Deriving Optimal Thresholds for Active Fire Detection

Abstract

In this paper, the optimal threshold for fire detection is derived based on the probability density functions of the fire and background pixels. The threshold values and the commission and omission errors are computed according to several detection criteria: maximum likelihood, null-hypothesis testing, and minimum cost. This statistical approach enables the determination of optimal threshold value according to the specific requirements of the detection tasks I. INTRODUCTION Active fire detection using satellite thermal sensors usually involves thresholding the detected brightness temperature in several bands. The frequently used features for fire detection are the brightness temperature in the 4-µm wavelength band (T4) and the brightness temperature difference between the 4- µm and 11- µm bands (∆T=T4-T11) (1), (2), (3). Due to the statistical nature of the fire and background temperature distribution, no matter how the thresholds are chosen, there are bound to be commission errors (i.e. false alarms) and omission errors (false negatives) in the detection outcomes. In the commonly used fire detection algorithms, the thresholds are often arbitrarily defined, and hence may not be optimal for a given fire detection task. The optimal threshold values are expected to be site dependent. They are different in different regions and for different fire conditions (such as smoldering and flaming fires). Hence, a global set of threshold values may not work optimally for a specific site. The task of active fire hot spot detection can be modeled as a stochastic target detection procedure (4). In this model, each pixel of the image occupies a point (T4, ∆T) in the two- dimensional feature space, and each pixel belongs to either the fire class or the non-fire background class. This approach considers the probability density functions of the fire and background pixels and optimal thresholds are derived depending on the specific objectives of the detection tasks. In a previous work (4), we implemented a method for deriving the optimal detection threshold by minimizing a cost function which is a weighted sum of the omission and commission errors. Alternatively, the threshold can also be derived based on other criteria. In this paper, we derive the optimal thresholds for detecting active fires in MODIS scenes using various detection criteria: maximum likelihood, constant false alarm rate, and null-hypothesis testing. The test data set consists of several MODIS scenes over Sumatra and Borneo islands and coincidental high resolution SPOT scenes (5). The SPOT data serves as ground truth for validation of MODIS hotspots detected by the new algorithms based on stochastic models. The probability density functions (pdf's) of the fire and background pixels are derived from this dataset and these pdf's are used to derive the optimal thresholds for active fire detection.