Abstract The synthesis of porous, lattice, or microstructure geometries has captured the attention of many researchers in recent years. Implicit forms, such as triply periodic minimal surfaces (TPMS) has captured a significant attention, recently, as tiles in lattices, partially because implicit forms have the potential for synthesizing with ease more complex topologies of tiles, compared to parametric forms. In this work, we show how variable offsets of implicit forms could be used in lattice design as well as lattice analysis, while graded wall and edge thicknesses could be fully controlled in the lattice and even vary within a single tile. As a result, (geometrically) heterogeneous lattices could be created and adapted to follow analysis results while maintaining continuity between adjacent tiles. We demonstrate this ability on several 3D models, including TPMS.

Abstract The synthesis of porous, lattice, or microstructure geometries has captured the attention of many researchers in recent years. Implicit forms, such as triply periodic minimal surfaces (TPMS) has captured a significant attention, recently, as tiles in lattices, partially because implicit forms have the potential for synthesizing with ease more complex topologies of tiles, compared to parametric forms. In this work, we show how variable offsets of implicit forms could be used in lattice design as well as lattice analysis, while graded wall and edge thicknesses could be fully controlled in the lattice and even vary within a single tile. As a result, (geometrically) heterogeneous lattices could be created and adapted to follow analysis results while maintaining continuity between adjacent tiles. We demonstrate this ability on several 3D models, including TPMS.

Enhancing the precision of segmenting coronary atherosclerotic plaques from CT Angiography (CTA) images is pivotal for advanced Coronary Atherosclerosis Analysis (CAA), which distinctively relies on the analysis of vessel cross-section images reconstructed via Curved Planar Reformation. This task presents significant challenges due to the indistinct boundaries and structures of plaques and blood vessels, leading to the inadequate performance of current deep learning models, compounded by the inherent difficulty in annotating such complex data. To address these issues, we propose a novel dual-consistency semi-supervised framework that integrates Intra-frame Topological Consistency (ITC) and Cross-frame Topological Consistency (CTC) to leverage labeled and unlabeled data. ITC employs a dual-task network for simultaneous segmentation mask and Skeleton-aware Distance Transform (SDT) prediction, achieving similar prediction of topology structure through consistency constraint without additional annotations. Meanwhile, CTC utilizes an unsupervised estimator for analyzing pixel flow between skeletons and boundaries of adjacent frames, ensuring spatial continuity. Experiments on two CTA datasets show that our method surpasses existing semi-supervised methods and approaches the performance of supervised methods on CAA. In addition, our method also performs better than other methods on the ACDC dataset, demonstrating its generalization.

We present a novel framework that enhances 3D Gaussian Splatting (3DGS) with improved computational efficiency and relighting capabilities through probabilistic optimization. While 3DGS enables real-time, high-quality scene reconstruction and rendering, it remains limited to static lighting environments and suffers from redundancy due to millions of Gaussians. To address these limitations, we introduce a Markov Chain Monte Carlo (MCMC)-based approach that adaptively prunes redundant Gaussians while preserving critical details. Our contributions include MCMC-based adaptive thresholding, surface normal learning for realistic shading under dynamic lighting, and gradient-guided light sampling via the Metropolis-Adjusted Langevin Algorithm (MALA). Experimental results demonstrate that our proposed method achieves significant memory reduction and faster convergence, enabling real-time relighting with fewer Gaussian primitives.

Enhancing the precision of segmenting coronary atherosclerotic plaques from CT Angiography (CTA) images is pivotal for advanced Coronary Atherosclerosis Analysis (CAA), which distinctively relies on the analysis of vessel cross-section images reconstructed via Curved Planar Reformation. This task presents significant challenges due to the indistinct boundaries and structures of plaques and blood vessels, leading to the inadequate performance of current deep learning models, compounded by the inherent difficulty in annotating such complex data. To address these issues, we propose a novel dual-consistency semi-supervised framework that integrates Intra-frame Topological Consistency (ITC) and Cross-frame Topological Consistency (CTC) to leverage labeled and unlabeled data. ITC employs a dual-task network for simultaneous segmentation mask and Skeleton-aware Distance Transform (SDT) prediction, achieving similar prediction of topology structure through consistency constraint without additional annotations. Meanwhile, CTC utilizes an unsupervised estimator for analyzing pixel flow between skeletons and boundaries of adjacent frames, ensuring spatial continuity. Experiments on two CTA datasets show that our method surpasses existing semi-supervised methods and approaches the performance of supervised methods on CAA. In addition, our method also performs better than other methods on the ACDC dataset, demonstrating its generalization.

Deep neural networks (DNNs) face substantial challenges in Long-Tail Visual Recognition (LTVR) due to the inherent class imbalances in real-world data distributions. The Mixture of Experts (MoE) framework has emerged as a promising approach to addressing these issues. However, in MoE systems, experts are typically trained to optimize a collective objective, often neglecting the individual optimality of each expert. This individual optimality usually contributes to the overall performance, as the goals of different experts are not mutually exclusive. We propose the Independent and Collaborative Learning (ICL) framework to optimize each expert independently while ensuring global optimality. First, Diverse Optimization Learning (DOL) is introduced to enhance expert diversity and individual performance. Then, we conceptualize experts as parallel circuit branches and introduce Competition and Collaboration Learning (CoL). Competition Learning amplifies the gradients of better-performing experts to preserve individual optimality, and Collaboration Learning encourages collaboration through mutual distillation to enhance optimal knowledge sharing. ICL achieves state-of-the-art accuracy in experiments on CIFAR-100/10-LT, ImageNet-LT, and iNaturalist 2018, respectively. Our code is available at https://github.com/PolarisLight/ICL.

The synthesis of porous, lattice, or microstructure geometries has captured the attention of many researchers in recent years. Implicit forms, such as triply periodic minimal surfaces (TPMS) has captured a significant attention, recently, as tiles in lattices, partially because implicit forms have the potential for synthesizing with ease more complex topologies of tiles, compared to parametric forms. In this work, we show how variable offsets of implicit forms could be used in lattice design as well as lattice analysis, while graded wall and edge thicknesses could be fully controlled in the lattice and even vary within a single tile. As a result, (geometrically) heterogeneous lattices could be created and adapted to follow analysis results while maintaining continuity between adjacent tiles. We demonstrate this ability on several 3D models, including TPMS.