1-1-3 
relations is combined into one measure, since the 
similarity of either numerical or symbolical attributes are 
judged by transition probability. Since the probability 
models are decided by the analysis of training values, it 
failed in dynamically evaluating the contribution from the 
matches with different probability distributions. In this 
research, we follows the formalism defined in Boyer and 
Kak, 1988; Vosselman, 1992. Extension can be founded in 
probabilistically evaluating the contributions from each 
corresponding primitive pair. Our matching method can be 
generalized as follows. 
1) Feature primitives 
Line segment is treated as the intrinsic structure of the 
image. It is represented using the group of image points 
surrounding it. Two kinds of attributes are defined. 
Geometric attributes include normal vector and 
orthogonal distance. They are obtained by doing linear 
regression on the group of points surrounded. Abstractive 
attributes stand for the reliabilities of parameter estimation 
of geometric attributes. It serves in dynamically evaluating 
the matches between corresponding primitives. 
2) Distance measure 
Distance measure is defined using conditional information 
of Z-lmages. Two components are evaluated, the matches 
between line segments and image points. 
3) Searching strategy 
Searching for the best match consists of two steps, 
coarse matching and fine adjustment. Coarse matching 
set an initial value, while in fine adjustment, a strength 
function is defined to lead to refine the matching. 
In the followings, we first discuss the reliability evaluation 
of parameter estimation in line segment extraction, then 
define the distance measure between Z-lmages. 
Searching strategy will be addressed subsequently. 
2.1.2 Reliability definition of line parameter estimation 
The reliability definitions in this research follow and 
subsequently extend the formalism of Kanatani, 1993. Let 
D:{r a \a = l,..., yvjbe a point measurement to line 
/:(n,d) with a standard error e. n, m and d are 
line normal, directional vector and orthogonal distance 
respectively. Suppose r a has its truth at r a , 
Ar a = r a -r a ~ N(0,o 2 ). Let l:(n,d) be the line 
parameters obtained by doing linear regression on D, A0 
be the small angle from n to n, Ad = d-d . Then it 
has, 
E[A6] = 0(£ 2 ) 
E[Ad] = 0(£ 2 ) 
v'[Ae]=^2l+o( £ 4 )=a„ 2 
U 
V[Ad]=?- + 0(e , ) = <J d 2 
Nv 
Where, 
[X^rJ] 2 
v = l--£± 
W^(m,rJ 2 
a=l 
u = A^(m,r a ) 2 -[^(m,r a )] 2 
a=l a=l 
(1) 
(2) 
(3) 
(4) 
(5) 
(6) 
Reliability of parameter estimation on n and d is evaluated 
by <j n and a d respectively. A large variance of 
AO and Ad stands for poor parameter estimation of n 
and d. 
2.1.3 Distance measure 
Let D=(P,R) be a structural description of Z-lmage. P 
stands for the group of image points, while R is the set of 
line segments extracted. Given two structural descriptions 
D, = (/*,,/?,) and D 2 =(P 2 ,R 2 ), and a mapping h 
from D, to d 2 , distance from D 2 to D ] are defined 
using conditional information as follows (Boyer and 
Kak,1988). 
I h (D 2 \D l ) = I h (P 2 \P l ) + I h (R 2 \R l ) (7) 
A. Conditional information of image points 
Given a mapping h from D 2 to D,, P 2 is divided into 
two groups. 
1 > p ou, = I'i I'« = 1 is the group of points 
having no match in P l . 
2) P,, 2 =('•,! l<,„ =1...., Nl) is the group in 
which each point primitive r? have a matched point 
r) in />,. 
Thus, 
I h (P 2 \P,) = I h (P 0 2 J + I h (P i 2 n \P l ) (8) 
Let R be the maximal dimension of Z-lmages, to describe 
a point primitive r. = (x n y.) T with resolution e (pixels),