GDLS-D: two-stage medical surface reconstruction via geometric diffusion least squares and iterative deformation optimization.

Surface representations of anatomical structures are crucial for medical applications including preoperative planning and biomechanical simulations, yet current methods face challenges from limited datasets and staircase artifacts. This study proposes a training-free two-stage optimization framework for accurate 3D reconstruction. First, a method named geometric diffusion least squares is proposed to generate the template which is homeomorphic to the anatomical structure. Second, the template mesh is iteratively refined through continuous mesh deformation to obtain the final optimal result. Evaluations on liver, ilium, and vertebrae achieved bi-directional chamfer distances (L1 norm) of 3.675 mm, 2.654 mm, and 2.508 mm, respectively. Compared to state-of-the-art deep learning methods (Voxel2Mesh and MeshDeformNet), our approach improves average accuracy by 33.11% across three metrics, effectively suppressed staircase artifacts, and demonstrated promising generalization across anatomical structures. While traditional methods yield better accuracy metrics due to overfitting to mask boundaries, our method produces watertight meshes with significantly lower aspect ratios and no staircase artifacts. The proposed framework overcomes current limitations, offering a precise, generalizable solution for surface reconstruction of volumetric medical images.