Rob Reeves 
  
pixel and DCT domain algorithms is the method by which the partial derivatives and their products are calculated for the 
least squares adjustment A matrix. In the pixel domain, the first difference is used. In the transform domain, the method 
effectively reconstructs the symmetrically extended continuous derivative, and samples it at the appropriate points. We 
conclude that this difference in the way derivative estimates are calculated is a significant factor in the improved matching 
quality of the DCT domain algorithm. 
8 SUMMARY AND CONCLUSIONS 
A hybrid least squares image matching algorithm was proposed, that performed least squares matching in the transform 
domain, but resampled between iterations in the pixel domain. Experiments were conducted to compare this algorithm 
with an algorithm operating completely in the pixel domain. There were two major differences between the algorithm, 
apart from the domain used for the least squares adjustment. These were a window side two pixels smaller in the pixel 
domain, and a difference in the method used to estimate the sampled partial derivatives used in the construction of the least 
squares adjustment A matrix. Since the energy compacting property of the DCT concentrates the signal energy into the 
low frequency DCT coefficients, it was proposed to match in the DCT domain with only low frequency DCT coefficients, 
The size of the A matrix could then be significantly reduced, without discarding any significant signal structure important 
for matching, and hence maintaining the quality of the matching process. Since the time taken to match is dependent 
on the size of the A matrix, it was hypothesized that this could be used to increase matching speed. While there was 
no improvement in matching speed for an 8 x 8 match window, the parameters which measured match quality, (the 
number of converging windows, and the mean and standard deviation of the disparity errors), were comparable or showed 
improvement in the transform domain when about 50% of the DCT coefficients were used in the matching process. 
For 16 x 16 and 32 x 32 windows, there were useful gains in matching speed, while the other measures of matching 
quality were comparable or better. The optimum percentage of DCT coefficients for these window sizes were 20% and 
10% respectively. The approach also incorporates derivative estimates that result in better accuracy than can be achieved 
using the first differences of our pixel domain approach. In addition, our results suggest that neglecting the higher order 
DCT coefficients, equivalent to low pass filtering, may increase the number of converging match windows in areas with 
repetitive regular texture. 
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768 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 
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