The International Archives of the Photogrammetry. Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beiiing 2008 
1070 
simple. Both the gradient cross correlation method and the least 
squares matching method require good approximation or small 
pull-in range in order to find the minimisation points (1 to 2 
pixels in average from our experience). 
The particular formulation of the affine transformation in 
Equation 2-2 leads to useful insights into the image matching. 
Model-IV (shift only, not allowing scaling and rotation) is the 
worst model for matching all kind of point, which means that it 
is essential to choose an appropriate geometric transformation 
for certain kind of sub-pixel matching. 
For the matching of TM images, the scaling is about 0.83 
(25m/30m) and is the same for line and pixel, while the angle of 
rotation is common for line and pixel, at around 10°. 
For the matching of TM and MSS images, the angle of rotation 
is common for line and pixel, again at around 10°, while the 
scalings are different for line and pixel, agreeing closely with 
the expected values of 0.44 (25m/57m) and 0.32 (25m/79m), 
respectively. 
For matching of a stereo pair of high-resolution images, the 
flexibility of varying the scaling and/or orientation gives a 
better matching correlation. It could be valuable to use 
bootstrap procedures (Efron and Gong, 1983; Efron and 
Tibshirani, 1993) to establish the typical range of variation for 
the matching correlation for Model-I (i.e. confidence limits) 
against which to judge the adequacy of the simpler models. 
Limited experience of experimental DEM generation using the 
gradient cross correlation with line search suggests that 
incorporating a quadratic line search with Model-I often 
improves the convergence and leads to a higher matching 
correlation, but requires some additional computing time. 
Given that editing a DEM requires more operator intervention, 
it may be desirable to ensure the best possible match, at the 
expense of increased computing time. 
7. REFERENCES 
'' i 
Ackermann, F., 1984. Digital Image Correlation: Performance 
and Potential Application in Photogrammetry. 
Photogrammetric Record, 11, pp.429-439. 
Adby, P., R. and Dempster, M. A. H., 1974. Introduction to 
Optimisation Methods. Chapman and Hall, London. 
Chambers, J., M., 1977. Computational Methods for Data 
Analysis. Wiley, New York. 
Efron, B. and Gong, G., 1983. A Leisurely Look at the 
Bootstrap, the Jackknife, and Cross-validation. American 
Statistician, 37, 36-48. 
I 
Efron, B. and Tibshirani, R., J., 1993. An Introduction to the 
Bootstrap. Chapman and Hall, New York. 
Forstner, W., 1982. On the Geometric Precision of Digital 
Correlation. International Archives of Photogrammetry and 
Remote Sensing, Symposium Helsinki Commission III, 24-Part 
3, 176-189. 
Gruen, A., W., 1985. Adaptive Least Squares Correlation: a 
Powerful Image Matching Technique. South African Journal of 
Photogrammetry, Remote Sensing and Cartography, 14, 
pp.175-187. 
Norvelle, F., R., 1992. Stereo Correlation: Window Shaping 
and DEM Corrections. Photogrammetric Engineering and 
Remote Sensing, 58, No 1, pp. 111-115. 
Rosenholm, D., 1987. Least Squares Matching Method: Some 
Experimental Results. Photogrammetric Record, 12, pp.493- 
512. 
Zhaltov, S., Y. and Sibiryakov, A., V., 1997. Adaptive Subpixel 
Cross-correlation in a Point Correspondence Problem. In A. 
Gruen and H. Kahmen (eds.), Optical 3-D Measurement 
Techniques IV, Wichmann Verlag, Heidelberg, pp.86-95.