Height Deviation and Constraint Condition

In the last section, the definitions of the two constraint conditions , range error and intersection angle was introduced. For simplicity the values of these two

constraint conditions are named constraint values . Here, it is of interest to know if

any relationship exists between the constraint values and height deviation. If it was the case, it is important to test whether this relationship is common for all data sets and therefore could be described by an unique function named constraint_height function. The ideal case for this c o n stra in tjieig h t function is a one-to-one correspondence, in other words, a certain given constraint value would lead to a particular height deviation. If the value is altered, the height deviation would also be influenced. Therefore, once a constraint value that could result in small height deviation is determined, say v, techniques could be employed to make the constraint values of all matching points equal to v, consequently obtaining greater DEM accuracy. Unfortunately, this is not possible in real practice as the relationship of the height deviation and constraint value is not unique. The above mentioned constraint value of V may only appear as an interval rather than a single value, and as a result, the strategy described earlier will not be so effective as expected. Instead, the effectiveness would be influenced by the width of the interval, such that the narrower the interval, the better the matching result would be obtained using the proposed method.

To facilitate the search for a relationship between the constraint value and height deviation, three sets of matching results were chosen from Chapter 7 for each stereo pair. These three sets included different types of data, including different PDL files and various number of image tiers, to check if the relationship is general, so that it is reliable and can be utilised. It should be noted here that for the same side stereo pair, the selection of three stereo pairs was not difficult since their matching results had no significant difference with respect to the DEM accuracy and coverage. For the opposite stereo pairs, in contrast, the selected data would have to cover varied height deviation in order to investigate the relationship more accurately. Thus, less number of image tiers were chosen for this opposite stereo pair and in total 9 data sets were selected as listed in Table 8.1.

SA OPl OP2

sa__grid32_tier8_l OP l_grid512_tier2_ 1 OP2 _grid512_tier2_l sa_grid32_tier8_2 OPl srid512 tier2 2 OP2_grid512_tier2_2 sa_grid32_tier6_l OP 1 _grid512_tier3_ 1 OP2_grid512_tier3_l Table 8.1; 9 data sets selected for testing the relationship of constraint values and

height deviation

After the selection had been completed, the matching points of different height deviation were appointed. In order to facilitate the establishment of this relationship, the whole range of height deviation (-1000m - l(X)Om) was divided into 9 intervals. These 9 intervals of height deviation and their corresponding constraint values for all nine data sets are listed in Table 8.2 ~ 8.7, where Table 8.2 ~ 8.4 shows the range error , while Table 8.5 ~ 8.7 specify the intersection angle. The parameters listed include the minimum, average and maximum constraint values .

It is observed that in Table 8.2 ~ 8.4 the average values of range error did not show any significant difference under a given height deviation for all three pairs. Even the largest difference did not exceed 6 m (-239.57m compared to -245.34m at height deviation 500m ~ 10(X)m, Table 8.4). Similarly, although variations did occur, the minimum and maximum values of range error in general, were very consistent. Comparing among these three pairs listed, 0P2 had the most variations. The same similarity in the intersection angle was obtained when comparing Table 8.5 ~ 8.7, such that for the opposite-side stereo pair, the average value were almost identical and the largest difference of minimum and maximum value did not exceed 0.02°. From Table 8.2 ~ 8.7, therefore, it was concluded that the two constraint values for a given interval of height deviation were almost identical. This finding encourages us to further investigate the possibility to use them to obtain greater DBM accuracy as suggested earlier.

For this purpose, one data set was chosen for each stereo pair, which were the sa_grid32_tier8_l for SA, OPl_grid512_tier2_l for O Pl and OP2_grid512_tier2_l for 0P2 respectively. In Fig. 8.3 ~ 8.5, the relationship between the average values

of range error and height deviation was represented in three pairs. For the same side

stereo pair, it is seen in Fig. 8.3 that range error decreased gradually from 13.54m to -31.47m as the height deviation increased from -1000m ~ -500m to 500m ~ 1000m. This trend was not observed for the OPl and 0P2 as can be seen in the Fig. 8.4 and 8.5. When plotting the intersection angle against DEM deviation, no significant

Chapter 8. Object Domain Approach

difference was observed under different height deviation (Fig. 8.6). In contrast, for O Pl and 0P2, the intersection angle is regularly increased as the height deviation increased from -1000 ~ -500 to 500 ~ 1000 (Fig. 8.7 & 8.8). These observations made from the above six figures provided preliminary evidence that the range erro r seemed a more suitable constraint condition for the same side, while the intersection angle was more for the opposite side. However, it would not be reliable to just consider the average values. Therefore, two other analyses were adopted to aid the finalisation of this study.