Detecting Faint Curved Edges in Noisy Images

A fundamental question for edge detection is how faint an edge can be and still be detected. In this paper we offer a formalism to study this question and subsequently introduce a hierarchical edge detection algorithm designed to detect faint curved edges in noisy images. In our formalism we view edge detection as a search in a space of feasible curves, and derive expressions to characterize the behavior of the optimal detection threshold as a function of curve length and the combinatorics of the search space. We then present an algorithm that efficiently searches for edges through a very large set of curves by hierarchically constructing difference filters that match the curves traced by the sought edges. We demonstrate the utility of our algorithm in simulations and in applications to challenging real images.