Image Processing Reference
In-Depth Information
Table C.1
The percentage of
samples within the interval
[
T
min
,T
max
]
, given that the
data are Gaussian distributed
α
Number of samples
1
68
.
26%
2
95
.
44%
3
99
.
73%
4
99
.
99%
T
min
=
Mean
−
α
·
Standard Deviation
(C.3)
T
max
=
Mean
+
α
·
Standard Deviation
(C.4)
where
α
is a constant defined by the designer. To get a better feeling of
α
let us look
at the histogram in Fig.
C.1
(b). Such a bell-shape is said to be Gaussian or Nor-
mal and is characterized by most samples (training pixels) being located around one
value (the mean) and a symmetrically decreasing number of samples further away
from the mean. Many natural phenomena actually have such a shape and therefore
this shape is of great importance in many fields—including video and image pro-
cessing. For the Gaussian shape Table
C.1
is true.
This means that if the histogram of your training data is Gaussian and you set
α
1, then you know that 68.26% of your training pixels have a value between
T
min
and
T
max
, etc. Even though your training samples are not completely Gaussian, you
can still use the table to get a feel for how much of you training data are within the
threshold values.
=
C.2
Initialization
When you train your system make sure to include training samples from as many
diverse situations as you expect the system to operate in. For example, if you train
your system on a rainy day where not much sunlight is present and then expect the
system to operate on a sunny day then, you will probably be disappointed.
Often it is not realistic to train the system to handle all different situations without
including too many false positives. A system can therefore include an
initialization
phase
prior to operation (sometimes also referred to as calibration). The initializa-
tion is a small program which is run before the “real” program is started. With the
example from above, the initialization program will ask the user to place his hand
in a number of different locations in front of the camera. The captured images are
(semi) automatically analyzed (Hue and Saturation values are extracted) and the
threshold values are defined. These are then input to the system when it commences
either manually or through a file.
One might argue that initialization is not desirable from a user's perspective since
it requires an extra effort, but often it is a small price to pay for achieving a much
more robust and hence successful system performance.
