Ανάπτυξη μοντέλου γεωμετρικής διόρθωσης δορυφορικών εικόνων υψηλής ανάλυσης

Abstract

The latest generations of high resolution satellites have the ability to acquire image stereopairs, with pixel size less than 0.5m, using pushbroom sensors, and to provide the necessary interior and exterior orientation parameters for photogrammetric processing. This research describes a new rigorous orientation model based on collinearity equations. The model uses the parameters of the interior orientation of the camera and orbital data for establishing a function ground-to-image. The advantages of this model are the use of less unknown parameters than in the normal use of collinearity equations and the use of three observation equations for each measured image point. The mathematical model is described and a selection of the necessary unknown parameters through statistical tests is made. The new model has been evaluated on stereopairs of ASTER-VNIR, Spot-V, EROS-B, QuickBird, WolrdView-2 and Pleiades-1B images; results using various set of parameters are given. It is shown that the ground point coordinate accuracies are adequate.An orbital parameter model can be applied to the pushbroom sensors in order to determine their exterior orientation parameters (Kratky, 1989; Baltsavias and Stallamann, 1996; Toutin, 2004; Poli, 2005). In this researchan orbital resection method has been developed to model continuous changing of position and attitude of the linear array sensor by finding the orbital parameters of the satellite during the period of its exposure of the image. A bundle adjustment has been implemented to determine these parameters using GCPs. The proposed model as mentioned above uses the collinearity equations combined with orbital and attitude data, in order to relate the points in the ECEF (Earth CEntered Fixed) object coordinate system to the corresponding points in the image coordinate system. The relationship between these two coordinate systems is based on:1. Three rotations, which are combinations of the Keplerian elements or the state vector, referred to the ECEF system, using the transformation parameters between the ECEF and ECI (Earth Centered Inertial) systems.2. Three rotations (ω, φ, κ) for the additional undefined rotations of the satellite at the time of imaging.3. The off-nadir viewing angles (α, β) of the linear array sensor, and4. the correction of scale for each object point, between the two coordinate systems, expressed as a second order surface polynomial.This model can be implemented on pushbroom sensors (linear array sensors) with narrow Field of View (FOV). The correction of scale, on account of narrow field of view and the significant difference between fly height of the satellite (approx. 450 km - 850 km) and ground elevation can be modelled by a second order surface polynomial. The benefit of this model is that the specific point scale has not been eliminated which allows the use of an additional equation (totally three equations are used, Fx, Fy, Fz) for each measured image point. As a consequence fewer GCPs for the calculation of the unknown’s coefficients are needed. Thus the exterior orientation for each linear array CCD may be figured out in order to establish a relationship between image points and ground objects.The benefit of this model is the usage of three observation equations, instead of two equations, for each measured image point, as the scale factor is not removed from the collinearity equations but is corrected by a second order polynomial surface dependant on dxi and dti quantities. The full model has 24 exterior orientation parameters that all have physical meaning. To estimate the value of these parameters at least eight (8) GCPs are required, in comparison to the usual model of the collinearity equations, where at least nine (9) GCPs are required for the calculation of 18 unknown parameters (Lee et al, 2000). The tests with simulation and real (spaceborn imagery) data proved that in most cases fewer parameters are necessary for the successful application of the proposed model. Images of QuickBird, WorldView-2 and Pleiades-1B satellites were used, whose pixel size (0.64 m, 0.5 m and 0.7 m respectively) covers almost the whole spectrum of the existing optical high resolution satellites.The impact of the terrain relief on the effectiveness of the proposed model and the accuracy of the calculated ground point coordinates were also checked. Areas with a broad variety of relief were selected and tested. It is proved that the number of the necessary unknown parameters depends on the terrain relief, the accuracy of the state vector (from GPS and IMU) that is boarded on satellite and the knowledge of the sensor’s interior orientation. Usually 14 parameters are used if the terrain is mountainous and if the precision of state vector is not very good, as in ASTER images. If the terrain is hilly and the orbital data are very precise the parameters can be reduced to 10. In order to find out which parameters affect the result of the proposed model, statistical criteria are implemented for the determination of the potential value of each unknown parameter of the model.

Οι τελευταίες γενιές των δορυφορικών συστημάτων παρατήρησης γης, υψηλής ανάλυσης, έχουν τη δυνατότητα να συλλέγουν εικόνες με μέγεθος εικονοψηφίδας, μικρότερο από 0.5 m. Οι κάμερες με τις οποίες είναι εφοδιασμένες τα δορυφορικά συστήματα είναι τύπου pushbroom και παρέχουν τα απαραίτητα στοιχεία του εσωτερικού και του εξωτερικού προσανατολισμού ώστε να είναι δυνατή η φωτογραμμετρική τους επεξεργασία. Στην παρούσα διατριβή προτείνεται ένα νέο αυστηρό γεωμετρικό μοντέλο για τη γεωαναφορά και προσανατολισμό των δορυφορικών εικόνων που έχουν ληφθεί από δορυφορικά συστήματα υψηλής ανάλυσης και βασίζεται στη συνθήκη συγγραμμικότητας. Χρησιμοποιεί τους παραμέτρους του εσωτερικού προσανατολισμού της κάμερας και τα τροχιακών δεδομένα που παρέχονται από τα δορυφορικά συστήματα με σκοπό να περιγράψει τη σχέση μεταξύ των αντικειμένων του εδάφους με αυτών που απεικονίζονται στις δορυφορικές εικόνες. Ο σκοπός του νέου προτεινόμενου μοντέλου είναι η χρήση λιγότερων φωτοσταθερών σημείων που απαιτείται για τη γεωαναφορά των εικόνων. Το προτεινόμενο μοντέλο έχει εφαρμοστεί και αξιολογηθεί σε στερεοσκοπικές δορυφορικές εικόνες ASTER - VNIR, SPΟΤ -V, EROS - B, QuickBird, WolrdView - 2 και εικόνες Pleiades - 1B και τα συμπεράσματα που προκύπτουν είναι ότι συνήθως αρκούν να μετρηθούν 5 φωτοσταθερά σημεία για να επιτευχθεί οριζοντιογραφική ακρίβεια καλλίτερη της μιας εικονοψηφίδας (sup-pixel). Η επίλυση του μοντέλου επιπρόσθετα χρησιμοποιεί συνθήκες δεσμεύσεων που υφίσταντο λόγω της γεωμετρίας των λήψεων των στερεοσκοπικών δορυφορικών εικόνων αυξάνοντας επιπλέον τον αριθμό παρατηρήσεων με συνέπεια να αυξάνεται η αξιοπιστία της επίλυσης του μοντέλου.