As intracranial aneurysms (IAs) are potentially fatal vascular abnormalities that can lead to severe strokes, their accurate segmentation from acquired imaging data is essential for diagnosis and treatment planning. Current automatic IA segmentation methods predominantly focus on directly processing medical images, whereas research exploring approaches beyond image-based modalities is limited. To address this gap, we propose Medical Diffusion Network (MedDiffusionNet), a novel segmentation network incorporating geometric deep learning, designed to directly work on three-dimensional mesh models of aneurysms. The core of MedDiffusionNet comprises multiple diffusion blocks grounded in the heat diffusion equation, which enable efficient information propagation on graphs. By incorporating learnable diffusion time and gradient features, MedDiffusionNet performs frequency-domain convolution with an adaptive receptive field. Notably, this architecture aligns with the geometric properties of vascular aneurysm models, allowing MedDiffusionNet to learn a powerful nonlinear mapping from the feature space onto the label space on the associated mesh. We validate MedDiffusionNet on an extremely imbalanced dataset reconstructed from data acquired through multiple imaging modalities. Experimental results show that MedDiffusionNet outperforms eight state-of-the-art networks in IA segmentation, accurately delineating IA boundaries across diverse vascular shapes and sizes. Moreover, our network achieves higher values of the associated intersection over union and Dice similarity coefficient while maintaining geometric consistency with the ground truths.

We present an effective spectral matching method based on a shape association graph for finding region correspondences between two cel animation keyframes. We formulate the correspondence problem as an adapted quadratic assignment problem, which comprehensively considers both the intrinsic geometric and topology of regions to find the globally optimal correspondence. To simultaneously represent the geometric and topological similarities between regions, we propose a shape association graph (SAG), whose node attributes indicate the geometric distance between regions, and whose edge attributes indicate the topological distance between combined region pairs. We convert topological distance to geometric distance between geometric objects with topological features of the pairs, and introduce Kendall shape space to calculate the intrinsic geometric distance. By utilizing the spectral properties of the affinity matrix induced by the SAG, our approach can efficiently extract globally optimal region correspondences, even if shapes have inconsistent topology and severe deformation. It is also robust to shapes undergoing similarity transformations, and compatible with parallel computing techniques.