Point cloud denoising is a fundamental yet challenging task in computer graphics. Existing solutions typically rely on supervised training on synthesized noise. However, real-world noise often exhibits greater complexity, causing learning-based methods trained on synthetic noise to struggle when encountering unseen noise-a phenomenon we refer to as noise misalignment. To address this challenge, we propose LaPDA (Latent-space Point cloud Denoising with Adaptivity), a neural network explicitly designed to mitigate noise misalignment and enhance denoising robustness. LaPDA consists of two key stages. First, we adaptively model noise in the latent space, aligning unseen noise distributions with the known training distributions or adjusting them toward distributions with lower noise scales. Training objectives at this stage are formulated based on controlled synthetic noise with varying intensity levels. Second, we introduce a gradual noise removal module that optimizes the spatial distribution of the adaptively adjusted noisy points. Extensive experiments conducted on both synthetic and scanned datasets demonstrate that LaPDA achieves enhanced accuracy and robustness compared to state-of-the-art methods.

Intracranial aneurysms (IAs) pose a significant risk due to their potential to rupture, leading to severe clinical outcomes. Accurate quantification of aneurysm morphology and assessment of rupture risk are crucial for timely intervention and treatment. In this study, we present an approach for the geometric quantification of IAs and clinical rupture risk evaluation based on the relationship between these measurements. Our approach includes a comprehensive set of geometric characteristics, such as height, width, neck width, arterial diameter, area, and volume. We applied these measurements to the public IntrA dataset, and to our knowledge, this is the first geometric analysis conducted on this dataset. By integrating these morphological characteristics with expert assessments, we developed a predictive model for IA rupture risk. Our findings reveal a strong correlation between aneurysm depth and rupture risk, with even stronger associations observed for higher-order dimension metrics like surface area and volume. This highlights the critical role of 3D automatic quantification in evaluating rupture risk. This research provides a foundation for further geometric analysis of IAs and offers potential advancements in automated diagnostics and precision medicine.

Accurate segmentation of cerebral aneurysms from 3D vessel meshes is an essential yet challenging task, complicated by diverse imaging modalities that produce multi-resolution representations. Existing methods often struggle to handle meshes of varying granularity and orientations while maintaining segmentation accuracy. In this paper, we propose an end-to-end multi-scale graph-based segmentation framework that incorporates SE(3)-equivariance and an uncertainty-aware loss function. Our approach constructs a multi-scale graph representation on the 3D mesh and leverages a self-attention mechanism over graph edges to achieve adaptive neighborhood awareness, enabling the network to effectively handle multiple mesh resolutions simultaneously. By introducing an SE(3)-equivariant backbone, rotational variations in aneurysm orientation are naturally accommodated, ensuring relevant and effective feature learning. Furthermore, we develop an uncertainty-aware loss that adaptively emphasizes ambiguous regions, improving segmentation quality and confidence. Experimental results on the public datasets IntrA demonstrate that our method outperforms existing techniques, offering improved accuracy, consistency and stability across different mesh resolutions for 3D aneurysm segmentation. Code is available on https://github.com/Dolphin4mi/se3meshseg.

A fast and fully automatic design of 3D cranial implants is highly desired in cranioplasty, and is key to the treatment of skull trauma. We have defined the repair of skull defects as a 3D shape completion task by proposing a two-stage diffusion model based on the representation of 3D shapes using signed distance function (SDF). Specifically, we design a diffusion model conditioned on partial shapes, we compress the 3D shape into a compact latent representation using the encoder in the vector quantized variational autoencoder (VQ-VAE) and learn the diffusion model based on this compressed discrete representation. Encoding the latent space with the autoencoder can achieve high-quality 3D cranial shape completion. In order to accurately capture local and fine-grained shape details, the training data is geometrically encoded from a compactly learned code-book. The two-stage diffusion generator with a coarse-to-fine approach possesses precise and expressive structural modeling capabilities to ensure the supplementation of detailed geometric information. Experimental results verified sufficient expressiveness of our model with generating high-fidelity results with fine-grained local details, outperforming the state-of-the-art methods.

Unsupervised learning-based action recognition methods have shown immense potential by leveraging vast amounts of unlabeled data, yielding competitive performance in action recognition tasks. To capture semantic information in action, many efforts have focused on multi-stream fusion techniques, which makes the models heavier and less flexible to train. However, existing single-stream methods struggle to provide rich semantic information through data augmentation. To address these challenges, we propose a novel joint-level semantic augmentation method based on a constructed motion manifold, which achieves significant performance gains with virtually no additional training costs. Our approach introduces random perturbations on the motion manifold constructed based on evolutionary metrics. We propose several semantic augmentation strategies, including directional semantic perturbations, magnitude semantic perturbations, and initial pose perturbations. To pay greater attention to samples with significant semantic differences, we introduce the Semantic Adaptive Weighted Loss (SAWL) based on motion manifold distance. SAWL encourages the model to pay more attention to these samples, leading to the learning of an embedding space with semantic invariance. Extensive experiments were conducted on three large-scale datasets, i.e., NTU-60, NTU-120, and PKU-MMD II. The results demonstrate that our single-stream approach, empowered by joint-level semantic augmentation, achieves state-of-the-art (SOTA) performance among single-stream methods and competitive performance among multi-stream methods.

3D human motion prediction is a challenging task due to the highly non-linear nature of movements. Existing deep learning-based action prediction methods emphasize the design of sophisticated network architectures to achieve state-of-the-art performance on datasets. However, in real-life scenarios, changes in skeletal size lead to a shift in data distribution, which presents challenges for accurate motion prediction. Additionally, the presence of stretching artifacts in predicted bone sequences significantly impacts the quality of the predictions. To address these issues, we propose a framework that combines geometric encoding with neural networks to achieve size-invariant and high-quality motion prediction without stretching artifacts. We consider the constraint of bone length and construct a motion space using Riemannian manifold theory, which remains unaffected by changes in skeletal size and can fully represent human motion. Furthermore, we propose the trajectory transport square-root velocity function to encode motion sequences into a flattened space. This transformation simplifies the distance calculation and linearizes the optimization problem in non-flattened space. Experiments on the Human 3.6M and CMU MoCap datasets demonstrated that the proposed method has achieved competitive performance without any stretching artifacts and exhibits robustness to changes in skeletal size.

Automatic detecting intracranial aneurysms (IAs) poses significant challenges due to their diversity, varying locations, and complex classifications by size, shape, and phenotype. Current shape-based IAs detection methods, while promising, often neglect the topological connectivity of IAs vertices and the variable traits of the aneurysm's neck, leading to fragmented detections. To address these issues, we present a mesh convolutional neural network based on gauge equivariant convolution to leverage the topological and geometric features of 3D mesh models. Our network comprises four key components: anisotropic message passing (AMP) on mesh surfaces, gauge equivariant convolution (GEC), vector-aware feature reconstruction (VFR), and a pooling-free convolutional architecture. AMP ensures accurate detection of IAs from surrounding vessels by utilizing topological connectivity and anisotropic relationships between mesh vertices. GEC offers rotational equivariance for consistently learning geometric features, improving feature learning stability and efficiency. VFR preserves the geometric and directional integrity of the vector features, enriching the representational capacity of the network. The pooling-free convolutional architecture captures local and global geometric nuances of 3D meshes, achieving precise IAs detection and producing sharper IAs boundaries. Tests on the IntrA dataset show our method outperforms the current best by 1.83% and 1.02% in mIoU and mDSC, respectively.

Traditional sign language teaching methods face challenges such as limited feedback and diverse learning scenarios. Although 2D resources lack reality sences, classroom teaching is constrained by a scarcity of teacher and methods based on VR and AR have relatively primitive interaction feedback mechanisms. This study proposes an innovative teaching model that uses real-time monocular vision and mixed reality technology. First, we introduce an improved hand-posture reconstruction method to achieve sign language semantic retention and real-time feedback. Second, a ternary system evaluation algorithm is proposed for a comprehensive assessment, maintaining good consistency with experts in sign language. Furthermore, we use mixed reality technology to construct a scenario-based 3D sign language classroom and explore the user experience of scenario teaching. Overall, this paper presents a novel teaching method that provides an immersive learning experience, advanced posture reconstruction, and precise feedback, achieving positive feedback on user experience and learning effectiveness.