  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.
