Model-Guided 3D Cranial Open Surface Reconstruction Based on Euler’s Elastica and Optimal Transport

Cranial reconstruction is a key technology in fields such as forensic science and archaeology. However, existing methods still face two major challenges for reconstructing a high-genus cranial open surface from computed tomography (CT) scan data: the inaccurate segmentation of complex anatomical structures, and the insufficient fidelity, which is often accompanied by loss of detail and topological errors. In this paper, we propose a cranial open surface reconstruction framework that fuses Optimal Transport (OT) theory and Unsigned Distance Fields (UDF). In the segmentation stage, we designed a novel segmentation network (EGCA-Net) that combines a graph convolutional attention mechanism (GCAM) and variational theory. This network utilizes graph convolution to capture global long-range dependencies and introduces a loss function based on Euler’s Elastica model as a geometric constraint, significantly improving the smoothness and anatomical accuracy of the segmentation results. In the reconstruction stage, we sample point clouds from the precise segmentation results and propose an enhanced unsigned distance field learning strategy. This strategy, by introducing OT-based geometric regularization and a projection consistency constraint, combined with an advanced surface extraction algorithm, can generate high-fidelity 3D mesh models that are topologically accurate and rich in detail. Experimental results demonstrate that our framework exhibits significant advantages in both segmentation accuracy and reconstruction quality, achieving excellent results in Cranial Open Surface reconstruction.