Fraser, Clive 
  
restitution of a stereo /RS-1C scene covering an area of approximately 25 x 25 km. This was achieved without the usual 
requirements associated with the collinearity equation approach utilising polynomials to model EO, namely the need for 
sensor calibration and satellite ephemeris data, and the requirement that careful attention be given to controlling parameter 
correlations and therefore parameter weighting. : 
4.4 An Affine Projection Model 
The final satellite triangulation approach to be discussed is a model based on affine as opposed to perspective projection. 
Under this approach, which is described in Okamoto et al. (1999) and Hattori et al. (2000), an initial transformation of the 
image from a perspective to an affine projection is first performed. A linear transformation from image to object space then 
follows, which depending on the particular affine model formulation adopted, may involve the modeling of coefficients as 
linear functions of time. Formulation of the affine model was motivated by a recognition that as the field of view of the 
linear array scanner becomes small, high correlations develop between EO parameters within a perspective projection since 
the narrow bundle of rays effectively approaches a parallel projection. It should be recalled that the field angle of the /konos 
sensor is less than 1?. 
The model for 3D analysis of line scanner imagery via a 2D affine model is given in the form (Okamoto et al., 1999) 
x, = DX+D,Y+D; Z (6) 
Ya =DX+DsY + DZ 
As mentioned, application of Eqs. 6 first requires an image conversion from central perspective (x,y:) to affine projection 
(X4y4), which although needing a prior knowledge of terrain height, approximate sensor position and look angle, is 
nevertheless reasonably insensitive to coarse initial estimates of both due to the iterative nature of the conversion (Okamoto 
et al., 1998). 
Practical implementation of the affine projection model has been performed using both stereo SPOT images and MOMS-2P 
imagery (forward- and backward-looking channels only). In one experiment, in the Kobe/Osaka test field in Japan, ground 
point triangulation accuracies to sub-pixel level, namely 6-8m, were obtained in planimetry and height (Okamoto at el., 
1999; Hattori et al. 2000) for a SPOT stereo pair under conditions of modest ground control point («10 points). A further 
test with a MOMS-2P stereo image pair over Bavaria also yielded ground point triangulation accuracies of better than 1 
pixel (18m), the RMS value at 50 checkpoints being 10-12m in planimetry and height. Given certain conditions, the *bundle 
adjustment' formulated using Eqs. 6 does not need to incorporate a linear variation function for the sensor EO parameters. 
In performing the bundle adjustment, attention to appropriate parameter weighting to enhance solution stability is usually 
warranted, though in the Kobe/Osaka test field, which covered 60 x 40 km and incorporated 130 check points, stable 
solutions were routinely obtained with as few as four control points. 
In spite of some theoretical shortcomings in the perspective to affine image conversion, and in spite of the modelling of 
coefficients D; in Eqs. 6 as time-invariant, the affine model has provided triangulation accuracies equivalent to and in some 
cases better than the central perspective model with multiple projection centres. Moreover, the method is equally applicable 
to along-track and cross-track stereo imaging configurations, and given the narrow view angle of high-resolution imaging 
satellites such as Jkonos, the affine approach may well be quite suited to the orientation of 1m resolution imagery. 
S. CONCLUDING REMARKS 
The aim of this paper has been effectively two-fold, firstly to highlight the metric potential of the new series of 1m resolution 
Earth observation satellites for cartographic product generation, and secondly to illustrate that moderately high ground point 
triangulation accuracies can be anticipated with 1m imagery through use of non-rigorous, though practical multi-image 
restitution models. The adoption of such models, rather than the rigorous collinearity equations with sensor orbital and 
attitude constraints, will become a necessity in situations where the camera model and precise ephemeris data are withheld 
from the user community. 
At this writing (February, 2000) we are only a month or so into full commercial sales of Zkonos imagery, and it is therefore 
not surprising that there is little experimental indication as yet of the true metric potential of 1m satellite imagery. 
  
458 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B7. Amsterdam 2000. 
  
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