Deep learning has been used as a powerful tool for various tasks in computer vision, such as image segmentation, object recognition and data generation. A key part of end-to-end training is designing the appropriate encoder to extract specific features from the input data. However, few encoders maintain the topological properties of data, such as connection structures and global contours. In this paper, we introduce a Voronoi Diagram encoder based on convex set distance (CSVD) and apply it in edge encoding. The boundaries of Voronoi cells is related to detected edges of structures and contours. The CSVD model improves contour extraction in CNN and structure generation in GAN. We also show the experimental results and demonstrate that the proposed model has great potentiality in different visual problems where topology information should be involved.
Data-driven approaches for edge detection have proven effective and achieve top results on modern benchmarks. However, all current data-driven edge detectors require manual supervision for training in the form of hand-labeled region segments or object boundaries. Specifically, human annotators mark semantically meaningful edges which are subsequently used for training. Is this form of strong, highlevel supervision actually necessary to learn to accurately detect edges? In this work we present a simple yet effective approach for training edge detectors without human supervision. To this end we utilize motion, and more specifically, the only input to our method is noisy semi-dense matches between frames. We begin with only a rudimentary knowledge of edges (in the form of image gradients), and alternate between improving motion estimation and edge detection in turn. Using a large corpus of video data, we show that edge detectors trained using our unsupervised scheme approach the performance of the same methods trained with full supervision (within 3-5 ). Finally, we show that when using a deep network for the edge detector, our approach provides a novel pre-training scheme for object detection. Contour detection has been a fundamental component in many image segmentation and object detection systems. Most previous work utilizes low-level features such as texture or saliency to detect contours and then use them as cues for a higher-level task such as object detection. However, we claim that recognizing objects and predicting contours are two mutually related tasks. Contrary to traditional approaches, we show that we can invert the commonly established pipeline: instead of detecting contours with low-level cues for a higher-level recognition task, we exploit object-related features as high-level cues for contour detection.  The author investigated automatic extraction of left ventricular contours from cardiac magnetic resonance imaging (MRI) studies. The contour extraction algorithms were based on active contour models, or snakes. Based on cardiac MR image characteristics, the author suggested algorithms for extracting contours from these large data sets. The author specifically considered contour propagation methods to make the contours reliable enough despite noise, artifacts, and poor temporal resolution. The emphasis was on reliable contour extraction with a minimum of user interaction. Both spin echo and gradient echo studies were considered. The extracted contours were used for determining quantitative measures for the heart and could also be used for obtaining graphically rendered cardiac surfaces. >  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. This paper describes a computational approach to edge detection. The success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points. These goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution. We define detection and localization criteria for a class of edges, and present mathematical forms for these criteria as functionals on the operator impulse response. A third criterion is then added to ensure that the detector has only one response to a single edge. We use the criteria in numerical optimization to derive detectors for several common image features, including step edges. On specializing the analysis to step edges, we find that there is a natural uncertainty principle between detection and localization performance, which are the two main goals. With this principle we derive a single operator shape which is optimal at any scale. The optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a Gaussian-smoothed image. We extend this simple detector using operators of several widths to cope with different signal-to-noise ratios in the image. We present a general method, called feature synthesis, for the fine-to-coarse integration of information from operators at different scales. Finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge. 