Algebraic Sphere Surface Fitting for Accurate and Efficient Mesh Reconstruction from Cine CMR Images

Accurate 3D modeling of the ventricles through cine cardiovascular magnetic resonance (CMR) imaging benefits precise clinical assessment of cardiac morphology and motion. However, the existing short-axis stacks exhibit low spatial resolution in the inter-slice orientation compared to the intra-slice direction, resulting in a sparse representation of the realistic heart. The anisotropic short-axis images pose challenges in directly reconstructing meshes from them. In this work, we propose a surface fitting approach based on the algebraic sphere, which serves as a previous step for various mesh-based applications, to reconstruct a natural ventricular shape from the segmented wireframe-type point cloud. Considering the sparse and layered nature of the point clouds, we first estimate the normals of the point cloud based on dynamic programming and neighborhood selection, followed by fitting a point set surface using a non-compact kernel adapted by layers. Finally, an implicit scalar field representing the signed distance between the query point and the projection point is obtained, and the manifold mesh is extracted by meshing zero iso-surface. Experimental results on two publicly available datasets demonstrate that the proposed framework can accurately and effectively reconstruct ventricular mesh from a single image with better cross-domain generalizability.