Optimized sequential infra red point detection

Detecting targets using Infra-Red (IR) sensor is a common field of investigation. The main problematic issue is that the target appears in front of a background that causes false alarms. Increasing the detection threshold decreases the false alarms but also decreases the probability of detection. Knowing the relation between the background's common correlation distance and the target's displacement between sequential samplings is an apriori information that may be used to improve the detection abilities. This apriori information may be estimated from the scene. In this paper we derive a model relating the movement of the target with the statistics of the background so that lower probability of false alarm may be obtained for similar probability of detection or on the other hand higher detection probability for equal probability of false alarm. The obtained improvement is due to the fact that instead of placing a global threshold chosen according to the total spatial and temporal variance of the background one may use a threshold which is adapted to the relation between the spatial statistics of the background and target's motion characteristics. The paper presents a complete mathematical derivation of the model as well as computer simulations that clearly demonstrate the hypothesis of the paper.