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 t on the condition that
Δ t is “small enough” compared to the possible variations of speed:
x ( t 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 t ) are:
x ( t t )= v . Δ t + x ( t )
x + ( t t )= v + . Δ t + x + ( t )
and therefore:
x ( t t ); x + ( t t ) = v ·
Δ t + x + ( t )
Δ t + x ( t ); v +
x ( t t )
·
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