Explicit Differentiable Slicing and Global Deformation for Cardiac Mesh Reconstruction

Mesh reconstruction of the cardiac anatomy from medical images is useful for shape and motion measurements and biophysics simulations to facilitate the assessment of cardiac function and health. However, 3D medical images are often acquired as 2D slices that are sparsely sampled and noisy, and mesh reconstruction on such data is a challenging task. Traditional voxel-based approaches rely on pre- and post-processing that compromises image fidelity, while mesh-level deep learning approaches require mesh annotations that are difficult to get. Therefore, direct cross-domain supervision from 2D images to meshes is a key technique for advancing 3D learning in medical imaging, but it has not been well-developed. While there have been attempts to approximate the optimized meshes' slicing, few existing methods directly use 2D slices to supervise mesh reconstruction in a differentiable manner. Here, we propose a novel explicit differentiable voxelization and slicing (DVS) algorithm that allows gradient backpropagation to a mesh from its slices, facilitating refined mesh optimization directly supervised by the losses defined on 2D images. Further, we propose an innovative framework for extracting patient-specific left ventricle (LV) meshes from medical images by coupling DVS with a graph harmonic deformation (GHD) mesh morphing descriptor of cardiac shape that naturally preserves mesh quality and smoothness during optimization. Experimental results demonstrate that our method achieves state-of-the-art performance in cardiac mesh reconstruction tasks from CT and MRI, with an overall Dice score of 90% on multi-datasets, outperforming existing approaches. The proposed method can further quantify clinically useful parameters such as ejection fraction and global myocardial strains, closely matching the ground truth and surpassing the traditional voxel-based approach in sparse images.

Differentiable Voxelization and Mesh Morphing

In this paper, we propose the differentiable voxelization of 3D meshes via the winding number and solid angles. The proposed approach achieves fast, flexible, and accurate voxelization of 3D meshes, admitting the computation of gradients with respect to the input mesh and GPU acceleration. We further demonstrate the application of the proposed voxelization in mesh morphing, where the voxelized mesh is deformed by a neural network. The proposed method is evaluated on the ShapeNet dataset and achieves state-of-the-art performance in terms of both accuracy and efficiency.