Image Processing Reference

In-Depth Information

Usually, the inaccuracy of measurement dating is not taken into account. The error

made on the acquisition date is assumed to lead to a negligible error in the data.

11.5. Evolutionary models

The method used to register data in time is based on the use of evolutionary models.

It can also be used to make up for the lack of data in time, for example, when the

sampling frequency is too small or in the case of a significant delay.

An evolutionary model is a knowledge model used for estimating a quantity at a

given time, knowing the value or values of this same quantity at previous times. The

model can be obtained by learning or from expert knowledge based, for example, on

the laws of physics, mechanics, physiology, etc. When the model is known, it is then

usually possible to predict the data in advance and particularly on the date of the data

registration.

This concept of model can be illustrated by the following example. If we know at

a time
t
the position
x
(
t
) and the speed
v
of an object along a line, it is possible, using

the well-known laws of kinematics, to predict the position
t
+Δ
t
on the condition that

Δ
t
is “small enough” compared to the possible variations of speed:

x
(
t
+Δ
t
)=
v.
Δ
t
+
x
(
t
)
.

The model should also allow the error of the new data to be calculated knowing

those of the previous data.

Let us assume, in the previous example, that the error on
x
and on
v
is modeled by

an interval:

∈
x
−
(
t
);
x
+
(
t
)

x
(
t
)

∈
v
−
;
v
+

v

Then the lower and upper limits of
x
(
t
+Δ
t
) are:

x
−
(
t
+Δ
t
)=
v
−
.
Δ
t
+
x
−
(
t
)

x
+
(
t
+Δ
t
)=
v
+
.
Δ
t
+
x
+
(
t
)

and therefore:

∈
x
−
(
t
+Δ
t
);
x
+
(
t
+Δ
t
)
=
v
−
·

Δ
t
+
x
+
(
t
)

Δ
t
+
x
−
(
t
);
v
+

x
(
t
+Δ
t
)

·

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