Sub-camera calibration of a Penta-camera

Abstract

Penta cameras consisting of a nadir and four inclined cameras are becoming more and more popular, having the advantage of imaging also facades in built up areas from four directions. Such system cameras require a boresight calibration of the geometric relation of the cameras to each other, but also a calibration of the sub-cameras. Based on data sets of the ISPRS/EuroSDR benchmark for multi platform photogrammetry the inner orientation of the used IGI Penta DigiCAM has been analyzed. The required image coordinates of the blocks Dortmund and Zeche Zollern have been determined by Pix4Dmapper and have been independently adjusted and analyzed by program system BLUH. With 4.1 million image points in 314 images respectively 3.9 million image points in 248 images a dense matching was provided by Pix4Dmapper. With up to 19 respectively 29 images per object point the images are well connected, nevertheless the high number of images per object point are concentrated to the block centres while the inclined images outside the block centre are satisfying but not very strongly connected. This leads to very high values for the Student test (T-test) of the finally used additional parameters or in other words, additional parameters are highly significant. The estimated radial symmetric distortion of the nadir sub-camera corresponds to the laboratory calibration of IGI, but there are still radial symmetric distortions also for the inclined cameras with a size exceeding 5μm even if mentioned as negligible based on the laboratory calibration. Radial and tangential effects of the image corners are limited but still available. Remarkable angular affine systematic image errors can be seen especially in the block Zeche Zollern. Such deformations are unusual for digital matrix cameras, but it can be caused by the correlation between inner and exterior orientation if only parallel flight lines are used. With exception of the angular affinity the systematic image errors for corresponding cameras of both blocks have the same trend, but as usual for block adjustments with self calibration, they still show significant differences. Based on the very high number of image points the remaining image residuals can be safely determined by overlaying and averaging the image residuals corresponding to their image coordinates. The size of the systematic image errors, not covered by the used additional parameters, is in the range of a square mean of 0.1 pixels corresponding to 0.6μm. They are not the same for both blocks, but show some similarities for corresponding cameras. In general the bundle block adjustment with a satisfying set of additional parameters, checked by remaining systematic errors, is required for use of the whole geometric potential of the penta camera. Especially for object points on facades, often only in two images and taken with a limited base length, the correct handling of systematic image errors is important. At least in the analyzed data sets the self calibration of sub-cameras by bundle block adjustment suffers from the correlation of the inner to the exterior calibration due to missing crossing flight directions. As usual, the systematic image errors differ from block to block even without the influence of the correlation to the exterior orientation.