A Contrario Decision: the LLD Method

In this chapter we will try to answer the question “does that shape element look like this one?”, and to measure the confidence level of this answer. This confidence level will be computed as the probability that two observed shapes match just by chance. This requires an a contrario or background model, which will be accurately computed from the shape database itself. The goal is to reach very high recognition confidence levels and therefore very small probabilities in the background model. How can we estimate very small probabilities? This cannot been done by simple counting. Indeed, the number of required samples grows as the inverse of the probability to be computed. There is, however, a classical way to circumvent this impossibility. It is enough to use independence. The probability of a very unlikely event can be estimated accurately provided it is a conjunction of independent events whose probabilities are larger, and therefore observable.