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Error-free data sets are presented and their processing demonstrated.

The generation of error-free data sets can be done using two ways:

  • the complete synthetic generation or
  • the simulation of a data set based on real data sets ([1] [3]).

The main advantage of a simulation is the possibility to consider aspects of real acquisition situations which can not be considered within synthetic data.

The image-coordinates are as observations the basis for each bundle adjustment. Additionally known or approximate values for the interior and exterior orientations of the cameras, information of object space and possibly fixed point information are added to the bundle adjustment. Based on real data sets for camera calibration purposes error-free data sets are generated and analyzed.

Within the data generation process (following figure) the interior and exterior orientations as well as the object points are used as fixed information. The corresponding error-free image coordinates are calculated with respect to their visibility in the real single images, derived from image coordinate files. The calculations are based on the collinearity equations [5]. The interior orientation of the camera is introduced to the process with c, x0', y0' and equations for radial-symmetric distortion (balanced form) with the parameters A1, A2 and A3 and for tangential-asymmetric distortion with the parameters B1 and B2.



 diagram datageneration

In a following step of data generation variations of basic data sets can be considered, e.g. with instable interior orientation, measurement uncertainties, blunder…[2]).

3D data set



The used set of 3D data, a data set for camera calibration purposes, images a test range based on the German guideline VDI/VDE 2634. It is acquired with a Nikon D2X camera with a 24mm lens. 90 images from different camera positions, in different position heights and variously rolled through the camera axis are acquired. Real values for the interior orientation of the camera are available. The data set includes 164 3D object points. Based on this an error-free data set is calculated.

The following figures show the 3D data set in different views.
Red - camera positions
Yellow - image rays
Blue - 3D object points
3d 1

3d 2 3d 3

The simulated error-free data set was calculated with a commercial bundle adjustment program. The resulting parameter do not show any change to the ingoing parameters. Therefore the simulation process does work correct.



2D data set



The 2D data set is based on a bundle for camera calibration purposes of a 2D test range. The images are acquired with a Nikon D2X in combination with a 24mm lens. 22 images are taken from different camera positions and variously rolled through the camera axis. The test range covers 72 object points. Then again an error-free data set was generated.

The following figures show the 3D data set in different views. Red - camera positions
Yellow - image rays
Blue - 3D object points
2d 1

2d 2 2d 3

The simulated error-free data set was calculated with a commercial bundle adjustment program. The resulting parameter do not show any change to the ingoing parameters. Therefore the simulation process does work correct.

 

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