1.2 Acquisition Probability 
Suppose the correct matching point is (*, j*). In practical 
systems, often it is the target point. So, it will be called 
‘target point’ in this paper. A good image matching system 
should make the matching point as close as possible to the 
target point. But because of the influence of noise, they 
generally do not coincide even if there exist no geometrical 
distortions between the two images. Therefore, we define 
acquisition probability P, as the probability where the image 
matching point coincides with the target point. For the 
MAD algorithm, we have 
Py = P{f(3,3) > f(&",5"),V(5,5) € G, (i #7) N (J # m 
2 
2. EVALUATION OF ACQUISITION 
PROBABILITY 
2.1 Johnson's Evaluation 
Different image correlation models result in different eval- 
uation approaches and results. In [2], based on the image 
model of pixel-independency, the following evaluation of ac- 
quisition probability for the MAD algorithm is derived: 
5 1 eo (= — 0)" pi 
Pers Le ro uem (3) 
and 
1 "eo (21 = F1)” 
Pole) ren La A 
where K = N,_,, N, is the number of all points in the 
searching area G; zo, cà represent the mean and variance of 
f(i*,j*) = z' respectively (see [1]); similarly, z1, o2 repre- 
sent the mean and variance in mismatching point(s, 7) and 
fla,ÿ)= 71, x = 7° = Tp: 
(3) also can be expressed as 
P, i Í^ ioni y X 
BE vel. 202 
P{f(i, 5) > a, V(hi)E G,li Ai*)N(i#j")}dx (5) 
}dz1 (4) 
In contrast to [2], we use the expression f(i,7) > 2’ instead 
of f(i,j) > z' in (5). In case of equality, at least two mini- 
mum points in the searching area G appear and the matching 
point can not be determined. 
2.2 The Acquisition Probability Based on the 
Pixel-Correlation Model 
In real images, neighbour pixels generally correlated[4]. There- 
fore, the evaluation of acquisition probability by (3) is not 
accurate. In order to get a more accurate evaluation, an 
image correlation model must be used. In [1], based on 
the image correlation model proposed in Reference [4], the 
probability density distribution function in a single-valley 
area containing the minimum point has been given. Now, 
we will give the probability density distribution function in 
the whole searching area G. In order to simplify the analy- 
sis, we transfer the 2-D searching area into a 1-D sequence 
by scanning. So, we have 
f(g) = f(6,5) (6) 
here g = (¢ — 1)m/ + j; (¢,7) is a mismatching point in the 
searching area(m/ x n/). 
376 
For every f(g), it is satisified with the following Gauss dis- 
tribution: 
f(g) ^ N (25,02) (7) 
where 
  
= 2 jlo}, |], 
Tg = TET = mpi c eer = nt *e2] 
2 eii 5-7] (8) 
2r 2 lg —1 1o 73" 
3 = a - DBeia - esp(- Pa P1. Ea ly 4 og 
(9) 
For random sequence {f(g9)}(¢ = 1,2, ...,N,_,), suppose 
their joint probability distribution is the N, ,-dimensional 
joint Gauss distribution 
PO Ya Ur) = 
1 1 T = 
aaa zum a FF v -Y» 
with 
Kz N.i 
Y- (91,92, 9k)" 
Y= (51.7.7) 
2 2 
Sz d pg pepe 
2 2 2 
kc Rau CK 
(10) 
of, are the covariances of f(k) and f(g): 
ot, = 0,0, (11) 
Peek Na 
So we have 
P(f(53) » 2, V(5j)eG, (iz i)n(G # j*)} 
Too roo Too 
j / wf Dini; ya; - V) dyidya dy, 
T r-Tro 
Too 
Il 
+Xo /x+To 
1 e d 2 
f rare ~ PF Tr - Py (12) 
with W = (w,w,...,w),w=2 + To = 2’ 
According to (5), the acquisition probability for the MAD 
algorithm is: 
  
Tow v1 (z — zo)? 
P = ex „DL X 
: -oo V2T00 pi 208 } 
+00 1 
ya (2m )K/2(det Y) X 
ezp[- (Y -Yyy'(v-YyaYde (13) 
W,Y,Y and Y, can be determined by (8) ~ (11) when the 
reference image's variance eZ, the signal to noise ratio SNR, 
the correlation length Az, A, and m,n, M, N are known. So, 
the acquisition probability for the MAD algorithm can be 
calculated from (13). 
2.3 The Evaluation of Acquisition Probability 
for the MAD Algorithm 
In image matching, usually N4 is very big. For example, 
when the reference image is of size 64 x 64 and the sensed im- 
age is of size 32x32, N,—1 = (64—32+1)(64—32+1) = 1088. 
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