Image Processing Reference

In-Depth Information

Fig. 9.3
(
a
) Framework for updating and predicting the state. (
b
) The effect of predicting the

position of the object in the next image

9.2

Prediction

Very often the object we want to follow is moving much slower than the framerate

of the camera. As a consequence the object is not moving very much from one

image to the next. So, having located an object in one image will allow us to
predict

where the object will approximately be in the next image. We want to exploit this

fact when detecting the object. This is done by introducing a ROI centered at the

position where we predict the object to be and only analyze the pixels within the

ROI, see Fig.
9.3
. This will save a significant amount of processing time.

The question is now
where
we predict the object to be. For this purpose a
motion

model
is introduced, that is, a model explaining how the object is moving. The most

simple model is a
zeroth order linear motion model
. It predicts the object to be

exactly at the same position in the next image as it is in the current image. The next

of the linear motion models is the
first order linear motion model
, which includes the

velocity of the object. Given the current position
p(t)
=[
x(t),y(t)
]

and velocity

v(t)
=[
v
x
(t), v
y
(t)
]

of the object, the predicted position will be

p
(t
+

1
)
=
v(t)
·
t
+
p(t)

(9.1)

where
p
(t
+

1
)
is the predicted position and
t
is the time between
p(t)
and

p(t
+

1
)
. Often the framerate is constant and
t
is simply the number of images

predicted into the future. Usually we are just interested in predicting one image

ahead and hence
t
can be removed from the equation.

The
second order linear motion model
also includes the current acceleration of

the object
a(t)
=[
a
x
(t), a
y
(t)
]

and the predicted position is given as

1

p
(t

2
·
a(t)

+
v(t)

+
p(t)

t
2

+

1
)

=

·

·

t

(9.2)

Again, with a fixed framerate and only predicting the next image, the two

terms become 1 and can therefore be ignored.

Motion models are not necessarily linear. If we for example are following an

object being thrown, we need a model that includes gravity. Another example could

be when tracking an object moving in a circle, the motion model would of course