Curvilinear object segmentation is critical for many applications. However, manually annotating curvilinear objects is very time-consuming and error-prone, yielding insufficiently available annotated datasets for existing supervised methods and domain adaptation methods. This paper proposes a self-supervised curvilinear object segmentation method that learns robust and distinctive features from fractals and unlabeled images (FreeCOS). The key contributions include a novel Fractal-FDA synthesis (FFS) module and a geometric information alignment (GIA) approach. FFS generates curvilinear structures based on the parametric Fractal L-system and integrates the generated structures into unlabeled images to obtain synthetic training images via Fourier Domain Adaptation. GIA reduces the intensity differences between the synthetic and unlabeled images by comparing the intensity order of a given pixel to the values of its nearby neighbors. Such image alignment can explicitly remove the dependency on absolute intensity values and enhance the inherent geometric characteristics which are common in both synthetic and real images. In addition, GIA aligns features of synthetic and real images via the prediction space adaptation loss (PSAL) and the curvilinear mask contrastive loss (CMCL). Extensive experimental results on four public datasets, i.e., XCAD, DRIVE, STARE and CrackTree demonstrate that our method outperforms the state-of-the-art unsupervised methods, self-supervised methods and traditional methods by a large margin. The source code of this work is available at https://github.com/TY-Shi/FreeCOS.

翻译：曲线物体分割对许多应用至关重要。然而，人工标注曲线物体非常耗时且易出错，导致现有监督方法和域适应方法可用的标注数据集不足。本文提出了一种自监督曲线物体分割方法，该方法从分形和未标注图像中学习鲁棒且独特的特征（FreeCOS）。关键贡献包括一个新颖的Fractal-FDA合成（FFS）模块和几何信息对齐（GIA）方法。FFS基于参数化分形L系统生成曲线结构，并通过傅里叶域适应将生成的结构集成到未标注图像中，从而获得合成训练图像。GIA通过比较给定像素的强度顺序与其邻近像素的值，减少合成图像与未标注图像之间的强度差异。这种图像对齐能显式消除对绝对强度值的依赖，并增强合成图像与真实图像共有的固有几何特征。此外，GIA通过预测空间适应损失（PSAL）和曲线掩膜对比损失（CMCL）对齐合成与真实图像的特征。在XCAD、DRIVE、STARE和CrackTree四个公开数据集上的大量实验结果表明，我们的方法大幅优于现有的无监督方法、自监督方法和传统方法。本工作的源代码已在https://github.com/TY-Shi/FreeCOS公开。