### Related Works  
A considerable number of frameworks aim at addressing the tooth segmentation task in 3D surface scans [3; 4; 5; 6; 7]. Research in this line mainly utilizes point cloud representation (point based), frequently combined with graph learning techniques (graph based). Instead of relying on PointNet [8] or PointNet++ [9], which are agnostic to capturing local geometric contexts, researchers often introduce more complex and sophisticated methods. One example is MeshSegNet [3], where the authors propose a dense fusion strategy to combine local-to-global geometric features for mesh cell labeling. Although it provides promising results in simple cases, its performance in real-world orthodontic scenarios remains uncertain since the evaluation was conducted on a dataset with restricted variability and complexity. Furthermore, the method relies on a Graph Cut-based refinement process sensitive to parameter tuning. Another point-based method, TSegNet [4], follows a detect-and-segment approach, enabling the localized segmentation of teeth masks. Its limitation lies in the fact that the detection module identifies tooth centroids, which are not very intuitive to adjust by clinicians. Consequently, any inaccuracies in the detection step leave no room for intermediate corrections and can lead to substantial errors in the segmented teeth masks. This leads to more labor-intensive refinements of the segmentation masks. The works discussed in references [6; 7] represent notable efforts towards clinically applicable solutions that do not rely on a large-scale annotated dataset. They achieve this by introducing self-supervision techniques and training with weak annotations. These detect-and-segment solutions demonstrate the feasibility of utilizing highly accurate detectors to significantly enhance the performance of segmentation networks. As aforementioned papers, they are homogeneous in terms of point cloud utilization. Two projection-based approaches have emerged in the literature [10; 11]. The method referenced in [10] encodes dental mesh into a plan view and panoramic depth image. It relies on hand-crafted feature engineering rather than employing a deep learning framework. In [11], the authors propose a deep learning approach, where each mesh face is encoded into a feature vector of geometric attributes. Each such descriptor is converted into a 2D feature map, an input to a 2D CNN. Since each encoded face is processed separately and the method relies on optimization algorithms, it is computationally heavy, which may present challenges in practical real-time applications. Additionally, the spatial relationships within these maps can be challenging to exploit by 2D convolutions, as the values are not inherently spatially correlated. Projection-based frameworks benefit from the well-explored field of 2D CNNs and are usually very efficient in training and inference speed. To widen the research field with a well-designed projection method, it begs the following question: could a projection-based method be on par with or even outperform 3D geometric approaches in robust mesh teeth segmentation? A common characteristic among all the teeth segmentation frameworks discussed is the unavailability of publicly released data. Consequently, any attempt to compare these methods lacks complete fairness, making it unclear which approach stands out as superior. Another common attribute is the heavy downsampling of the input point cloud, losing important anatomical features captured in the fine geometric details. In this work, we propose a projection-based method that does not need any mesh decimation and effectively builds upon the detect-and-segment idea. Opposite to previous projection-based approaches, we represent the 3D shape as a sequence of 2D maps that locally encode the depth and geometry of each tooth in a form, where functional proximity coincides with physical proximity, which introduces an important inductive bias to 2D learning.