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Fig. 4.2. Final state of the region growing by layers. 
The edge segment pixels are shown in gray. The 
labels surrounding the edge segments are the layer 
indices. The bold lines are borderlines between edge 
regions. Next neighbours are A-B, A-E, B-C, B-D, 
B-E, C-D and D-E. 
which does not, is solved by evaluating the cost of the 
integration of the pixel in question into the edge-support 
region. 
Relational parameters give information about the 
neighbourhood relations between an edge and adjacent 
edges. They have either topologic or geometric content. 
Relational parameters are determined by the next- 
neighbour relations of the edge segments. 
4.2.1 Evaluation of Edge-Support Regions 
The edge-segment pixels as well as the pixels in the 
vicinity of an edge segment form the edge-support region 
which characterizes an edge. The edge-support property 
of pixels has to be determined efficiently. Here, the 
arbitrary decision was made that only pixels belonging to 
an edge region established during the generation of the 
RAG can be members of the edge-support region. This 
enables us to establish the edge-support regions along 
with the RAG. Each pixel that is integrated into an edge 
region is tested for membership in the edge-support 
region. This is done by a cost evaluation similar to the 
minimum-cost search conducted during the generation of 
edge segments. If the cost of integration is less than a 
user-defined threshold, the pixel will be regarded as an 
edge-support pixel and will take part in a statistical 
evaluation for the determination of descriptive edge 
parameters. 
The evaluated cost components are 
l. the difference Og of the gradient direction of the 
pixel in question and the average of the eight 
neighbouring pixels, 
2. the difference Ôgs in gradient direction between the 
pixel evaluated and the closest pixel of the edge 
segment (chain), 
3. the difference Aj; in gradient magnitude between 
the pixel in question and the closest pixel of the edge 
segment, 
4. the distance d of the pixel from the closest pixel of 
the edge segment. 
The fourth cost component is not self-explanatory. It was 
introduced as a simple way of keeping the edge support 
region limited to the immediate vicinity of the edge 
310 
segment. Otherwise, the edge-support regions are often 
fragmented and partially unconnected with the edge 
segment. 
The cost is computed according to 
C = Cg + Cgs + Cms + Ca (4.1), 
where 
Ces = 100 * Ögs (4.3), 
Ög, Ögs in radians, 
Cms = Âms (4.4), 
Ams: difference in gradient magnitude in 
percent of the gradient magnitude of p, , 
C4 2 Ax? + Ay? (4.5), 
Ax, Ay: x-, y-difference between pixel and 
closest pixel of the segment chain. 
Although the distance component c, initially appears to be 
odd, it proved to be very useful as it is neglegibly small 
for short distances, but imposes a heavy influence on the 
cost of pixels far away from the edge segment. 
The descriptive edge parameters derived from the 
edge-support regions are 
l. maximum brightness, 
minimum brightness, 
contrast (maximum - minimum brightness), 
width (support region size / segment length), 
steepness (contrast / width), 
An Miss N 
average brightness in the edge-support region. 
For reasons of completeness, the other descriptive 
edge parameters are also listed here, namely: 
l. segment length (derived during edge-streak 
generation and corner detection), 
2. segment direction (direction from beginning to 
end of a segment), 
3. segment curvature (derived during corner 
detection). 
4.2.2 Parameterization of Neighbourhood 
Relations 
The relational parameters of the edge description 
are determined when the next neighbourhood of two edge 
segments is detected as the RAG is generated. The 
relational parameters are 
1. the closest distance between two pixels of the 
segment chains (i.e. the layer index), 
2. direction from the center of the chain to the 
center of the neighbouring chain, 
3.  perpendicularity, 
4.  parallelity, 
5. collinearity (This property is not detected 
precisely. If the edge segments belong to the 
same edge streak, they are assumed to be 
"collinear" for matching purposes.), 
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