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raction. We 
n so that the 
f techniques 
observations 
  
recorded at a set of known locations by structuring error 
covariance matrix. Cressie (Cressie, 1993) details Kriging. 
3.2 Background Subtraction 
Background subtraction technique is based on taking pixel-by- 
pixel difference between the current frame and a background 
image (Haritaoglu et al., 2000). A pixel wise median filter over 
time is applied to several frames of sequential image to 
construct the initial background image. The background image 
cannot be expected to stay the same for long periods of time. 
There could be illumination changes. Therefore, the 
background updating has to be performed whenever 
illumination changes. Kalman filter is utilized as the updating 
algorithm. 
A simple and common background subtraction uses absolute 
difference of grey-value (Fathy and Siyal, 1995). The 
difference of grey-value, however, is invalid when grey-value of 
vehicle and background is similar. To deal with this problem, 
we examined the effectiveness of distance in following colour 
space (Sangwine and Horne, 1998). 
(a) RGB colour space 
(b) HSV colour space 
(c) CIE colour space 
Through application of above colour spaces to real images, 
RGB colour space was adopted. Accordingly, the value of 
background subtraction b as a feature is defined as follows: 
(7, (x,y)- B, (x,y)) (1) 
( 
where /(x, y) is the current image and B(x, y) is a background 
image, and the suffixes represent colours. 
3.3 Shadow Detection 
Shadows cast by vehicles cannot be separated from foreground 
region by background subtraction fundamentally. The shadows 
will affect results of spatio-temporal clustering, for example two 
vehicles may be connected by neighbouring shadows. It is 
necessary to distinguish between shadows and vehicles. 
A shadow detection technique based on HSV colour space can 
be applied to separation of shadows from the vehicles. The 
algorithm is based on the comparison between the current frame 
I(x, y) and a background image B(x, y) (Cucchiara et al., 2000): 
1 ir les) er 
B, (x.y 
SP(x,y)= ^l (xy) - By (xp) zu Q) 
^l, (x,y) = Be (x. y) St. 
0 otherwise 
y 
  
where SP(x, y) is set to 1 if pixel (x, y) is classified as shadow, 0 
otherwise, and eand the suffixes represent threshold and the 
colour information, respectively. Equation (2) states that a pixel 
(x, y) is classified as shadow if three properties hold: 
(a) the ratio of the V (Value) component of current frame and 
background image respects both a upper bound; 
(b), (c) the differences of the H (Hue) and S (Saturation) 
components are limited. 
The rationale of the equation comes from the observation that 
when an area is covered by a shadow, this often results in a 
significant change in lightness without a great modification of 
the colour information. 
3.4 Optical Flow Extraction 
Ideally optical flows of all pixels are computed. Extraction 
methods of optical flow of all pixels can be divided into 
(a) gradient-based approach 
(b) area-based approach 
We reviewed the gradient-based approaches theoretically and 
compared their performance empirically from the point of view 
of application to vehicle motion analysis (Fuse et al., 2000). 
The accuracy of the optical flow obtained with this method was, 
however, not up to the required level. We also examined the 
comparison between above-mentioned approaches, and 
confirmed area-based approach was more robust. Accordingly, 
we adopt sequential similarity detection algorithm (SSDA): 
R(x»)- Y: 
m=ln=l 
  
1,5 (mn) -T(m,n) — min. (3) 
where 7 is a template, M and N are size of the template. The 
optical flow (u, v) acquired by SSDA is defined as another 
feature. 
3.5 Spatio-Temporal Clustering 
With features f, that are value of background subtraction b and 
optical flow (u, v), all pixels in a spatio-temporal image are 
clustered. The spatio-temporal clustering means unifying pixels 
which meet homogeneous property, namely similarity of 
features. We adopt the weighted Euclidian distance measure as 
similarity metric. To perform this operation, we simply compute 
the distance d between adjacent pixels in the feature space: 
dr f) w(b, —b,) EC -u,y * (v, -wy| (4) 
where w is weight coefficients and R is reliability function to 
estimated optical flow. 
  
I. (mn) =T (m,n) (5) 
1 M N 
R=l- 
25543 22 
m=ln=l 
Adjacent pixels in spatio-temporal domain are added to the 
region as long as the region satisfies the desired homogeneity 
property. The number of reference pixels in spatio-temporal 
domain is 26. This procedure results in many regions in the 
spatio-temporal image. 
There may be the case that the pixels belonging to a same 
vehicle are not adjacent in sptio-temporal domain. To deal with 
such kind of situation, we developed probabilistic relaxation- 
based approach (Fuse and Shimizu, 2000). 
The result by only applying the clustering described above may 
not be enough to recognize vehicles. The most characteristic 
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