The third step of our fire detection algorithm is to keep track of the frequency history of pixels in the fire colored region and analyze the history. In order to detect flicker or oscillations in pixels due to fire in a reliable manner, the video capture rate should be high enough to capture high-frequency flicker in flames. To capture 10 Hz flicker, the video should capture at least 20 frames per second (fps). However, in some surveillance systems, the video capture rate is below 20 Hz. If the video is available at a lower capture rate, aliasing occurs but flicker due to flames can still be observed in the video. For example, 8 Hz sinusoid appears as 2 Hz sinusoid in a 10 fps video.
Each pixel of the binary mask
is fed to a two stage-filter
bank as shown in Fig.
. The signal
is a one-dimensional
signal representing the temporal variations in color values at location
in the
frame. Temporal wavelet analysis can be carried out using either the luminance (Y component) in YUV color representation or the red component
in RGB color representation. In our implementation the red channel values of
the pixels are used. The two-channel subband decomposition filter bank is
composed of half-band high-pass and low-pass filters with filter coefficients
{-0.25, 0.5, -0.25} and {0.25, 0.5, 0.25}, respectively, as shown in
Fig.
. The filter bank produces wavelet subsignals
and
. If there is high frequency activity at pixel location
, high-band subsignals
and
get non-zero values. However, in a stationary pixel, the values of these two subsignals
should be equal to zero or very close to zero because of high-pass
filters used in subband analysis. If the pixel is part of a flame
boundary at some time (see Fig.
), then there
will be several spikes in one second due to transitions from background
colors to flame colors and vice versa. If there is an ordinary fire-colored
moving object going through pixel
, then there will be a single spike
in one of these wavelet subsignals because of the transition from the background
pixel to the object pixel as shown in Fig.
. The number of zero
crossings of the subband signals
and
in a few seconds is used to
discriminate between a flame pixel and an ordinary fire colored object pixel.
If this number is above some threshold, then an alarm can be issued for this pixel.
The temporal history of the red channel of a pixel which is part
of a flame, and the corresponding wavelet signals are shown in Fig.
.
A flicker in the red channel values of this flame pixel is obvious from the figure.
The pixel is part of a flame for image frames
, n=1, 2, 3, 19, 23, 24, 41 and 50.
It becomes part of the background for n=12,...,17, 20, 21, 26, 27, 31,...,39, 45, 52,...,
and 60. Wavelet domain subsignals
and
reveal the fluctuations of the pixel
at [111, 34] with several zero crossings. Due to a down-sampling operation during
wavelet computation, the length of wavelet signals are halved after each stage of
subband filtering. As a result, the value of a sample in a subband signal corresponds
to several samples in the original signal, e.g., the value of
corresponds
to the values of
and
, and the value of
corresponds to the values of
,
,
and
, in the original signal.
The temporal history of the red channel of a pixel , which is part
of a fire colored object, and the corresponding wavelet signals are shown in
Fig.
. As shown in this figure, neither the original nor the
wavelet signals exhibit oscillatory behavior. The pixel is part of a
white-colored background for n=1, 2, and 3, becomes part of a fire colored
object for n=4, 5, 6, 7, and 8, then it becomes part of the background again
for
. Corresponding wavelet signals
and
do not exhibit
oscillatory behavior as shown in Fig.
. Small variations
due to noise around zero after the
frame are ignored by setting
up a threshold.
The number of wavelet stages needed for used in flame flicker analysis
is determined by the video capture rate. In the first stage of dyadic wavelet
decomposition, the low-band subsignal and the high-band wavelet subsignal
of the signal
are obtained. The subsignal
contains [2.5 Hz, 5 Hz] frequency band information of the original signal
in 10 Hz video frame rate. In the second stage the low-band
subsignal is processed once again using a dyadic filter bank, and the
wavelet subsignal
covering the frequency band [1.25 Hz, 2.5 Hz]
is obtained. Thus by monitoring wavelet subsignals
and
, one can detect fluctuations between 1.25 to 5 Hz in the pixel
.