Detection of a target from multiple images: a new probabilistic theory with correlation

One way to detect an underwater target is to take images of the seabed by an autonomous underwater vehicle and then analyze the images, [1-14]. There are many features that can be extracted from an image such as the shadow size, the physical size, the contrast of a potential target etc. Based on these features, we could model the probability of detecting a target. However, unlike the process of flipping a coin which results in a head or a tail, an image does not change whether we decide it is a target or not i.e. there are no corresponding head (target detection) or tail (not a target detection) in an image. If we keep flipping a fair coin then the probability of getting at least a head (target detection) will keep increasing. However, analyzing the same image multiple times does not provide additional information and therefore does not improve the probability of detection. This means that the process of detecting a target from its images is not a Bernoulli's process. Hence, we need a new probabilistic theory.