  Understanding body part geometry is crucial for precise medical diagnostics.
Curves effectively describe anatomical structures and are widely used in
medical imaging applications related to cardiovascular, respiratory, and
skeletal diseases. Traditional curve detection methods are often task-specific,
relying heavily on domain-specific features, limiting their broader
applicability. This paper introduces a novel approach for detecting
non-branching curves, which does not require prior knowledge of the object's
orientation, shape, or position. Our method uses neural networks to predict (1)
an attraction field, which offers subpixel accuracy, and (2) a closeness map,
which limits the region of interest and essentially eliminates outliers far
from the desired curve. We tested our curve detector on several clinically
relevant tasks with diverse morphologies and achieved impressive subpixel-level
accuracy results that surpass existing methods, highlighting its versatility
and robustness. Additionally, to support further advancements in this field, we
provide our private annotations of aortic centerlines and masks, which can
serve as a benchmark for future research. The dataset can be found at
https://github.com/neuro-ml/curve-detection.
