We introduce Soft Anisotropic Diagrams (SAD), an explicit and differentiable image representation parameterized by a set of adaptive sites in the image plane. In SAD, each site specifies an anisotropic metric and an additively weighted distance score, and we compute pixel colors as a softmax blend over a small per-pixel top-K subset of sites. We induce a soft anisotropic additively weighted Voronoi partition (i.e., an Apollonius diagram) with learnable persite temperatures, preserving informative gradients while allowing clear, content-aligned boundaries and explicit ownership. Such a formulation enables efficient rendering by maintaining a per-query top-K map that approximates nearest neighbors under the same shading score, allowing GPU-friendly, fixed-size local computation. We update this list using our top-K propagation scheme inspired by jump flooding, augmented with stochastic injection to provide probabilistic global coverage. Training follows a GPU-first pipeline with gradient-weighted initialization, Adam optimization, and adaptive budget control through densification and pruning. Across standard benchmarks, SAD consistently outperforms Image-GS and Instant-NGP at matched bitrate. On Kodak, SAD reaches 46.0 dB PSNR with 2.2 s encoding time (vs. 28s for Image-GS), and delivers 4–19× end-to-end training speedups over state-of-the-art baselines. We demonstrate the effectiveness of SAD by showcasing the seamless integration with differentiable pipelines for forward and inverse problems, efficiency of fast random access, and compact storage. You can find the code here: https://luckyiyi.github.io/SAD.
论文检索
输入标题、作者或关键词，从 2,164 篇学术成果中精准定位
We present an algorithm for global knit structure planning that leverages a generalization of power diagrams to triangulated surfaces. This generalization is based on modified geodesic heat kernels and is used to quantize the curl measure of a normalized knitting time function gradient. Knit singularity positions are optimized jointly in a global fashion via an iterative Lloyd-type algorithm, leading to faster and more optimal placement of singularities than prior work, allowing for practical creation of denser knit graphs. In this denser setting, we present singularity ordering constraints that more robustly achieve helix-free knit graphs. The speed and robustness of the method is demonstrated via a diverse array of knits, and a virtual gallery of helix-free knit graphs. We also provide further demonstration of user constraints for knit singularity masking, level set alignment constraints, and apparent seam placement via curl boosting.
College of Computing and Data Science, Nanyang Technological University, Singapore Multi-layer perceptrons (MLPs) are a standard tool for learning and function approximation, but they inherently produce globally smooth outputs. Consequently, they struggle to represent functions that are continuous yet intentionally non-differentiable (i.e., functions with prescribed C0 sharp features) without ad hoc post-processing. We present SharpNet, a modified MLP architecture that encodes user-specified sharp features by augmenting the network with an auxiliary feature function defined as the solution to Poisson's equation with jump Neumann boundary conditions. This feature function is evaluated via an efficient local integral and is fully differentiable with respect to the feature locations, allowing us to jointly optimize both the feature locations and the MLP parameters to recover the target function or geometry. This construction provides precise control over where non-differentiability occurs, enforcing the desired C0 behavior at feature locations while preserving smoothness elsewhere. We validate SharpNet on 2D problems and 3D CAD reconstruction, and compare it with several state-of-the-art baselines. In both settings, SharpNet accurately recovers sharp edges and corners while remaining smooth away from them, whereas existing methods tend to blur gradient discontinuities. Qualitative and quantitative results demonstrate the effectiveness of our approach. Our project page, code and models are publicly available at https://sharpnettech.github.io.
We propose a system for differentiating through solutions to geometry processing problems. Our system differentiates a broad class of geometric algorithms, exploiting existing fast problem-specific schemes common to geometry processing, including local-global and ADMM solvers. It is compatible with machine learning frameworks, opening doors to new classes of inverse geometry processing applications. We marry the scatter-gather approach to mesh processing with tensor-based workflows and rely on the adjoint method applied to user-specified imperative code to generate an efficient backward pass behind the scenes. We demonstrate our approach by differentiating through mean curvature flow, spectral conformal parameterization, geodesic distance computation, and as-rigid-as-possible deformation, examining usability and performance on these applications. Our system allows practitioners to differentiate through existing geometry processing algorithms without needing to reformulate them, resulting in low implementation effort, fast runtimes, and lower memory requirements than differentiable optimization tools not tailored to geometry processing.
Sampling strategies in computer graphics have long been divided between local approaches, which optimize sample distributions independently at each pixel, and global approaches, which use high-dimensional low-discrepancy sequences to ensure uniformity across all dimensions, including adjacent pixels. While global samplers are most-commonly used thanks to generally having better convergence rates, it comes at a cost of very limited user control over the distribution of samples on subspaces, making it difficult to handle common aliasing artifacts. We introduce a novel modular meta-sampler architecture that bridges local and global sampling, allowing integrator designers to employ specialized low-dimensional samplers while still achieving high-dimensional uniformity. Our approach leverages high-dimensional low-discrepancy sequences to orchestrate sample generation by a collection of local samplers operating over power-of-two hierarchical intervals. We demonstrate how existing local sampling techniques, including stratified, blue noise, and dyadic nets sampling, can be reformulated to be used with this framework, enabling hybrid sampling strategies that combine the benefits of both paradigms.
We present an efficient B-spline finite element method (FEM) for cloth simulation. While higher-order FEM has long promised higher accuracy, its adoption in cloth simulators has been limited by its larger computational costs while generating results with similar visual quality. Our contribution is a full algorithmic pipeline that makes cloth simulation using quadratic B-spline surfaces faster than standard linear FEM in practice while consistently improving accuracy and visual fidelity. Using quadratic B-spline basis functions, we obtain a globally C1-continuous displacement field that supports consistent discretization of both membrane and bending energies, effectively reducing locking artifacts and mesh dependence common to linear elements. To close the performance gap, we introduce a reduced integration scheme that separately optimizes quadrature rules for membrane and bending energies, an accelerated Hessian assembly procedure tailored to the spline structure, and an optimized linear solver based on partial factorization. Together, these optimizations make high-order, smooth cloth simulation competitive at scale, yielding an average 2× speedup over linear FEM in our tests. Extensive experiments demonstrate improved accuracy, wrinkle detail, and robustness, including contact-rich scenarios, relative to linear FEM and recent higher-order approaches. Our method enables realistic wrinkling dynamics across a wide range of material parameters and supports practical garment animation, providing a new promising spatial discretization for high-quality cloth simulation.
Freeform surfaces are popular in architectural design for their expressive aesthetics, yet they remain challenging to fabricate. A common strategy is to approximate them with assemblies of planar polygonal panels in a process we term panelization, enabling cost-effective fabrication from sheet materials such as wood, metal, or glass. Our goal is to compute panelizations that are both geometrically faithful and structurally robust. A two-stage pipeline, i.e. geometric panelization followed by structural optimization, can be effective, but joint optimization may yield better outcomes by letting mechanics influence the panelization itself. The challenges are that the panelization task is inherently combinatorial, and structural objectives depend on stresses that have a complex, global dependence on the geometry and are costly to evaluate. Moreover, improving structural performance must be balanced against preserving the input surface's design intent. To address these challenges, we formulate panelization as a continuous surface flow coupled to stress analysis, by modeling candidates as creased elastic shells. We define a global objective by integrating an arbitrary function of stress over the shell and derive efficient gradients with respect to the surface shape to enable optimization. We further introduce flow terms that better preserve the input shape and show that running BFGS in a Sobolev space substantially outperforms standard BFGS and Sobolev gradient descent. We evaluate our method on architectural models, showing that incorporating stress during panelization yields substantial stress reductions and more robust designs compared to optimizing stress after fixing the panelization.
Following the success of deep neural networks in 2D pose estimation, reconstruction-based approaches have significantly advanced multi-person 3D pose estimation from sparse multi-view images. These methods typically detect 2D poses independently in each view and then associate them for 3D reconstruction. However, despite strong progress, recent state-of-the-art methods still face critical limitations: 1) They often depend on global optimization over a large and complex set of multi-view 2D joints to jointly infer 3D poses for all individuals, making the process highly complex and prone to suboptimal solutions; 2) Their tight coupling with the bottom-up detector OpenPose hinders the use of more advanced top-down or single-stage 2D pose estimators and restricts the integration of richer instance-level cues learned by these models. To address these limitations, we propose TwinPose, a novel framework that alleviates the complexity of global pose inference by optimizing within person-specific 3D pose subspaces, while fully supporting diverse 2D pose detectors and effectively leveraging pose-instance cues. The key idea is to introduce a twin pose — a 3D counterpart of each 2D pose — that inherits its instance representation and aggregates geometrically consistent 2D joints from other views. All twin poses are unified in a common 3D space, where those belonging to the same individual naturally share a number of bones. This structural property enables association by counting shared bones, forming person-specific subspaces from which each individual's 3D pose can be inferred independently in an efficient and robust manner. Extensive experiments demonstrate that TwinPose achieves state-of-the-art performance in both accuracy and efficiency across multiple public and proprietary datasets. Importantly, it is fully detector-agnostic, allowing seamless integration with current and future advances in 2D pose estimation while remaining highly robust to noisy or imperfect 2D predictions. Project page with code and additional resources: https://github.com/zgspose/TwinPose
We describe a method for computing signed distance to point clouds that allows fast pointwise evaluation at arbitrary spatial resolution. As input, our method takes a point cloud with normals; as output, it provides an analytical parameterization that allows queries of signed distance to the approximate underlying surface at arbitrary points — simultaneously providing reconstruction and distance. Our key idea is to reconstruct shapes by locally fitting point clouds with tori, which have closed-form signed distance functions. Tori are fitted in a feed-forward manner, using a pre-trained network to output per-point curvature and shift parameters. Importantly, our method does not require costly global optimization or spatial discretization, and is easily parallelizable. Underlying our method is a new theory that unifies signed distance with the classic reconstruction methods of winding numbers and Poisson surface reconstruction. We use our method to compute signed distance to point clouds arising from photogrammetry, meshes, 3D Gaussians, and neural implicits. Our method allows point clouds to be used directly in applications, without explicit surface reconstruction: as examples, we take offsets of point clouds, apply morphological and Boolean operations, and directly visualize offset surfaces using sphere tracing.
We present a GPU-based system for automatic differentiation (AD) of functions defined on triangle meshes, designed to exploit the locality and sparsity in mesh-based computation. Our system evaluates derivatives using perelement forward-mode AD, confining all computation to registers and shared memory and assembling global gradients, sparse Jacobians, and sparse Hessians directly on the GPU. By avoiding global computation graphs, intermediate buffers, and device-host synchronization, our approach minimizes memory traffic and enables efficient differentiation under both static and dynamically changing sparsity. Our programming model lets users express energy terms over mesh neighborhoods, while our system automatically manages parallel execution, derivative propagation, sparse assembly, and matrix-free operations such as Hessian-vector products. Our system supports both scalar- and vector-valued objectives, dynamic interaction-driven sparsity updates, and seamless integration with external GPU sparse linear solvers. We evaluate our system on applications including elastic and cloth simulation, surface parameterization, mesh smoothing, frame field design, ARAP deformation, and spherical manifold optimization. Across these tasks, our system consistently outperforms state-of-the-art differentiation frameworks, including PyTorch, JAX, Warp, Dr.JIT, EnzymeAD, and Thallo. We demonstrate speedups across a range of solver types, from Newton and Gauss-Newton for nonlinear least squares to L-BFGS and gradient descent, and across different derivative usage modes, including Hessian-vector products as well as full sparse Hessian and Jacobian construction. Our system is available as open source at https://github.com/owensgroup/RXMesh.
Online 3D reconstruction from monocular image sequences is a challenging and ongoing research topic. 3D Gaussian Splatting (3DGS), leveraging its high-quality real-time rendering capability, empowers online 3D reconstruction to represent dense scenes with enhanced expressiveness, and thus holds great promise for a wide range of applications such as robotics and AR/VR. However, existing online 3DGS methods still suffer from some key challenges: fragile camera pose estimation due to the lack of global optimization, and low optimization efficiency in large-scale or long-sequence scenarios. To address these issues, we propose a robust and efficient online voxelized 3DGS reconstruction framework integrated with global Sim(3) optimization, which enables reliable camera tracking and efficient global loop closure for both camera poses and voxelized 3DGS. To accelerate the convergence of the voxelized 3DGS, we further introduce a color residual learning strategy, which not only boosts optimization speed but also enhances rendering quality. Extensive experiments on diverse indoor and outdoor datasets demonstrate that our method achieves state-of-the-art performance in both camera pose estimation accuracy and rendering quality, while retaining real-time efficiency. Additionally, we develop and deploy a real-world UAV-based active reconstruction system grounded on our proposed method, validating its robustness and generalizability for practical online 3D reconstruction tasks. Our code and data are available at https://github.com/TrickyGo/MoonSplat..
3D Gaussian Splatting (3DGS) has become the method of choice for reconstructing and real-time rendering of captured scenes. To capture a scene with good visual quality, continuous image sequences are usually combined with out-of-order shots for better scene coverage. Structure from motion can reconstruct such captures, but only after they are all available and often with high computational cost. Incremental reconstruction methods – often derived from SLAM solutions – provide immediate feedback, but cannot handle the out-of-order capture we require. We provide the first immediate feedback solution for such radiance field capture that provides global consistency. We first introduce a method for fast matching in out-of-order sequences, by repurposing visual place recognition models and a covisibility graph, and provide an efficient way to find highly connected keyframes, improving quality even for ordered sequences. We show how these steps – together with GPU optimization and careful Gaussian primitive placement – provide fast local reconstruction, in our challenging radiance field reconstruction case. We then introduce a novel cluster-based method, again using the covisibility graph, to provide efficient loop closure that does not require sequential input. Finally, to handle large scenes in our context, we introduce a progressive hierarchy that allows our method to scale to large environments, without compromising efficiency. Our results show we provide immediate feedback 3DGS reconstruction with good visual quality in several datasets, with up to thousands of input images.
Coordinate-motion assemblies can only be disassembled by the simultaneous motion of multiple parts along distinct paths, providing high structural stability and enabling efficient robotic assembly. Existing examples are largely limited to architectural structures using joint-based connections, or puzzles created through trial-and-error, as the relationship between part geometry and coordinate motion remains poorly understood. Computationally designing such assemblies is challenging because it requires jointly achieving distributed contacts across the entire assembly and a unique coordinate motion for disassembly that rules out other feasible motions. We address this challenge by establishing a theoretical connection between part geometry and unique coordinate motion, enabling us to rigorously verify whether a given assembly admits a unique coordinate motion. Building on this theory, we introduce a two-stage algorithm that optimizes contact interfaces for a target motion and constructs physically feasible part geometries that conform to a user-specified global shape. We demonstrate our approach on models with complex geometries and topologies, including assemblies with large part counts, and validate it through physical fabrication and experiments.
We present a global, discrete optimization framework for quad-dominant mesh reduction that formulates simplification as an edge selection problem under coupled topological and geometric constraints. Unlike greedy edge-collapse heuristics, which make irreversible local decisions, and rigid poly-chord removal schemes, which over-constrain global structure, our method casts quad-dominant reduction as an Integer Linear Programming (ILP) problem that jointly optimizes edge flow continuity and geometric fidelity in a single global optimization. To make this formulation both tractable and adaptive, we segment poly-chords at geometrically meaningful breakpoints to relax otherwise rigid topological constraints, and introduce geometry-aware soft constraints that steer the optimization toward preserving high-curvature and deformation-critical regions. Extensive experiments demonstrate that our approach consistently outperforms state-of-the-art methods in preserving quad structure and edge flow, while achieving competitive geometric accuracy and significantly benefiting downstream editing applications.
Recent radiance-field-based reconstruction methods, such as NeRF and 3DGS, achieve high visual fidelity for indoor scenes, but often break down under scene editing due to baked illumination and the lack of explicit light transport. In contrast, inverse path tracing methods based on mesh representations enforce correct light transport but require highly accurate geometry, making them difficult to apply robustly to real indoor scenes. We present Emission-Aware Gaussians and Path Tracing (EAG-PT), a method for physically based reconstruction and rendering of indoor scenes using a unified 2D Gaussian representation, targeting editable diffuse global illumination. Our approach consists of three key ideas: (1) representing indoor scenes with 2D Gaussians as a transport-friendly geometric proxy that avoids explicit mesh reconstruction; (2) explicitly separating emissive and non-emissive components during reconstruction to support editing; and (3) decoupling reconstruction from final rendering by using efficient single-bounce optimization and high-quality multi-bounce path tracing, respectively. Experiments on synthetic and real indoor scenes show that EAG-PT produces more natural and physically consistent edited renderings than radiance-field reconstructions, while preserving finer geometric detail and avoiding mesh-induced artifacts compared with mesh-based inverse path tracing. These results highlight the potential of our approach for applications such as interior design, XR content creation, and embodied AI.
Computing injective, flip-free embeddings of simplicial meshes is a fundamental challenge in geometry processing. While the Total Lifted Content (TLC) energy provides a smooth functional with theoretically guaranteed injective global minima, its non-convex nature presents significant optimization hurdles. In this work, we propose a Nonlinear Multigrid (MG/Opt) framework specifically tailored for efficient TLC energy minimization. Our approach leverages a topology-preserving mesh hierarchy to rapidly eliminate low-frequency errors on coarse scales while maintaining rigorous gradient consistency between hierarchical levels through linear correction terms. To address the persistent challenge of local inversions, we introduce a targeted smoothing strategy and an adaptive parameter scheduling mechanism that balances global convergence speed with local injectivity precision. Experimental evaluations across extensive 2D and 3D benchmark datasets demonstrate the robustness of our approach. Our method achieves a 100% convergence success rate across all tested 2D cases and all but one 3D dataset (the VOLMAP benchmark). Furthermore, our MG/Opt framework delivers substantial performance gains, achieving up to 63 × speedup on high-resolution subdivided datasets compared to traditional solvers. These results confirm that our multigrid strategy provides a scalable and reliable solution for large-scale injective mapping problems. Code and data for this paper are at https://github.com/distmeshM/MGOpt_TLC
The fundamental limitation of traditional strand-based modeling is not simply data scarcity, but the ill-posedness of inferring complex 3D fields from 2D imagery without structural constraints. This unconstrained regression leads to catastrophic failures in resolving both global occlusion (e.g., in ponytails) and local directionality (e.g., in curls), resulting in over-smoothed, plausible-but-incorrect geometries. To resolve this, we integrate the strong geometric priors of Large Reconstruction Models (LRMs) into the strand generation pipeline. Using the LRM mesh as a structural anchor, we employ a novel Dual Orientation AutoEncoder to lift coarse geometry into high-fidelity strands. By resolving vector field singularities through latent-space optimization and surface-guided refinement, our method effectively disentangles complex topological structures, setting a new benchmark for robustness and accuracy in hair reconstruction.
Reconstructing dynamic fluids from sparse-view videos is a severely under-constrained problem due to complex volumetric visibility and turbulent, topology-changing motion. Current dynamic deformation-based 3D Gaussian Splatting (3DGS) methods use heuristic image-space warps, which often overfit limited observations via non-physical primitive scaling or drifting, producing floaters and geometric distortions. To address these challenges, we propose a hybrid, physics-aware fluid representation that injects physical constraints directly into the 3DGS pipeline. We develop a Beer–Lambert volumetric model mapping Gaussian primitives to a continuous, physically-grounded density field, bridging optical observations with fundamental physical laws. A physically-guided optimization evolves primitives under a global, volume-preserving velocity field, avoiding arbitrary per-particle deformations and effectively preserving volume while recovering fine-scale turbulent details. This unified formulation tightly couples fluid dynamics with differentiable rendering, enabling high-quality, joint predictions of velocity and density. Experiments on synthetic and real smoke datasets demonstrate that our approach surpasses state-of-the-art methods in both visual fidelity and physical consistency, achieving stable 3D reconstructions even from sparse views.
Reconstructing high-fidelity, animatable, and relightable 3D hand avatars from a single RGB image is a challenging yet critical task for immersive VR/AR applications. State-of-the-art hand reconstruction methods achieve impressive reconstruction and relighting results, but they mostly leverage dense observations, such as multi-view images or monocular video sequences and rely on per-scene optimization. Moreover, it is difficult for these methods to generate plausible appearance in occluded regions. In contrast, existing single-view hand reconstruction methods typically struggle to disentangle global illumination, resulting in textures with baked-in shading artifacts. To address these challenges, we propose FLASHand, the first feed-forward relightable and animatable 3D hand reconstruction model from a single RGB image. Our method bridges the gap between efficiency and fidelity, enabling instant creation of personalized hand avatars with disentangled appearance that can be rendered under novel lighting and poses. To ensure plausible geometry generation and achieve high-fidelity animation and relighting, we introduce a mesh-based disentangled 2D Gaussian splatting hand representation. We leverage the NIMBLE parametric prior to define a canonical attribute space, and define geometry and appearance attributes explicitly. We then propose the Feed-forward Hand Attributes Generator (FHAG) to predict these attributes from a single image. By leveraging a cross attention module to fuse canonical geometric information with input image features, FHAG effectively lifts pixel-level visual cues into the 3D hand canonical space, directly generating spatially-aligned geometry and appearance attributes. This allows us to bypass iterative optimization and instantly reconstruct a high-fidelity hand avatar from a single RGB image. Extensive experiments on both synthetic and in-the-wild datasets demonstrate that FLASHand achieves state-of-the-art performance in novel view synthesis and supports real-time animation and relighting. Code and data are available at https://github.com/IGLICT/FLASHand.
Monocular video–based human mesh recovery (HMR) has made significant progress in recent years, yet existing methods often fail to reconstruct physically plausible motion during highly dynamic airborne movements such as jumping or acrobatics. These failure cases arise from motion blur, rapid orientation changes, and the lack of suitable training data, leading to temporally inconsistent and physically implausible results. We propose a novel method for reconstructing 3D airborne motion by refining inaccurate estimates produced by state-of-the-art HMR systems. Our approach extracts key physical quantities, identifies reliable motion segments based on physical consistency, and connects them using a homotopy-aware trajectory optimization. A global angular momentum constraint is then enforced over the entire motion, and global motion and local poses are jointly optimized under physical and temporal smoothness constraints. Experiments on challenging in-the-wild videos demonstrate that our method produces more physically consistent and temporally coherent airborne motions than existing refinement approaches.