Geometry-Aware Tumor Classification via Mean Curvature Flow on 3D Surface Meshes

Abstract

This study presents a geometry-aware framework for binary tumor classification based on mean curvature flow (MCF) applied to reconstructed 3D surface meshes. Segmented medical image slices are converted into surface meshes and evolved under MCF. During the evolution, geometric descriptors, including quasi-conformal ratio, radial variance, and evolution speed, are extracted and concatenated into feature vectors. These descriptors are used with standard vector-based machine learning models for classification. Experimental results indicate that the proposed pipeline achieves competitive performance compared to a 3D CNN while providing practical advantages in terms of efficiency and structural interpretability.