International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
1 N N 
$3 ARR apo) 
CONSE. 
| N 
x 
2 > JG xy y t Yo » 
^ 
(IET 
(CN + D) YXz-N yz 
V. (xo. yo. N) 
where f(x, y)- image brightness in point with coordinates 
X, y. 
The examples of variances for two consecutive frames are 
shown in the Figure 2. The operator of maximum variance was 
Figure 2. Variance fields (window size 3x3) 
taken as the operator of interest for image due to simple 
structure and computational stability. At first step a list of 
candidate points is extracted by maximum operator with 
window size 5x5. The lists of candidate points for left and right 
images are shown in the Figure 3 and, in general, depends on 
the 
  
Figure 3. Candidate points lists for features 
window size. At the next step the informativity size of each’ 
feature is defined and then used to select stable features. The 
informativity size is defined in the following way. Consider 
variance V in the given point as function of window size N, the 
typical form of the function is presented in the Figure 4. 
V 
N 
Figure 4. Informativity size 
  
Abscissa of the maximum is considered to be the informativity 
size I of the given feature. This valuable parameter is used in 
filtering of the lists of candidate features for left and right 
images. Those features with 1 « Im Where I, is threshold, are 
filtered out. Small features should be filtered out because they 
could arise due noise maxima. The lists of candidate points for 
left and right images after filtering are shown in the Figure 5. 
Figure 5. Lists of features after filtering, Ll, 7 11 
2.3 Features matching 
Now we should set up a correspondence between features at the 
left and right images. For that the set of K parameters 
describing features should be introduced. Two features, close in 
K-dimensional space of parameters, are considered as the 
conjugate pair. The obligatory condition the parameters should 
satisfy is the invariance to shift, rotation and scale. Suitable 
theoretical basis for tasks of this type was laid by Hu, M.K 
(Hu, M.K., 1962), who developed the algebraic theory of 
invariant moments for image recognition. He proposed to use 
seven invariants for this purpose: 
Ly =f Moo 
f= (ty — May FAL 
I s MY + Otte 7 Ha 
Lets) tn + 493) (2) 
I, = ts 7345: to 42s * 142 y- 34, * Ha ]+ 
* Qus = Hos hay + ys DG, ttis y- (Us t fias ] 
Is = ts — 4 Ato * 42 y- t + Hoy »] +4, (fag + 12 Xt) + Hes) 
I SH = Ms Who + Hip Mts + 200 Fe = 00 + fl 1 
* Quis = Han (Hay t 4003 [30430 + 442 y- (t, + Hoa] 
where on™ S. Y Gin EV Que XY FL 1) = central moment 
xeQ yeQ 
of the order (p+q) for window centered in x,y 
P.4=012,... 
f(x, y) * normalized image brightness 
Q - image area in x,y coordinates 
These invariants are taken to form the K-dimensional parameter 
space to compare the point features. Account must be taken of 
the fact that invariant propertied were established for 
continuous case. In discrete scheme some errors of 
discretization can arise, especially in rotation of images more 
then 45 degrees. 
International A 
Correspondenc 
images is no 
space. Features 
are L 
where I: 
image 
R j^ 
10x 
right image 
Let i=1,N, a 
candidates on 
considered as c 
At given stage 
criteria (4), N= 
2.4 Features 
In order to veri 
properly, the a 
of points posit 
features at le 
distribution its 
Consider the s 
image, Figure ( 
Distances betw 
matrix ||A;| as 
CS EN