial rotation of the model system in relation to the object coordinate system. are the object coordinates of the origin of the model system. Scaling , translation and rotation are thus carried out. The equation thus represents a spatial similarity transformation (also called "spatial Helmert transformation"). ${\displaystyle \mathbf {R} }$ ${\displaystyle X_{u},Y_{u},Z_{u}}$

See also

• Inner and outer orientation