  Tooth segmentation is a pivotal step in modern digital dentistry, essential
for applications across orthodontic diagnosis and treatment planning. Despite
its importance, this process is fraught with challenges due to the high noise
and low contrast inherent in 2D and 3D tooth data. Both Convolutional Neural
Networks (CNNs) and Transformers has shown promise in medical image
segmentation, yet each method has limitations in handling long-range
dependencies and computational complexity. To address this issue, this paper
introduces T-Mamba, integrating frequency-based features and shared
bi-positional encoding into vision mamba to address limitations in efficient
global feature modeling. Besides, we design a gate selection unit to integrate
two features in spatial domain and one feature in frequency domain adaptively.
T-Mamba is the first work to introduce frequency-based features into vision
mamba, and its flexibility allows it to process both 2D and 3D tooth data
without the need for separate modules. Also, the TED3, a large-scale public
tooth 2D dental X-ray dataset, has been presented in this paper. Extensive
experiments demonstrate that T-Mamba achieves new SOTA results on a public
tooth CBCT dataset and outperforms previous SOTA methods on TED3 dataset. The
code and models are publicly available at: https://github.com/isbrycee/T-Mamba.
