5 Model Generalization
91
Fig. 5.5. Generalization example in five steps from detailed to coarse (see Fig. 5.4 for the first
three steps)
5.3.1 Faces in the Topological GAP-tree
In the example above, in every step the least important object is removed and its
area is assigned to the most compatible neighbor (as in the original GAP-tree). In the
first step in Fig. 5.4, the least important object, face ‘6,’ has been added to its most
compatible neighbor, face ‘2.’ This process is continued until there is only one face
left. A little difference with the original GAP-tree is that a new id is assigned to the
face, which is enlarged, that is the more important face. The enlarged version of face
‘2’ (with face ‘6’) is called face ‘7,’ and faces ‘2’ and ‘6’ are not used at this detail
level. However, this face keeps its classification as indicated by the color of the faces.
In the example, face ‘7’ has the same classification as face ‘2,’ but the importance
of face ‘7’ is recomputed: as it becomes larger the importance increases from ‘0.4’
to ‘0.5.’ In the next step, face ‘1’ (the least important with importance value ‘0.3’)
is added to face ‘7’ (the most compatible neighbor) and the result is called face ‘8’
(and its importance raises from ‘0.5’ to ‘0.6’). Then face ‘5’ (with importance ‘0.35’)
is added to face ‘4’ (best neighbor) and the result is called face ‘9’ (with increased
importance from ‘0.5’ to ‘0.6’). This process continues until one large area object is
left, in the example this is face ‘11.’
From the conceptual point of view the generalization process for the faces is
the same as with the original, non-topological GAP-tree (Fig. 5.6). Quite different
91
Fig. 5.5. Generalization example in five steps from detailed to coarse (see Fig. 5.4 for the first
three steps)
5.3.1 Faces in the Topological GAP-tree
In the example above, in every step the least important object is removed and its
area is assigned to the most compatible neighbor (as in the original GAP-tree). In the
first step in Fig. 5.4, the least important object, face ‘6,’ has been added to its most
compatible neighbor, face ‘2.’ This process is continued until there is only one face
left. A little difference with the original GAP-tree is that a new id is assigned to the
face, which is enlarged, that is the more important face. The enlarged version of face
‘2’ (with face ‘6’) is called face ‘7,’ and faces ‘2’ and ‘6’ are not used at this detail
level. However, this face keeps its classification as indicated by the color of the faces.
In the example, face ‘7’ has the same classification as face ‘2,’ but the importance
of face ‘7’ is recomputed: as it becomes larger the importance increases from ‘0.4’
to ‘0.5.’ In the next step, face ‘1’ (the least important with importance value ‘0.3’)
is added to face ‘7’ (the most compatible neighbor) and the result is called face ‘8’
(and its importance raises from ‘0.5’ to ‘0.6’). Then face ‘5’ (with importance ‘0.35’)
is added to face ‘4’ (best neighbor) and the result is called face ‘9’ (with increased
importance from ‘0.5’ to ‘0.6’). This process continues until one large area object is
left, in the example this is face ‘11.’
From the conceptual point of view the generalization process for the faces is
the same as with the original, non-topological GAP-tree (Fig. 5.6). Quite different