  Medical image segmentation, which aims to automatically extract anatomical or
pathological structures, plays a key role in computer-aided diagnosis and
disease analysis. Despite the problem has been widely studied, existing methods
are prone to topological errors. In medical imaging, the topology of the
structure, such as the kidney or lung, is usually known. Preserving the
topology of the structure in the segmentation process is of utmost importance
for accurate image analysis. In this work, a novel learning-based segmentation
model is proposed. A {\it topology-preserving segmentation network (TPSN)} is
trained to give an accurate segmentation result of an input image that
preserves the prescribed topology. TPSN is a deformation-based model that
yields a deformation map through a UNet, which takes the medical image and a
template mask as inputs. The main idea is to deform a template mask describing
the prescribed topology by a diffeomorphism to segment the object in the image.
The topology of the shape in the template mask is well preserved under the
diffeomorphic map. The diffeomorphic property of the map is controlled by
introducing a regularization term related to the Jacobian in the loss function.
As such, a topology-preserving segmentation result can be guaranteed.
Furthermore, a multi-scale TPSN is developed in this paper that incorporates
multi-level information of images to produce more precise segmentation results.
To evaluate our method, we applied the 2D TPSN on Ham10000 and 3D TPSN on
KiTS21. Experimental results illustrate our method outperforms the baseline
UNet segmentation model with/without connected-component analysis (CCA) by both
the dice score and IoU score. Besides, results show that our method can produce
reliable results even in challenging cases, where pixel-wise segmentation
models by UNet and CCA fail to obtain accurate results.
