Fire Detection Algorithms Using Multimodal ... - Bilkent University

CHAPTER 2. FLAME DETECTION IN VISIBLE RANGE VIDEO 24The states of HMMs are defined as follows: at time n, if |w(n)| < T 1 , thestate is in S1; if T 1 < |w(n)| < T 2 , the state is S2; else if |w(n)| > T 2 , thestate S3 is attained. For the pixels of regular flame-colored moving objects, likewalking people in red shirts, no rapid changes take place in the pixel values.Therefore, the temporal wavelet coefficients ideally should be zero but due tothermal noise of the camera the wavelet coefficients wiggle around zero. Thelower threshold T 1 basically determines a given wavelet coefficient being close tozero. The state defined for the wavelet coefficients below T 1 is S1. The secondthreshold T 2 indicates that the wavelet coefficient is significantly higher than zero.The state defined for the wavelet coefficients above this second threshold T 2 isS3. The values between T 1 and T 2 define S2. The state S2 provides hysteresisand it prevents sudden transitions from S1 to S3 or vice versa. When the waveletcoefficients fluctuate between values above the higher threshold T 2 and below thelower threshold T 1 in a frequent manner this indicates the existence of flames inthe viewing range of the camera.In flame pixels, the transition probabilities a’s should be high and close to eachother due to random nature of uncontrolled fire. On the other hand, transitionprobabilities should be small in constant temperature moving bodies becausethere is no change or little change in pixel values. Hence we expect a higherprobability for b 00 than any other b value in the non-flame moving pixels model(cf. Fig.4.3), which corresponds to higher probability of being in S1. The stateS2 provides hysteresis and it prevents sudden transitions from S1 to S3 or viceversa.The transition probabilities between states for a pixel are estimated during apre-determined period of time around flame boundaries. In this way, the modelnot only learns the way flame boundaries flicker during a period of time, but alsoit tailors its parameters to mimic the spatial characteristics of flame regions. Theway the model is trained as such, drastically reduces the false alarm rates.During the recognition phase, the HMM based analysis is carried out in pixelsnear the contour boundaries of flame-colored moving regions. The state sequenceof length 20 image frames is determined for these candidate pixels and fed to