  Edge detection is a fundamental problem in different computer vision tasks.
Recently, edge detection algorithms achieve satisfying improvement built upon
deep learning. Although most of them report favorable evaluation scores, they
often fail to accurately localize edges and give thick and blurry boundaries.
In addition, most of them focus on 2D images and the challenging 3D edge
detection is still under-explored. In this work, we propose a novel logical
refinement network for crisp edge detection, which is motivated by the logical
relationship between segmentation and edge maps and can be applied to both 2D
and 3D images. The network consists of a joint object and edge detection
network and a crisp edge refinement network, which predicts more accurate,
clearer and thinner high quality binary edge maps without any post-processing.
Extensive experiments are conducted on the 2D nuclei images from Kaggle 2018
Data Science Bowl and a private 3D microscopy images of a monkey brain, which
show outstanding performance compared with state-of-the-art methods.
