We introduce a bottom-up model for jointly finding many boundary elements in an image, including edges, curves, corners and junctions. The model explains boundary shape in each small patch using a junction with M angles and a freely-moving vertex. Images are analyzed by solving a non-convex optimization problem using purposefully-designed algorithms, cooperatively finding M+2 junction values at every pixel. The resulting field of junctions is simultaneously an edge detector, a corner/junction detector, and a boundary-aware smoothing of regional appearance. We demonstrate how it behaves at different scales, and for both single-channel and multi-channel input. Notably, we find it has unprecedented resilience to noise: It succeeds at high noise levels where previous methods for segmentation and for edge, corner and junction detection fail.

该论文提出了一种自下而上的模型，用于同时找到图像中的许多边界元素，包括轮廓、角落和交点，并使用广义M形交将每个小区域的边界形状进行解释。通过非凸优化，使用一种新颖的正则化器对每个位置的M+2个交点值进行协同查找，同时在保留角落和交点的同时减少曲率，从而强制施加空间一致性。整个过程是同时进行轮廓检测、角/交点检测和区域外观的边界感知平滑，而其对轮廓、角落、交点和均匀区域的统一分析使其在高噪声水平下成功，而其他分割和边界检测方法则失败。

低信噪比条件下提取交界区域结构