the window be 
the matching 
| that only the 
run through the 
d as matching 
S either along 
ed out and be 
edge detection 
applied due to 
positions, the 
n the matching 
difficult as the 
using for the 
> satisfied the 
'eometrical or 
ransformation, 
erences among 
properties. 
larity of the 
The edges can 
negative one. 
ive x-direction 
otherwise it is 
or) /Marr1982/ 
candidates are 
rrect matching 
is either local 
edge segment. 
ation invariant 
scribes such a 
| of one close 
0, k] can be 
Q.1) 
ward and then 
local Fourier 
formula (2.1) 
toker1969/, a 
vithin a rigid 
e arc length C, 
ese values are 
? digitization. 
eir numerical 
zalez1992/. In 
order to use them in digital image processing procedure, some 
stabilization strategies may be applied. In our case we avoid to 
compute the second derivative directly, but use the differences 
of neighboring tangent vectors on the curve to get out the 
approximated curvature. And we use it as curve signature: 
  
  
2 2 
Ho N AZ mm LOU 
Jat +b? jas Jat +b Jad +B? 
(2.2) 
where, V,=a,i + b,-j and V,=a,i + b,j are two neighboring 
tangent vectors on the curve. 
2.2.2 Radiometric aspects The following two radiometric 
noises invariant properties can be used together or individually. 
They reflect the radiometric properties of the edge segment in x 
and y direction respectively. 
The one in y-direction can be described as following model: 
The gray-value of the edge segment in the window is g(i+p, 
j+q) where (i, j) are the coordinates of the crossing point. At 
the same time they are also the coordinates of the window 
center, and {p, q € window}. The gray-value of the 
neighboring pixels of this edge segment are g(i*p-l, j*q), 
where / is the edge step. First step is to eliminate the image 
gray-value independent part of noise, for example for edge with 
two pixel step: 
Ag(p, q) = g(i+p+2, j+q) - gli+p, j*+q) {p. q € window} 
(2.3) 
The second step is to delete the image gray-value proportional 
noise, 
R,(i,j)=Ag(p',g')/ Ag(wv) {(mv) e(pg)(p',a') #(wv)} 
(2.4) 
R y j) reflects almost the nude gray-value property of the cross 
point at (i, j) along the edge segment inside the window. Due to 
the fact that only those edges are to be used when they run 
through the horizontal epipolar line semi-perpendicularly, we 
say that R y j) is the radiometric noise invariant property of the 
point (i, j) in y-direction. Together with LoG (Laplacian of 
Gaussian) operator, we can define the edge steps for different 
edge types, for example step, ramp, roof, spike edge etc. 
In direction of epipolar line, we have to introduce weight index 
for the gray-value ratio map. If the position of the crossing 
point, say at (i, j), there are two neighboring points along the 
same epipolar line outside the edge range. Their coordinates are 
(p, J) and (q, j) respectively, where 0 € p « i and i « q S x- 
dimension. But in our case we select these two points mostly 
inside the window, that means p,, € p « i and 
i « q Xqw, (p,,, A, € Window} 
vod (drin (e ft 
q-p 
where g(i, j) is the gray-value at the point (i, 7). 
2.3 Management of the different properties 
Along two epipolar lines we find out sets of searching 
positions. At every position, there are several geometrical and 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
radiometric noises invariant properties. Together we name them 
as local descriptor. The first element of local descriptor is edge 
polarity. With this zero-one element, we select the matching 
candidates into two parts. Inside each part, we do the following 
operations: 
First of all one matching table based on one element set of the 
local descriptor will be setup. The other element sets will be 
used as support-index in form of weight matrix added to this 
ground matching table. For example, the weight matrix for R, 
can be derived like following: 
R D) R.(v,j 
Wa (i) = win CAD a B (2:6) 
R,(v,j) R,(w j) 
at j position in y direction, u is x-position of one line and v is 
the one the other line. 
2.4. Optimal extrinsic matching 
Now the matching procedure itself should satisfy the following 
two conditions: 
1. based on the local invariant properties, the matching 
process should be a global one; 
2. it should be processed optimally in order to avoid the rest 
local ambiguous parameter. 
Along this direction, the bipartite weighted matching with 
conserved order is applied in our procedure. Detailed, properties 
of this matching method is presented by /Tan1996/. Here we 
describe its mathematics model. 
There are two ordered data sets, denoted by 
Let the weight of matching between element i in the set L and 
element j in the set R be Wij and the weight matrix W be given. 
Let 
I= {ip d eMe 
J= Und SE RoG 
(© means empty set) be two ordered subsets, i.e. there exist the 
relations 1 € k, € m and 1 X k x n. A possible matching set 
between L and R is denoted as 
$- (4LI7)VIcLuG,JcFu6| (2.7) 
where: 
i uu Ù El 
(1,7) = C 2 7 A) 2.8) 
As JaoUJ4ps am JR) 
(i,, j,,) is one correspondent pair, and the objective function at 
#(1,J) can be written in (2.9): 
LAO 
OÙ) = X wi, (2.9) 
P= 
985