On Detection of Faint Edges in Noisy Images
This work addresses edge detection in noisy images, which is crucial for fields like medical imaging, but it is incremental as it builds on existing multiscale methods with specific algorithmic improvements.
The paper tackles the problem of detecting faint edges in noisy images by introducing a formalism to determine detection thresholds and proposing computationally efficient multiscale algorithms for straight and curved edges, demonstrating their utility in simulations and real-world applications like nerve axon enhancement in microscopy.
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.