When looking at the average of the slope values that were used as thresholds (Figures 7 and 8), one can see that the window size has an effect on the values since all the values from the 3 x 3 are lower then those from 5 x 5 and 7 x 7; these two are however resulting in very similar values. Also the SA seems to have a limited effect on the slope values for landscape with no SA and a difference between regional averages equal to 2: when the window is kept constant, the changes are very subtle following changes in SA. With a difference between regional average of 10, SA value influences the slope value when comparing the 3 x 3 windows. The difference in regional average influences only the filtering from 3 x 3 windows; the values obtain for 5 x 5 and 7 x 7 are almost the same between the two differences. From the 3 x 3 filtering, the slope values are increased when the difference between the regional averages is higher. Globally, one can state that the slope values used as thresholds are sensitive to a global variation of the pixel values. The local variability (i.e., clusters created by the SA) does not have an impact as important as the difference in regional averages.

Unlike the slope values, the number of edge pixels (BEs) that were correctly identified is very sensitive to all the different conditions and filters (Figure 9 and 10). With the exception of the filtering with a 5 x 5 on the landscape with high SA and a difference between regional averages of 2, the effect of the window size is constant: passing from the 3 x 3 to a 5 x 5, the number of BEs correctly identified (BECI) decreases but increases to a higher value than the 3 x 3 when using a 7 x 7. This could indicate that the 5 x 5 scale is the less appropriate for that type of analysis. One can also see clearly the effect of the SA that, by creating small patches within each region, creates other edges that cam be picked up as BEs by the Laplacian filter. Generally, the more SA there is in a landscape, the less BECI there is. This influence is even stronger when the difference between regional averages is equal to 2 since a higher difference will limits the effect of edges from small patches; the fact that the two regions are more different, the boundary is more easily found.

The computation of average distances of BEs from all the different landscapes intended to confirm the results obtained by the crosstabulation (i.e., BECI). The Figures 11 and 12 show that roughly, the trends observed with the BECI are found in the distance of BEs from the true boundary. That is the value of SA has an influence by creating other boundaries and thus, to move away the BEs detected by the filter from the true boundary (this effect being more obvious with a difference between regional of 10). One can also see the effect on the window size (same as BECI) and the influence of the difference in regional averages that, again, plays a role by defining more or less clearly the two regions so that the boundary is more easily found when the difference is high (i.e., average distance from the true boundary is lower); this effect is especially clear when there is no SA in the landscape.

Following this experiment one can conclude that it is very important to define correctly the window size of a filter. This paper has shown different results when the window size was changing but also when the statistical parameters were different. Since the statistical properties of a landscape seem to have an impact on the boundary recognition using Laplacian edge-enhancement filter, further research can be done on other techniques for edge detection.