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For a $k$-uniform hypergraph (or simply $k$-graph) $F$, the codegree Tur\'{a}n density $\pi_{\mathrm{co}}(F)$ is the supremum over all $\alpha$ such that there exist arbitrarily large $n$-vertex $F$-free $k$-graphs $H$ in which every $(k-1)$-subset of $V(H)$ is contained in at least $\alpha n$ edges. Recently, it was proved that for every $3$-graph $F$, $\pi_{\mathrm{co}}(F)=0$ implies $\pi_{\therefore}(F)=0$, where $\pi_{\therefore}(F)$ is the uniform Tur\'{a}n density of $F$ and is defined as the supremum over all $d$ such that there are infinitely many $F$-free $k$-graphs $H$ satisfying that any induced linear-size subhypergraph of $H$ has edge density at least $d$. In this paper, we introduce a layered structure for $3$-graphs which allows us to obtain the reverse implication: every layered $3$-graph $F$ with $\pi_{\therefore}(F)=0$ satisfies $\pi_{\mathrm{co}}(F)=0$. Along the way, we answer in the negative a question of Falgas-Ravry, Pikhurko, Vaughan and Volec [J. London Math. Soc., 2023] about whether $\pi_{\therefore}(F)\leq\pi_{\mathrm{co}}(F)$ always holds. In particular, we construct counterexamples $F$ with positive but arbitrarily small $\pi_{\mathrm{co}}(F)$ while having $\pi_{\therefore}(F)\ge 4/27$., Comment: 17 pages. This work will be merged with arXiv:2312.02879

Diffusion models have demonstrated great success in text-to-video (T2V) generation. However, existing methods may face challenges when handling complex (long) video generation scenarios that involve multiple objects or dynamic changes in object numbers. To address these limitations, we propose VideoTetris, a novel framework that enables compositional T2V generation. Specifically, we propose spatio-temporal compositional diffusion to precisely follow complex textual semantics by manipulating and composing the attention maps of denoising networks spatially and temporally. Moreover, we propose an enhanced video data preprocessing to enhance the training data regarding motion dynamics and prompt understanding, equipped with a new reference frame attention mechanism to improve the consistency of auto-regressive video generation. Extensive experiments demonstrate that our VideoTetris achieves impressive qualitative and quantitative results in compositional T2V generation. Code is available at: https://github.com/YangLing0818/VideoTetris, Comment: Code: https://github.com/YangLing0818/VideoTetris

Automatic 3D facial texture generation has gained significant interest recently. Existing approaches may not support the traditional physically based rendering pipeline or rely on 3D data captured by Light Stage. Our key contribution is a progressive latent space refinement approach that can bootstrap from 3D Morphable Models (3DMMs)-based texture maps generated from facial images to generate high-quality and diverse PBR textures, including albedo, normal, and roughness. It starts with enhancing Generative Adversarial Networks (GANs) for text-guided and diverse texture generation. To this end, we design a self-supervised paradigm to overcome the reliance on ground truth 3D textures and train the generative model with only entangled texture maps. Besides, we foster mutual enhancement between GANs and Score Distillation Sampling (SDS). SDS boosts GANs with more generative modes, while GANs promote more efficient optimization of SDS. Furthermore, we introduce an edge-aware SDS for multi-view consistent facial structure. Experiments demonstrate that our method outperforms existing 3D texture generation methods regarding photo-realistic quality, diversity, and efficiency.

In this paper, we introduce the Volumetric Relightable Morphable Model (VRMM), a novel volumetric and parametric facial prior for 3D face modeling. While recent volumetric prior models offer improvements over traditional methods like 3D Morphable Models (3DMMs), they face challenges in model learning and personalized reconstructions. Our VRMM overcomes these by employing a novel training framework that efficiently disentangles and encodes latent spaces of identity, expression, and lighting into low-dimensional representations. This framework, designed with self-supervised learning, significantly reduces the constraints for training data, making it more feasible in practice. The learned VRMM offers relighting capabilities and encompasses a comprehensive range of expressions. We demonstrate the versatility and effectiveness of VRMM through various applications like avatar generation, facial reconstruction, and animation. Additionally, we address the common issue of overfitting in generative volumetric models with a novel prior-preserving personalization framework based on VRMM. Such an approach enables high-quality 3D face reconstruction from even a single portrait input. Our experiments showcase the potential of VRMM to significantly enhance the field of 3D face modeling., Comment: Accepted to SIGGRAPH 2024 (Conference); Project page: https://vrmm-paper.github.io/

For a $k$-uniform hypergraph (or simply $k$-graph) $F$, the codegree Tur\'{a}n density $\pi_{\mathrm{co}}(F)$ is the infimum over all $\alpha$ such that any $n$-vertex $k$-graph $H$ with every $(k-1)$-subset of $V(H)$ contained in at least $\alpha n$ edges has a copy of $F$. The uniform Tur\'{a}n density $\pi_{\therefore}(F)$ is the supremum over all $d$ such that there are infinitely many $F$-free $k$-graphs $H$ satisfying that any linear-size subhypergraph of $H$ has edge density at least $d$. Falgas-Ravry, Pikhurko, Vaughan and Volec [J. London Math. Soc., 2023] asked whether for every $3$-graph $F$, $\pi_{\therefore}(F)\leq\pi_{\mathrm{co}}(F)$. We provide a positive answer to this question provided that $\pi_{\mathrm{co}}(F)=0$. Our proof relies on a random geometric construction and a new formulation of the characterization of $3$-graphs with vanishing uniform Tur\'{a}n density due to Reiher, R{\"o}dl and Schacht [J. London Math. Soc., 2018]. Along the way, we answer a question of Falgas-Ravry, Pikhurko, Vaughan and Volec about subhypergraphs with linear minimum codegree in uniformly dense hypergraphs in the negative., Comment: 10 pages

In this paper, we propose a novel framework, Tracking-free Relightable Avatar (TRAvatar), for capturing and reconstructing high-fidelity 3D avatars. Compared to previous methods, TRAvatar works in a more practical and efficient setting. Specifically, TRAvatar is trained with dynamic image sequences captured in a Light Stage under varying lighting conditions, enabling realistic relighting and real-time animation for avatars in diverse scenes. Additionally, TRAvatar allows for tracking-free avatar capture and obviates the need for accurate surface tracking under varying illumination conditions. Our contributions are two-fold: First, we propose a novel network architecture that explicitly builds on and ensures the satisfaction of the linear nature of lighting. Trained on simple group light captures, TRAvatar can predict the appearance in real-time with a single forward pass, achieving high-quality relighting effects under illuminations of arbitrary environment maps. Second, we jointly optimize the facial geometry and relightable appearance from scratch based on image sequences, where the tracking is implicitly learned. This tracking-free approach brings robustness for establishing temporal correspondences between frames under different lighting conditions. Extensive qualitative and quantitative experiments demonstrate that our framework achieves superior performance for photorealistic avatar animation and relighting., Comment: Accepted to SIGGRAPH Asia 2023 (Conference); Project page: https://travatar-paper.github.io/

Effective scaffolds for bone tissue-engineering are those that combine adequate mechanical and chemical performance with osseointegrative, angiogenetic and anti-bacterial modes of bioactivity. To address these requirements via a combined approach, we additively manufactured square strut scaffolds by robocasting precipitation-derived strontium/copper co-substituted diopside. Microstructure, mechanical performance, bioactivity, biocompatibility, and antibacterial activity were examined. The results show that the presence of strontium and copper in the diopside lattice reduces the grain size and increases the density of the ceramics. The compressive strength, hardness, and fracture toughness of the diopside showed improvement, attributed to a finer microstructure and improved sintering. Scaffolds had excellent compressive strength with a high porosity (68 to 72 %), which is attributed to the structure of the stacked square struts. All materials showed good in vitro bioactivity and favorable proliferation of osteogenic sarcoma cells, while strontium and copper co-doped materials exhibited the strongest anti-Escherichia coli activity. We show that across multiple indicators this system offers pathways towards high-performance bone substitutes.

Recovering detailed facial geometry from a set of calibrated multi-view images is valuable for its wide range of applications. Traditional multi-view stereo (MVS) methods adopt an optimization-based scheme to regularize the matching cost. Recently, learning-based methods integrate all these into an end-to-end neural network and show superiority of efficiency. In this paper, we propose a novel architecture to recover extremely detailed 3D faces within dozens of seconds. Unlike previous learning-based methods that regularize the cost volume via 3D CNN, we propose to learn an implicit function for regressing the matching cost. By fitting a 3D morphable model from multi-view images, the features of multiple images are extracted and aggregated in the mesh-attached UV space, which makes the implicit function more effective in recovering detailed facial shape. Our method outperforms SOTA learning-based MVS in accuracy by a large margin on the FaceScape dataset. The code and data are released in https://github.com/zhuhao-nju/mvfr., Comment: AAAI 2022 Oral, updated to camera ready version

In this paper, we present a large-scale detailed 3D face dataset, FaceScape, and the corresponding benchmark to evaluate single-view facial 3D reconstruction. By training on FaceScape data, a novel algorithm is proposed to predict elaborate riggable 3D face models from a single image input. FaceScape dataset releases $16,940$ textured 3D faces, captured from $847$ subjects and each with $20$ specific expressions. The 3D models contain the pore-level facial geometry that is also processed to be topologically uniform. These fine 3D facial models can be represented as a 3D morphable model for coarse shapes and displacement maps for detailed geometry. Taking advantage of the large-scale and high-accuracy dataset, a novel algorithm is further proposed to learn the expression-specific dynamic details using a deep neural network. The learned relationship serves as the foundation of our 3D face prediction system from a single image input. Different from most previous methods, our predicted 3D models are riggable with highly detailed geometry under different expressions. We also use FaceScape data to generate the in-the-wild and in-the-lab benchmark to evaluate recent methods of single-view face reconstruction. The accuracy is reported and analyzed on the dimensions of camera pose and focal length, which provides a faithful and comprehensive evaluation and reveals new challenges. The unprecedented dataset, benchmark, and code have been released at https://github.com/zhuhao-nju/facescape., Comment: Accepted to T-PAMI 2023; Extension of FaceScape(CVPR 2020); Code & data are available at https://github.com/zhuhao-nju/facescape

This paper presents a novel framework to recover \emph{detailed} avatar from a single image. It is a challenging task due to factors such as variations in human shapes, body poses, texture, and viewpoints. Prior methods typically attempt to recover the human body shape using a parametric-based template that lacks the surface details. As such resulting body shape appears to be without clothing. In this paper, we propose a novel learning-based framework that combines the robustness of the parametric model with the flexibility of free-form 3D deformation. We use the deep neural networks to refine the 3D shape in a Hierarchical Mesh Deformation (HMD) framework, utilizing the constraints from body joints, silhouettes, and per-pixel shading information. Our method can restore detailed human body shapes with complete textures beyond skinned models. Experiments demonstrate that our method has outperformed previous state-of-the-art approaches, achieving better accuracy in terms of both 2D IoU number and 3D metric distance., Comment: Accepted by TPAMI. arXiv admin note: substantial text overlap with arXiv:1904.10506