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 , ) =
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
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),
