3D Geometric Tooth Alignment Planning via Deep Reinforcement Learning

3D geometric tooth alignment planning, which determines sequential trajectories from initial malocclusion to the final target alignment, is a cornerstone of modern digital orthodontics. This paper presents a novel deep reinforcement learning (DRL) framework to automate the generation of these alignment paths. We formulate the planning process as a Markov Decision Process (MDP) to capture its sequential decision-making nature, focusing on optimizing geometric trajectories while integrating essential spatial constraints, such as inter-dental collision avoidance and path efficiency. The proposed method leverages the Deep Deterministic Policy Gradient (DDPG) algorithm, enhanced by three key innovations: (1) a Transformer-based agent to model complex spatial interactions between teeth and manage high-dimensional state-action spaces; (2) a dynamic masking scheme that restricts movement to a sparse subset of teeth per step, better reflecting the clinical logic of sequential alignment; and (3) a two-stage curriculum learning strategy that gradually increases task difficulty to ensure training stability and efficient path discovery. We evaluate our approach on a dataset of 10K expert-designed treatment plans based on clinical data. Experimental results demonstrate that our method outperforms existing baselines in terms of path safety and geometric efficiency, providing a robust and automated solution for 3D geometric orthodontic alignment planning.