tion 
lest 
deas 
near 
for 
rete 
vd 
o 
reas 
d as 
tion 
Then 
are 
RL, (A)} = oËrexpl-(F,,4)1 
Az 4) 
T = Gr Toy) (1.2) 
Tp = Oen) 
fy V 
Let us suppose that for the time distance 
denoted as T moving object pattern is 
displaced to LL. value. Here L, is a 
characteristic pattern size. Four 
peculiar regione can be distinguished in 
the frame difference field: 
€ Toms, 
S et 
> 
| 
em 
md 
F/T yo, 
bo 
| 
Mm 
MN 
3 
t=t, 
CMM A 
=, 
(1.3) 
c 
| 
il 
€ FM, 
= Het, 
These definitions are illustrated by 
Fig.1 in which pattern position at 
moment t, is shown by dotted lines and 
at moment ta by unbroken lines. 
AA 
h> 1 
D: e.T 
eH 
  
  
  
  
  
Fig.1 Peouliar regions of the 
frame difference field. Pattern 
position at moment p is shown by 
dotted lines and at moment i5 by 
unbroken lines. 
We assume that frame fragment size is 
sufficientl y small in | order to 
Y A € FAT =» D(A)- D 
and pattern displacement has the 
determinate value and an accidental 
direction. That is 
Y A eT" L(A)- L. 
Then with neos to paper (Jess, 
1989) we can confirm that all ragions of 
frame differenoe field are also 
homogeneous Gaussian. Their averages may 
be easily defined by Eq.(1.1)-Eq. (1.3). 
2. SUBOPTIMAL DETECTOR STRUCTURE 
Let's put restrictions to suboptimal 
detector structure. For this purporse we 
assume that the movi object pattern is 
in the middle of first frame fragment if 
429 
it is present there. Then let's reduce 
frame quantity to two and substitute 
time-spatial filtering for separate time 
one and spatial filteri Let's also 
suppoused that the reu filter is 
linear one and it's area of definition is 
resiricted to pattern size. 
We shall simply assert without proof that 
the best result is reached for this task 
if time distance 
T = LV"! (2.1) 
and fragment size 
1 = 3; + (2.2) 
Here V is design speed of pattern moving. 
It can be shown too that for the oase of 
simple detection (Raftmmreft, 1960) with 
above restrictions optimum detector of 
non-point movi objects has to make 
following operations: 
(1) Frame difference field formi 
(2) Frame difference field filtering by 
ripple mask (Pratt, 1978) with restricted 
to pattern size area of definition and 
constant impuls response. 
(3) Extremal pixels at the filter 
output 
z (nh hot 
x (Ort? man! 
searching. 
(4) Decision funotion denoted as 
caloulating for hypothesises 
H (A) = Ael A c (A) = Ae] : 
13° S n 
Here i,jce(A,B,C,D). 
(5) Searched pixels classification. 
It's olear that moving object pattern is 
detected if 
Go) - mintg, G2 
Let's define the based on operations 
(1)-(5) detector as suboptimal. 
3. ANALYSIS OF THE SUBOPTIMAL DETECTOR 
As it was stated above frame difference 
image consists of a disorete homogeneous 
Gaussian fields. Therefore hypothesis Hq 
a posteriori probability subjects double 
Gaussian distribution law. Then 
G, 4X) = X'+8 13% + Wi. X + Vy, (3.1) 
and separating surfaces which are 
associated as show Eq.(3.1) and Eq.(3.2) 
Goo D 7 9,,0) (3.2) 
are the hyperquadrieos (Duda, 1973). 
In Kg. (3.1): 
zem -1 
914 D, 5: 4