Image Processing Reference
In-Depth Information
be that of a circle, or if we are tracking a drunken human, the motion model might
be more like a sinus curve than a straight line.
Sometimes the movement of an object cannot be explained by just one motion
model. If we for example are tracking a fish in an aquarium, we will need two motion
models. One model for when the fish is just swimming slowly around and another
model for when the fish needs to get away from something fast. The first type of
movement could be modeled by a first order linear model, while the other type of
movement could be modeled by a random direction with maximum acceleration.
Having two (or more) motion models will result in two (or more) ROIs.
No matter how good our motion model is, it is still just a model of the movement,
i.e. an approximation. The object is therefore not likely to be located exactly at
the predicted location. For this reason we look for the object within a ROI. The
question is now how to define the size of the ROI. The simplest approach is to try
different sizes and see which works best. A more scientific approach, which will
render a smaller ROI and hence save processing time, is to define the size based on
the uncertainty of the prediction. Say we in the last image predicted the x-position
of the object to be at position 370, but found the object at position 350. Whether this
difference is due to a bad prediction or a bad detection we do not know. What we do
know is that there is some uncertainty in the x-direction. The bigger the uncertainty
is, the bigger the ROI should be in the x-direction. Normally it is not recommended
to let the difference control the ROI directly since it is sensitive to noise. A more
conservative way of changing the ROI based on the difference is here shown for the
width of the ROI:
1 ) = α · x (t) x(t) + ( 1
width (t +
α) ·
WIDTH
(9.3)
where α is a small value, x( t) is the predicted x-value of the object at time t , x(t) is
the detected x-value of the object at time t , and WIDTH is a predefined minimum
width of the ROI. The same can of course be done in the vertical direction.
Similar to the uncertainty of the prediction, we also have an uncertainty associ-
ated with the detection. Imagine that we in one image have a bad segmentation of
the object we are tracking. The effect of this could be that we only detect a small
part of the object. We can still calculate the position of the object, but the number
of object pixels used in this calculation is much smaller than in previous images,
see Fig. 9.4 . This would suggest that the detection has become more uncertain and
ultimately we could have a situation where the object is not found and hence no
detection is available. In both cases it might be better using the prediction than the
detection when updating the state. Following along this line of thinking, the update
of the state could be
w 1
w 2
s(t) =
w 1 + w 2 · p (t) +
w 1 + w 2 · p(t)
(9.4)
where w 1 should be controlled by the uncertainty associated with the prediction and
w 2 by the uncertainty associated with the detection.
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