the same scene region, although they are divided over two 
image regions. Since the predictor will always choose the 
smallest t-score, the assignment of pixels to one of the two 
regions will be done rather randomly, resulting in ragged 
boundaries which becomes apparently clear for region 11 in 
2 fig. 5. Further a noise pixel is recognized as a region (region 
6) and also a mixed pixels boundary (region 10). 
  
  
  
  
5.2.2 Stage II: The Merging Stage 
  
Stage I results in 12 regions, with 20 possible merging com- 
binations. First the t-score of all 20 combinations are com- 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
Fig. 3 A scene consisting of 6 regions. 
  
  
Since the smallest z-score belongs to region 8 and z = 
1.21 < 1.96, the critical value at the 95% confidence level, 
pixel (8, 11) is grouped with region 8. Now the predictor is 
shifted one pixel to the right to evaluate pixel (8,12) and 
so on. 
The prediction result is shown in fig. 5. Note that phan- 
tom regions are created, due to the dependency on the mov- 
ing direction of the predictor. The horizontal boundary 
between region 1 and 2 in fig. 3 causes that the predictor 
when crossing the left vertical boundary between 1 and 2, 
will not recognize to step into region 2. Consequentely, a 
new region is created. If the operator encounters the right 
vertical boundary between 1 and 2, it will cover pixels of 
  
  
  
  
  
  
10 
12 
  
11 
  
  
  
  
  
Fig. 5 Segmentation result after the Stage I. Region 5 
and 11 are typical a result of the scan dependency of the 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
predictor. 
3 42 |41 4243 43|82 808075 |83 81 | puted according Eq.( 10) and stored in a table (for simplic- 
ity of this example the mean value instead of the median 
4 80817978 79|82 82 | 79 | 79 |85 | 81 is used). Next we examine the entire table to trace the 
smallest t-score. If this value is smaller than the critical 
5 81 80576 78 |77|83 80 |81 |82 #79 | 75 value, than the two concerning regions are merged. Here 
6 84 |80 79 | 80 | 78 | 75 |80 | 78 | 775 81| 78 we list only the t-scores, which are accepted at the 95 % 
confidence level: 
7 85 8257876 )77| 89/80 81 82584 | 81 : 
Ry — R, | t-score | v | tgs, | merging 
8 719811 /13 | 9 84 | 81 79 | 85 1-2 1.50 7-1-2.37 yes 
3-5 1.63 11 | 2.20 yes 
9 11 (14 |13 | 14 [12 (12 [1083 | 83 | 86 | 79 3-11 0.30 | 10 | 223 yes 
10 |15| 12  10|60 | e1| 9 | 7 |77 | 81/82 | 7o Ses 1m be 
i Table 2 
a 6 7 8. 9:30 11 12 18 14.15 46 The combination 3-11 gives the smallest t-score (0.30). 
EN raster lines So, 3 and 11 are merged to form region 13, the new statis- 
tics of 13 are computed, and the table with t-scores is up- 
——- boundaries dated. The new region 13 has 2, 4, 5, 6, 7 and 8 as neigh- 
bours, so for these combinations new t-scores are computed. 
Again we examine the entire table to find the smallest t- 
score. This iterative process is repeated until no regions are 
merged anymore, which is here reached after 4 iterations. 
outline of the predictor 
pixel to be predicted 
  
Fig. 4 Subimage taken from the image of the scene in 
Fig. 3. The outline of the predictor is shown in the posi- 
tion to estimate the grey value of pizel (8,11). The four 
adjacent pizels that have received labels in previous steps 
(8,10), (7,10), (7,11) and (7,12) all belong to different re- 
gions. Hence, pizel (8,11) is predicted four time. 
The final regions after stage Ila are shown in Fig. 6. 
Regions smaller than 3 pixels are removed. Only region 
6 fulfils this condition. It is merged with its best fitting 
neighbour, region 16, forming the new region 17. 
Next the non-significant regions are removed at the 99% 
confidence level, i.e. zo; = 2.58, using v, = 1. Examples: 
797 
Rs : À = 4,64 = 1.41,z = 2.8 > 20 
Rio : À = 4,04 = 2.00,2 = 2,0 < zo