A Probabilistic Approach to Pattern Matching in the Continuous Domain

The goal of this paper is to solve the following basic problem: Given discrete noisy samples from a continuous signal, compute the probability distribution of its distance from a fixed template. As opposed to the typical restoration problem, which considers a single optimal signal, the computation of the entire probability distribution necessitates integrating over the entire signal space. To achieve this, we apply path integration techniques. The problem is studied in one and two dimensions, and an accurate solution as well as an efficient approximation scheme are provided.