Detecting edges is a fundamental problem in computer vision with many applications, some involving very noisy images. While most edge detection methods are fast, they perform well only on relatively clean images. Indeed, edges in such images can be reliably detected using only local filters. Detecting faint edges under high levels of noise cannot be done locally at the individual pixel level, and requires more sophisticated global processing. Unfortunately, existing methods that achieve this goal are quite slow. In this paper we develop a novel multiscale method to detect curved edges in noisy images. While our algorithm searches for edges over a huge set of candidate curves, it does so in a practical runtime, nearly linear in the total number of image pixels. As we demonstrate experimentally, our algorithm is orders of magnitude faster than previous methods designed to deal with high noise levels. Nevertheless, it obtains comparable, if not better, edge detection quality on a variety of challenging noisy images.
@cite_18: Edges are prominent features in images. The detection and analysis of edges are key issues in image processing, computer vision and pattern recognition. Wavelet provides a powerful tool to analyze the local regularity of signals. Wavelet transform has been successfully applied to the analysis and detection of edges. A great number of wavelet-based edge detection methods have been proposed over the past years. The objective of this paper is to give a brief review of these methods, and encourage the research of this topic. In practice, an image is usually of multistructure edge, the identification of different edges, such as steps, curves and junctions play an important role in pattern recognition. In this paper, more attention is paid on the identification of different types of edges. We present the main idea and the properties of these methods.
Another set of edge detection algorithms utilize a Wavelet-based bank of filters that vary in length and width, see a review in @cite_18 . Given the availability of fast-wavelet transforms, these methods are also quite fast. However, a key difference from our approach is that these wavelet methods do not adapt to the shape of actual curved edges. Hence, their performance at very low SNRs is sub-optimal.