- 86 - 
from the list structure mentioned above. 
Lower Picture 
Figure 4. Procedure for generating intermediate points 
3.4 Process of grid unit 
Because making correspondence between contours is difficult, 
intermediate points are exploited in this research. Without the 
search of corresponding points between contour, faces filling a 
gap between adjacent slice images are successfully set as shown 
in the Figure 5 using intermediate points. 
Figure 5. Face extension for each unit grid 
3.5 Labeling 
There is the face that should be distinguished as shown in the 
Figure 6 when faces are dealt with grid unit. In other words it is 
a remaining portion obtained by removing both ‘AND portion’ 
and ‘Exception of OR portion’. We don't set up face on this 
portion. We have only to perform face tension particularly. 
Hand Information 
[Zkxception of OR Information! 
Figure 6. Areas in which face extension is 
3.6 Face tension algorithm 
The face tension is performed with respect to both grid unit and 
label unit. Tracing picture elements according to the direction 
of list structure, surfaces are set up as shown in the Figure 7. 
Because the direction of the face (normal) vector is the 
direction of the right screw as shown in the Figure 8, we define 
the list structure of the upper slice as the clockwise direction, 
and we define the list structure of the lower slice as the counter 
clockwise direction. This allows every surface to be set up 
smoothly. A twisted portion can be patched up without any 
problem. Further for a set of grids where only intermediate 
points exist, the direction of a face can be easily determined 
from relationship between the top and bottom image. 
• Upper Point 
O Intermediate Point 
O Lower Point 
Figure 7. Face extension for a unit grid 
3.7 Surface model generation 
Pasting the surface of all grids, a surface model of an object is 
generated as shown in the Figure 9. Because the model becomes 
a stair stepping when the intermediate point is constant, we 
specify the height of the intermediate point using the ratio with 
distance to the upper and lower slice image. Repeating this 
process over the consecutive pair of contours, a surface model 
is completed. 
Normal Vector 
Lower Edge 
Figure 8. The direction of the normal vector