1.2 General remarks on bundle block adjustment

This manual describes and explains the mathematic contexts of bundle adjustments being of importance in BINGO, including all necessary details. A general introduction into the method of bundle adjustment with marks for useful exposure layouts and the distribution of control points or other relevant information is given in photogrammetric text books.

Since BINGO computes the standard deviations of all unknowns and the reliability of observations, the user is given precise information on the suitability of the selected photo layout by the program.

Some general remarks on the bundle block adjustment are in order, however. These remarks will hardly be found in text books.

The symmetric distribution of at least 9 tie points per photograph, shown in photogrammetric text books, must be regarded as the absolutely lowest limit for bundle block adjustment. When using such an arrangement of points, observation errors are difficult to detect. Wrong measurements cannot be eliminated without adversely affecting the block geometry. Additional measurements will be necessary. If 15 to 25 points are measured for each photo, however, stabile block geometry is achieved. Wrong observations can then be easily detected and can be eliminated. For automatic tie-point matching about 50 points per photo provide a good and stabile solution. More than 100 points per photo are not really recommended. They will just increase the computation time and the time to filter faulty measurements.

If the photographs are strongly tied together, individual gross errors cannot easily cause the block adjustment to diverge, as can happen if the ties are weak. Also, small gross errors have much less influence on the adjusted unknowns. Economics also play a role, however, and we recommend in case of manual measurement at least 15 points for each photograph.

On the other hand, even a photograph with as few as four points adds to the redundancy of the block if these four points are reliably defined by other observations in the block. Blocks with high overlap (e.g. 80% forward overlap and 60% side lap) may contain rather fewer points per photograph if dictated by economics. Good ties are always the best to ensure a smooth and accurate block adjustment, however.

With the automatic measurement of tie points, it must be taken into account that with 100 or more measurements per photograph the influence of control points, GPS and IMU data on the adjustment result is greatly reduced. It is recommended not to substantially exceed the number of 50 measurements per photograph. Great care must be taken to ensure that these points are then measured in all photographs in which they appear.

The average number of points per photograph will decrease at the edges of the block, which may cause a loss of accuracy towards the edges. Therefore, the bundle block covered by tie points should exceed the size of the object at the block edges by one base length. Control points must then be arranged at the edges of the object to be measured.

The measured points should be distributed across the photograph as uniformly as possible. Some authors recommend increasing the density of points, at the edges of the photographs. This suggestion is reasonable for aerial photographs only if these points can then be measured in more photographs. One must bear in mind that the accuracy of measurements at the edges of the photographs is lower than that of the inner area /Kruck 1985/. If this effect is taken into account, the redundancy (see Section 2.3.1) of photo measurements for aerial photographs is nearly constant over the entire photograph.

If, instead of single tie points, groups of two or three points each are used in aerial photographs to improve accuracy, the points within a group should be at least 5 mm, better 10 mm (related to an aerial photo 230mm by 230mm), distant from each other. This separation is necessary because photo coordinates of points which are very close to each other are strongly correlated and this correlation cannot be considered during adjustment.

No detailed investigations are available yet for the smaller photo formats which are normally used in terrestrial photogrammetry. From experience, a distance of 5 mm between points is considered fully sufficient, however. Another possibility to increase accuracy is to take several photographs from one station. Then the exposure directions of each photograph should vary slightly in order to achieve a difference of approximately 5 mm in photo coordinates.

Control points, or points integrated in a geodetic network to strengthen the block, should be measured in at least three photographs. Otherwise, no check of measurements is possible. In principle, this requirement is valid for all points which take part in the adjustment, as points which are defined in only two photos by stereoscopic measurement of photo coordinates are unchecked. This remark applies even if the redundancies of the photo measurements should indicate controllability. This apparent controllability results only because correlation of the photo measurements has been neglected.

We emphasise in case of analogue images the special importance of measurement and numbering of fiducial marks. For details, see Section 4.1. If the fiducial marks have been correctly numbered the angles κ in aerial photos must differ by 200 gon for reverse flight directions (see Fig. 5.7-2).