Edge detection is a fundamental task in computer vision. It has made great progress under the development of deep convolutional neural networks (DCNNs), some of which have achieved a beyond human-level performance. However, recent top-performing edge detection methods tend to generate thick and noisy edge lines. In this work, we solve this problem from two aspects: (1) leveraging the precise edge pixel location characteristics of second-order image derivatives, and (2) alleviating the issue of imbalanced pixel distribution. We propose a second-order derivative-based multi-scale contextual enhancement module (SDMC) to help the model locate true edge pixels accurately and construct a hybrid focal loss function (HFL) to alleviate the imbalanced distribution issue. We test our method on three standard benchmarks and the experiment results illustrate that our method can make the output edge maps crisp and achieves a top performance among several state-of-the-art methods on the BSDS500 dataset (ODS F-score in standard evaluation is 0.829, in crispness evaluation is 0.720), NYUD-V2 dataset (ODS F-score in standard evaluation is 0.768, in crispness evaluation is 0.546), and BIPED dataset (ODS F-score in standard evaluation is 0.903).

翻译：边缘检测是计算机视觉中的一项基础任务。在深度卷积神经网络（DCNNs）发展的推动下，该领域已取得巨大进展，其中一些方法甚至超越了人类水平。然而，近期表现最优的边缘检测方法往往生成较粗且含有噪声的边缘线。本工作从两个方面解决此问题：（1）利用图像二阶导数所具备的精确定位边缘像素的特性；（2）缓解像素分布不均衡的问题。我们提出了一个基于二阶导数的多尺度上下文增强模块（SDMC），以帮助模型准确定位真实边缘像素，并构建了一个混合焦点损失函数（HFL）来缓解分布不均衡问题。我们在三个标准基准数据集上测试了我们的方法，实验结果表明，我们的方法能够使输出的边缘图变得清晰，并在多个最先进方法中取得了领先的性能，具体表现在：BSDS500数据集（标准评估中的ODS F分数为0.829，清晰度评估中为0.720）、NYUD-V2数据集（标准评估中的ODS F分数为0.768，清晰度评估中为0.546）以及BIPED数据集（标准评估中的ODS F分数为0.903）。