Stereo Model Generation

Object points that appear in the overlap area of a stereopair mainly help in constituting a stereomodel. The mathematical calculation of 3D ground coordinates of points in the stereomodel by analytical photogrammetric techniques forms an analytical stereomodel. Theoretically, after constructing accurate exterior orientation elements of images, measurable stereo models can be created using model restoration, by which automatic surveying and mapping of terrain and objects can be done.

 

The steps involved in analytical stereo model generation are very similar to those which apply to single photo orthorectification. These steps are briefly reviewed below.

Inner/Interior Orientation – This has already been described.

Relative Orientation – After the individual photos used for the stereo model generation are separately oriented (inner orientation) in terms of the original camera model, it is necessary to orient them with respect to each other. In other words, before corresponding points in images are chosen, it is extremely important to determine the position and orientation of one camera relative to the other. This is the classic photogrammetric problem of relative orientation. Therefore, relative orientation determines the relative angular attitude and positional displacement between the photographs that existed when the photos were taken.

Thus the process of analytical relative orientation involves defining (assuming) certain elements of exterior orientation and calculating the remaining ones. If “n” points are used in analytical relative orientation, a system of “4n” equations is required (i.e. a single point gives 2 equations in a single photo, and hence in 2 photos we get 4 equations, so if n=1, number of equations = 4×1=4) in order to solve “4n-1” unknowns.

For each point in the left photo, since all the interior orientation parameters are known, their object space coordinates can be calculated using collinearity equations.

Absolute Orientation – This is the last step in stereo model generation. Absolute orientation enables the exposure station to be oriented relative to a ground based coordinate system. It is very similar to that of the process of absolute orientation of a single photograph. In this case, the coordinates of selected tie points are related to their 3D coordinates in a (real, earth based) ground coordinate system. A DEM is often used for providing the orientation reference points. For a small stereomodel such as that computed from one stereopair, analytical absolute orientation can be performed using a 3D conformal coordinate transformation. It needs a minimum of two horizontal and three vertical control points. Additional control points could create the problem of redundancy, enabling a least squares solution. (In this context, the horizontal control refers to the position of the point in object space, known with respect to a horizontal datum. Vertical control refers to the the elevation of the point known with respect to a vertical datum). Once the transformation parameters have been retrieved, they can be applied to the remaining stereomodel points for further computation. This gives the coordinates of all stereomodel points in the ground system.