Detecting edges in images is a fundamental problem in computer vision with many applications. Many edge detection algorithms have been proposed over the past several decades. These algorithms can deal effectively with the problem, but often face difficulties when applied to images taken under poor visual conditions of faint edges and noisy backgrounds. Such conditions occur frequently in various imaging domains including biomedical, satellite, and high shutter speed, and may even occur in natural images. In this work, the proposed method introduces an efficient method to detect faint edges in noisy images. The first question addressed is how to detect curved edges efficiently. Previous work showed that faint edges can be detected by applying a search over the space of possible curves. While this search space is exponentially large in the number of image pixels, the proposed algorithm novel multiscale algorithm carries a search through a large subset of the space in practical polynomial time. The introduced algorithm is based on a novel hierarchical partitioning of the image into triangular or rectangular tiles. In addition, the second question addressed is how to decide if a curve in the image indeed corresponds to a (possibly faint) edge. To that end, the paper introduces a Bayesian approach that incorporates the intensity and shape features of an edge. The proposed method utilizes relevant statistical priors on edge contrast and shape. Finally, the algorithm utilizes natural images to derive a prior on-edge contrast. As the manuscript experiments demonstrate, in comparison to previous works the proposed algorithm is efficient and obtains higher quality of edge detection.