We introduce cut-cell skinning, a geometric prior designed to augment data-driven skinning weight generation. While data-driven methods show promise in producing high-quality skinning weights, they often lack the generalizability of classic geometric approaches. To bridge this gap, we propose a geometric prior that can be robustly computed for in-the-wild meshes and is efficient for large-scale machine learning workflows. The key idea of our cut-cell skinning is a fast graph-based approximation of the volumetric geodesics distances, motivated by their importance in classic skinning weight computation. Our method achieves orders of magnitude speedup compared to optimization-based solvers and remains resilient to topological artifacts common in cage- or voxel-based alternatives. We demonstrate the efficacy of the cut-cell skinning prior by integrating it into recent neural skinning models, showing consistent improvements across existing methods and achieving state-of-the-art results. Project page: https://wenchao-m.github.io/CutCell.github.io/
Medical image segmentation is a crucial task in the field of clinical analysis and applications. Though deep learning techniques recently play a crucial role in several scenarios, the training at the individual pixel level leads to a lack of geometric prior information. Scholars proposed to integrate the Chan-Vese model into the loss function for training which can take into account the region and length of the region inside and outside the segmentation process and then improve the performance in medical image segmentation. However, these methods still lack an effective characterization of the segmented region. To overcome this problem, we introduce the mean curvature as a geometric natural constraint and propose a Deep Active Contour and Mean Curvature (DACMC) loss function where the convolution kernel is used to approximate the mean curvature to save computational cost. We have validated the performance of our method on the liver and spleen dataset. Our proposed method demonstrates new state-of-the-art performance on several segmentation datasets.