A fundamental question for edge detection in noisy images is how faint can an
edge be and still be detected. In this paper we offer a formalism to study this
question and subsequently introduce computationally efficient multiscale edge
detection algorithms designed to detect faint edges in noisy images. In our
formalism we view edge detection as a search in a discrete, though potentially
large, set of feasible curves. First, we derive approximate expressions for the
detection threshold as a function of curve length and the complexity of the
search space. We then present two edge detection algorithms, one for straight
edges, and the second for curved ones. Both algorithms efficiently search for
edges in a large set of candidates by hierarchically constructing difference
filters that match the curves traced by the sought edges. We demonstrate the
utility of our algorithms in both simulations and applications involving
challenging real images. Finally, based on these principles, we develop an
algorithm for fiber detection and enhancement. We exemplify its utility to
reveal and enhance nerve axons in light microscopy images.

介绍一种正式研究边缘检测中的微弱边缘问题的形式化方法，并引入了一些旨在检测嘈杂图像中微弱边缘的计算有效的多尺度边缘检测算法，其中包括针对直线和弯曲曲线的算法。这些算法可以有效地搜索大量的候选边缘，并展示了本文算法在模拟和挑战性实际图像的应用中的效用，并且最后基于这些方法开发了一种纤维检测和增强算法。