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Figure 1: The parametric Kalman model, as a continuum 
between two extreme estimators. Three motion estimators, 
respectively E=0.1, Fx-og and Ex-10, are applied to the 
case of an horizontally moving synthetic 2D gaussian form, 
with a displacement of one pixel per frame. (a) Exact or- 
thogonal motion field. (b) Result of an E,-01 estimation. 
The model converges toward the estimate of the orthogonal 
The idea is to test, while estimating, if there is a change 
in the innovation output of the Eg estimator. A PAGE- 
HINKLEY cumulated sum test is used for the detection of 
abrupt changes [2]. When a change is detected, the E, 
model is re-initialized. This is to insure the non integra- 
tion of information which is related to two different homo- 
geneously moving areas of the image. 
4 Experimental results 
This section describes the results obtained when applying 
the ideas described in this paper to a sequence of real In- 
fra Red images. Such images have been acquired using the 
thermic camera “ATHOS” of the SAT company. A pair of 
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motion field. (c) Result of an F,—og estimation. The es- 
timation of the exact motion field (horizontal motion field) 
begins to appear. In this case however, one may notice that 
the right boundary tends to vanish. (d) Result of an Ey_; 
estimation. The exact motion field is estimated, but the 
right boundary of the form is now completely lost. 
two consecutive images of the sequence is shown on figure 2. 
The images show a traffic road of Paris and were taken with 
a camera mounted on a moving vehicle. The size of the raw 
images is 256x512 pixels. 
The two cooperative Kalman filters have been applied 
to this pair of images. In order to better show the found 
changes of the motion field, we give the detection result only 
in a small window corresponding to the left car of the raw 
images (refer to Figure 2). The orthogonal motion field re- 
lated to this car is estimated using the Ej— estimator (refer 
to Figure 3). The innovation of the Kalman filter, associated 
to the dotted line of Figure 3, is represented in Figure 4. 
A detection of abrupt changes in the innovation signal is 
done, using à PAGE-HINKLEY cumulated sum test. Four 
changes are found, directly associated to the limits of the