Where: t has the same or similar relational attribution as 
s. Indeed, F(t) is the set which can label t labeling 
relation subset. The practical meaning of expression | s 
|>| t | is that some units of object may be lost, because of 
occluding. So the number of label relational subset 
which is labeled for units can be even more. 
Define o(u) to express the set of unit relational subset 
that include unit u, that is : 
o(u)={ teT,| teU} (3) 
Then: 
H(u- no^ (VS) (4) 
tew(u) seF(t) 
Where: H;(u) is the set of that can give u label according 
to constraint j. Obviously, we hope that the relational 
sub-isomorphism searched can meet all K relations. So 
the unit-label table H finally should be: 
k 
H(u») ~ Hj) ueU j=1...k (5) 
j=1 
3.2 The trimming algorithm using one to one 
correspondence 
Assume that U,L are unit set and label set, respectively, 
and we have j units (u,,uz....u;) C U, and that H(u;) 
CL'cL, and | L' | -J. It means that those j labels can be 
labeled for the J units, and other units can not be labeled 
by those labels. 
As to the subset (U,, L,, ), Where: U, c U, |U|=n, L,cL, 
| L4 [*m. for every u, cU, and H(u) c L, , we can get the 
conclusion as: 
l. if m<n, then the relational sub--isomorphism is 
not exist. It means that a label can not label for more 
than two units, and the one to one correspondence is not 
exist. 
2. if m>n, do not trimming. 
444 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
3. if m=n, the trimming algorithm can be defined as: 
m H(u)-( le H(u)] IeL,, if uieU,) (6) 
and 
mH={n Hw) } i=12M (7) 
Where: u;c U. 
The trimming algorithm is iterative to execute for H, 
until the following equation is valid. 
Nı “= mi ‘H (8) 
Usually, we begin the trimming processing from the 
subset which has the least units. 
For the same principle, as to the relational sub- 
isomorphism, the correspondence of relational subset is 
also the one to one correspondence. So the ; trimming 
algorithm can also be applied for the trimming of 
relation subset tables. 
3.3 Trimming algorithm using the correspondence 
between relational subset and unit-label table 
In the procedure of making unit-label table, relational 
subset and unit-label table are acting each other. The 
correspondence between the relational subset and the 
unit-label table can help us to trim unit-label table. 
Assume that: We have got a unit-label table H;(u) based 
on the constraint relation T; and subset (U,L,) is 
existing, where: U, cU,Ln c L. It means that the n 
labels should be labeled to the n units, and other units 
can not be labeled to those labels. The correspondence 
also exists between other unit-label table H;(u)and 
relational subset T;. 
If unit-relation subset t and label--relation subset si are 
exited to the constraint relation Ti, define Q(u) expressed 
unit-relation subset including unit u,, u € U, and define 
f(I) expressed label relational subset including 11, 1 € L, , 
Then define trimming algorithm n, as: 
      
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