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.
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.
@cite_18
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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. In this work, we propose the construction of two-channel wavelet filter banks for analyzing functions defined on the vertices of any arbitrary finite weighted undirected graph. These graph based functions are referred to as graph-signals as we build a framework in which many concepts from the classical signal processing domain, such as Fourier decomposition, signal filtering and downsampling can be extended to graph domain. Especially, we observe a spectral folding phenomenon in bipartite graphs which occurs during downsampling of these graphs and produces aliasing in graph signals. This property of bipartite graphs, allows us to design critically sampled two-channel filter banks, and we propose quadrature mirror filters (referred to as graph-QMF) for bipartite graph which cancel aliasing and lead to perfect reconstruction. For arbitrary graphs we present a bipartite subgraph decomposition which produces an edge-disjoint collection of bipartite subgraphs. Graph-QMFs are then constructed on each bipartite subgraph leading to “multi-dimensional” separable wavelet filter banks on graphs. Our proposed filter banks are critically sampled and we state necessary and sufficient conditions for orthogonality, aliasing cancellation and perfect reconstruction. The filter banks are realized by Chebychev polynomial approximations. Abstract We present a novel convolutional neural network (CNN) based pipeline which can effectively fuse multi-level information extracted from different intermediate layers generating hybrid convolutional features (HCF) for edge detection. Different from previous methods, the proposed method fuses multi-level information in a feature-map based manner. The produced hybrid convolutional features can be used to perform high-quality edge detection. The edge detector is also computationally efficient, because it detects edges in an image-to-image way without any post-processing. We evaluate the proposed method on three widely used datasets for edge detection including BSDS500, NYUD and Multicue, and also test the method on Pascal VOC’12 dataset for object contour detection. The results show that HCF achieves an improvement in performance over the state-of-the-art methods on all four datasets. On BSDS500 dataset, the efficient version of the proposed approach achieves ODS F-score of 0.804 with a speed of 22 fps and the high-accuracy version achieves ODS F-score of 0.814 with 11 fps . Edge detection is a fundamental problem in computer vision. Recently, convolutional neural networks (CNNs) have pushed forward this field significantly. Existing methods which adopt specific layers of deep CNNs may fail to capture complex data structures caused by variations of scales and aspect ratios. In this paper, we propose an accurate edge detector using richer convolutional features (RCF). RCF encapsulates all convolutional features into more discriminative representation, which makes good usage of rich feature hierarchies, and is amenable to training via backpropagation. RCF fully exploits multiscale and multilevel information of objects to perform the image-to-image prediction holistically. Using VGG16 network, we achieve state-of-the-art performance on several available datasets. When evaluating on the well-known BSDS500 benchmark, we achieve ODS F-measure of 0.811 while retaining a fast speed (8 FPS). Besides, our fast version of RCF achieves ODS F-measure of 0.806 with 30 FPS. We also demonstrate the versatility of the proposed method by applying RCF edges for classical image segmentation.