We present a differentiable model that explicitly models boundaries --
including contours, corners and junctions -- using a new mechanism that we call
boundary attention. We show that our model provides accurate results even when
the boundary signal is very weak or is swamped by noise. Compared to previous
classical methods for finding faint boundaries, our model has the advantages of
being differentiable; being scalable to larger images; and automatically
adapting to an appropriate level of geometric detail in each part of an image.
Compared to previous deep methods for finding boundaries via end-to-end
training, it has the advantages of providing sub-pixel precision, being more
resilient to noise, and being able to process any image at its native
resolution and aspect ratio.

我们提出了一个可微分模型，用于明确地建模边界，包括轮廓、角点和交叉点，并使用我们称之为边界注意力的新机制。我们展示了即使边界信号非常弱或被噪声淹没，我们的模型也能提供准确的结果。与找到微弱边界的先前经典方法相比，我们的模型具有可微的优势，适用于更大的图像，并自动适应图像每个部分的适当几何细节水平。与通过端到端训练找到边界的先前深度方法相比，它具有提供亚像素精度、更具噪声鲁棒性以及能够以原生分辨率和长宽比处理任何图像的优势。

边界注意力：学习在任何分辨率下找到微弱的边界

Boundary Attention: Learning to Find Faint Boundaries at Any Resolution

Accurate detection and localization of X-corner on both planar and non-planar
patterns is a core step in robotics and machine vision. However, previous works
could not make a good balance between accuracy and robustness, which are both
crucial criteria to evaluate the detectors performance. To address this
problem, in this paper we present a novel detection algorithm which can
maintain high sub-pixel precision on inputs under multiple interference, such
as lens distortion, extreme poses and noise. The whole algorithm, adopting a
coarse-to-fine strategy, contains a X-corner detection network and three
post-processing techniques to distinguish the correct corner candidates, as
well as a mixed sub-pixel refinement technique and an improved region growth
strategy to recover the checkerboard pattern partially visible or occluded
automatically. Evaluations on real and synthetic images indicate that the
presented algorithm has the higher detection rate, sub-pixel accuracy and
robustness than other commonly used methods. Finally, experiments of camera
calibration and pose estimation verify it can also get smaller re-projection
error in quantitative comparisons to the state-of-the-art.

本文提出了一种新的检测算法，能够在多种干扰条件下保持高次像素精度，包括镜头畸变、极端姿态和噪声。该算法基于粗到细的策略，包含 X 型角检测网络和三种后处理技术，以及混合亚像素细化技术和改进的区域增长策略。实验证明，与其他常用方法相比，该算法具有更高的检测率、亚像素精度和鲁棒性。最后，相机标定和姿态估计实验也验证了其在定量比较中能够获得更小的重投影误差。