1-1-4
it takes 2 log —bits (Forstner, 1989; Vosselman, 1992).
£
Thus
mp„L)=S'(0 =2/v «> gj
i„ u , =1 t
(9)
On the other hand, conditional information has been
defined in Ingels, 1971; Blahut, 1987 by conditional
probability as follows.
I(a i \b j ) = -\og?vob(a i I b¡) (10)
Thus,
/.(£ !/’,)= I -l°g<
27T<7
(jr* ~/l(xf m )) 2 +( Vj )) 2
2a 2
)
(11)
Since a matched point should use fewer bits in description
than an unmatched one, it has
2 (x)-h(xf)) 2 +(y'j-h(yì)) 2
-log
27TC7 2
<21og-
£
Let
= 2(7 Jin
R
yfbra
(12)
Image points r) = (x), y))‘ and r 2 = (xf, yf) T are
matched ones, if and only if it has
(13)
B. Conditional information of line segments
image points, angle between line normal and difference
between orthogonal distance. Thus
l h {l-\l)) = l h iP-\Pj) ( 16 )
+ I h (angle(n), nf )) + I h (dis(d), df )).
Suppose A0* and Ad k s be the estimation error of n k s
and d k s in l k (s=i,j; k=l,2), following normal
distribution, then it has
angle 2 (!) Mlf))
I h (angle(n],nf)) = - log(
yfïna.
)
(17)
I h (dis(d),d?)) = - log(
dis 2 {!) Ml?))
2a d , '
)
dij
(18)
Where
=V (
=^jj) 2 +(^,-) 2 •
Since a matched line segment should use fewer bits in
description than an unmatched one. Thus, line segments
l'. and if are matched, if and only if it satisfies
/»(/, 2 l/;)<2W i 2 log-=i i 2 . (19)
£
Given a mapping h from d 2 to D,, L 2 is divided into
two groups.
1 ) L l„ = Vl 1 c = ) is the group of line
segments having no match in L,.
2) Lf n '= {if I i in = } is the group in which each
line segments if have a match l\ in L,.
Thus,
K (/? 2 1 R x ) = I h (L 2 1 L x ) = /„ (L 2 0Ut ) + l h (Li I L,)
(14)
Line segments without match can be represented using
their point primitives. Thus,
$oui D
/»aL)=2£w,io g — (is)
r =1 £
l oul 1
Where, w,. is the number of image points in 1..
Conditional information between two matched line
segments is analyzed by three components, match in
2.1.4 Searching for best matching
A. Coarse matching
Searching for coarse matching is conducted in an
exhaustive mode. Searching space concerns with the
angle between non-parallel line segments and distance
between parallel line segments. Line segment pairs with
the same intersection angle or distance (if parallel), are
tried to match the images. The best match is selected to
be the one yielding minimum distance measure. It set the
initial value to the transformation between two images. Let
it be T°.
B. Strength definition in fine adjustment
In fine adjustment, strength between each matched pair of
line segments are analyzed to lead the adjusting
procedure. Let T k be a transformation from D, to D,.
