Abstract

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 im- ages. 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 hi- erarchically 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.