Neural fields are a highly effective representation across visual computing. This work observes that fitting these fields is greatly improved by incorporating spatial stochasticity during training, and that this simple technique can replace or even outperform custom-designed hierarchies and frequency-space constructions. The approach is formalized as implicitly operating on a blurred version of the field, evaluated in-expectation by sampling with Gaussian-distributed offsets. Querying the blurred field during optimization greatly improves convergence and robustness, akin to the role of preconditioners in numerical linear algebra. This implicit, sampling-based perspective fits naturally into the neural field paradigm, comes at no additional cost, and is extremely simple to implement. We describe the basic theory of this technique, including details such as handling boundary conditions, and extending to a spatially-varying blur. Experiments demonstrate this approach on representations including coordinate MLPs, neural hashgrids, triplanes, and more, across tasks including surface reconstruction and radiance fields. In settings where custom-designed hierarchies have already been developed, stochastic preconditioning nearly matches or improves their performance with a simple and unified approach; in settings without existing hierarchies it provides an immediate boost to quality and robustness.
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Differentiable rendering has become a key ingredient in solving challenging inverse problems in computer graphics and vision. Existing systems can simulate and differentiate the spatial propagation of light. We exploit the duality of light transport simulations and geometric acoustics to apply differential rendering techniques to established acoustic simulation methods. The resulting system is capable of simulating sound according to the geometrical acoustics model and computing derivatives of the output energy spectrograms with respect to arbitrary parameters of the scene, including materials, emitters, microphones, and scene geometry. Contrary to current differentiable transient rendering, we can handle arbitrary simulation depths and achieve constant memory and linear execution times by presenting a temporal extension of Path Replay Backpropagation [Vicini et al. 2021]. We verify our model against established simulation software, and demonstrate the capabilities of optimization with gradients at examples of inverse acoustics and optimizing room parameters. This opens up a new field of research for acoustic optimization that could be as impactful for the acoustic community as differentiable rendering was for the graphics community.
Physically based differentiable rendering has established itself as key to inverse rendering, in which scenes are recovered from images through gradient-based optimization. Taking the derivative of the rendering equation is made difficult by the presence of discontinuities in the integrand at object silhouettes. To obtain correct derivatives w.r.t. changing geometry, accounting e.g. for changing penumbras or silhouettes in glossy reflections, differentiable renderers must compute an integral over these silhouettes. Prior work proposed importance sampling of silhouette edges for a given shading point. The main challenge is to efficiently reject parts of the mesh without silhouettes during sampling, which has been done using top-down traversal of a tree. Inaccuracies of this existing rejection procedure result in many samples with zero contribution. Thus, variance remains high and subsequent work has focused on alternatives such as area sampling or path space differentiable rendering. We propose an improved rejection test. It reduces variance substantially, which makes edge sampling in a unidirectional path tracer competitive again. Our rejection test relies on two approximations to the triangle planes of a mesh patch: A bounding box in dual space and dual quadrics. Additionally, we improve the heuristics used for stochastic traversal of the tree. We evaluate our method in a unidirectional path tracer and achieve drastic improvements over the original edge sampling and outperform methods based on area sampling.
All rendering methods aim at striking a balance between realism and efficiency. This is particularly relevant for differentiable rendering, where the additional aspect of differentiablity w.r.t. scene parameters causes increased computational complexity while, on the other hand, in the common application of inverse rendering, the diverse effects of real image formation must be faithfully reproduced. An important effect in rendering is the attenuation of light as it travels through different media (visibility, shadows, transmittance, transparency). This can be modeled as an integral over non-negative functions and has been successfully approximated in forward rendering by so-called moments. We show that moment-based approximations are differentiable in the parameters defining the moments, and that this leads to efficient and practical methods for inverse rendering. In particular, we demonstrate the method at the examples of shadow mapping and visibility in volume rendering, leading to approximations that are similar in efficiency to existing ad-hoc techniques while being significantly more accurate.
Computing derivatives of path integrals under evolving scene geometry is a fundamental problem in physics-based differentiable rendering, which requires differentiating discontinuities in the visibility function. Warped-area reparameterization is a powerful technique to compute differential visibility, and key is construction of a velocity field that is continuous in the domain interior and agrees with defined velocities on boundaries. Robustly and efficiently constructing such fields remains challenging. We present a novel velocity field construction for differential visibility. Inspired by recent Monte Carlo solvers for partial differential equations (PDEs), we formulate the velocity field via Laplace's equation and solve it with a walk-on-spheres (WoS) algorithm. To improve efficiency, we introduce a fixed-step WoS that terminates random walks after a fixed step count, resulting in a continuous but non-harmonic velocity field still valid for warped-area reparameterization. Furthermore, to practically apply our method to complex 3D scenes, we propose an efficient cone query to find the closest silhouettes on a boundary. Our cone query finds the closest point under the geodesic distance on a unit sphere, and is analogous to the closest point query by WoS to compute Euclidean distance. As a result, our method generalizes WoS to perform random walks on spherical caps over the unit sphere. We demonstrate that this enables a more robust and efficient unbiased estimator for differential visibility.
Generating photorealistic videos of digital humans in a controllable manner is crucial for a plethora of applications. Existing approaches either build on methods that employ template-based 3D representations or emerging video generation models but suffer from poor quality or limited consistency and identity preservation when generating individual or multiple digital humans. In this paper, we introduce a new interspatial attention (ISA) mechanism as a scalable building block for modern diffusion transformer (DiT)-based video generation models. ISA is a new type of cross attention that uses relative positional encodings tailored for the generation of human videos. Leveraging a custom-developed video variation autoencoder, we train a latent ISA-based diffusion model on a large corpus of video data. Our model achieves state-of-the-art performance for 4D human video synthesis, demonstrating remarkable motion consistency and identity preservation while providing precise control of the camera and body poses. Our code and model are publicly released at https://dsaurus.github.io/isa4d/.
We derive closed-form expressions of biharmonic coordinates for 2D high-order cages, enabling the transformation of the input polynomial curves into polynomial curves of any order. Central to our derivation is the use of the high-order boundary element method. We demonstrate the practicality and effectiveness of our method on various 2D deformations. In practice, users can easily manipulate the Bézier control points to perform the desired intuitive deformation, as the biharmonic coordinates provide an enriched deformation space and encourage the alignment between the boundary cage and its interior geometry.
We present closed-form expressions for Green and biharmonic coordinates with respect to polynomial curved 2D cages, enabling reliable cage-based image deformation both to and from a curved cage. We further provide closed-form expressions for first- and second-order derivatives of these coordinates with respect to the encoded position. This enables the use of variational solvers for interacting with the 2D shape at arbitrary points while keeping the fast decoding strength of cage-based deformation, which we illustrate for a variety of elastic deformation energies.
Storyboarding is widely used for creating 3D animations. Animators use the 2D sketches in storyboards as references to craft the desired 3D animations through a trial-and-error process. The traditional approach requires exceptional expertise and is both labor-intensive and time-consuming. Consequently, there is a high demand for automated methods that can directly translate 2D storyboard sketches into 3D animations. This task is under-explored to date and inspired by the significant advancements of motion diffusion models, we propose to address it from the perspective of conditional motion synthesis. We thus present Sketch2Anim, composed of two key modules for sketch constraint understanding and motion generation. Specifically, due to the large domain gap between the 2D sketch and 3D motion, instead of directly conditioning on 2D inputs, we design a 3D conditional motion generator that simultaneously leverages 3D keyposes, joint trajectories, and action words, to achieve precise and fine-grained motion control. Then, we invent a neural mapper dedicated to aligning user-provided 2D sketches with their corresponding 3D keyposes and trajectories in a shared embedding space, enabling, for the first time, direct 2D control of motion generation. Our approach successfully transfers storyboards into high-quality 3D motions and inherently supports direct 3D animation editing, thanks to the flexibility of our multi-conditional motion generator. Comprehensive experiments and evaluations, and a user perceptual study demonstrate the effectiveness of our approach. The code, data, trained models, and sketch-based motion designing interface are at https://zhongleilz.github.io/Sketch2Anim/.
We propose a novel segment-based light transport framework that uses segments as the basic unit of light transport. Unlike vertex-based formulations, our segment-based formulation naturally accommodates the disconnected subpaths encountered in photon density estimation and path filtering methods, and opens the door to a wide range of new rendering methods that consider segments as a sampling primitive. To facilitate the development of segment-based rendering methods, we introduce several segment sampling techniques and estimation strategies, including a highly-performant recursive estimator. One of our key contributions is a general-purpose segment sampling framework based on marginal multiple importance sampling (MMIS). To demonstrate the practicality of our sampling framework, we show how it allows us to easily implement a robust bidirectional path filtering method — challenging under a vertex-based formulation — achieving superior filtering efficiency and convergence compared to state-of-the-art approaches.
Global illumination combines direct and indirect lighting to create realistic lighting effects, bringing virtual scenes closer to reality. Static global illumination is a crucial component of virtual scene rendering, leveraging precomputation and baking techniques to significantly reduce runtime computational costs. Unfortunately, many existing works prioritize visual quality by relying on extensive texture storage and massive pixel-level texture sampling, leading to large performance overhead. In this paper, we introduce an illumination reconstruction method that effectively reduces sampling in fragment shader and avoids additional render passes, making it well-suited for low-end platforms. To achieve high-quality global illumination with reduced memory usage, we adopt a spherical harmonics fitting approach for baking effective illumination information and propose an inverse probe distribution method that generates unique probe associations for each mesh. This association, which can be generated offline in the local space, ensures consistent lighting quality across all instances of the same mesh. As a consequence, our method delivers highly competitive lighting effects while using only approximately 5% of the memory required by mainstream industry techniques.
Recent advances in large models have significantly advanced image-to-3D reconstruction. However, the generated models are often fused into a single piece, limiting their applicability in downstream tasks. This paper focuses on 3D garment generation, a key area for applications like virtual try-on with dynamic garment animations, which require garments to be separable and simulation-ready. We introduce Dress-1-to-3, a novel pipeline that reconstructs physics-plausible, simulation-ready separated garments with sewing patterns and humans from an in-the-wild image. Starting with the image, our approach combines a pre-trained image-to-sewing pattern generation model for creating coarse sewing patterns with a pre-trained multi-view diffusion model to produce multi-view images. The sewing pattern is further refined using a differentiable garment simulator based on the generated multi-view images. Versatile experiments demonstrate that our optimization approach substantially enhances the geometric alignment of the reconstructed 3D garments and humans with the input image. Furthermore, by integrating a texture generation module and a human motion generation module, we produce customized physics-plausible and realistic dynamic garment demonstrations. Our project page is https://dress-1-to-3.github.io/.
Impossible objects, geometric constructions that humans can perceive but that cannot exist in real life, have been a topic of intrigue in visual arts, perception, and graphics, yet no satisfying computer representation of such objects exists. Previous work embeds impossible objects in 3D, cutting them or twisting/bending them in the depth axis. Cutting an impossible object changes its local geometry at the cut, which can hamper downstream graphics applications, such as smoothing, while bending makes it difficult to relight the object. Both of these can invalidate geometry operations, such as distance computation. As an alternative, we introduce Meschers, meshes capable of representing impossible constructions akin to those found in M.C. Escher's woodcuts. Our representation has a theoretical foundation in discrete exterior calculus and supports the use-cases above, as we demonstrate in a number of example applications. Moreover, because we can do discrete geometry processing on our representation, we can inverse-render impossible objects. We also compare our representation to cut and bend representations of impossible objects.
A ruled surface is a shape swept out by moving a line in 3D space. Due to their simple geometric forms, ruled surfaces have applications in various domains such as architecture and engineering. In the past, various approaches have been proposed to approximate a target shape using developable surfaces, which are special ruled surfaces with zero Gaussian curvature. However, methods for shape approximation using general ruled surfaces remain limited and often require the target shape to be either represented as parametric surfaces or have non-positive Gaussian curvature. In this paper, we propose a method to compute a piecewise ruled surface that approximates an arbitrary freeform mesh surface. We first use a group-sparsity formulation to optimize the given mesh shape into an approximately piecewise ruled form, in conjunction with a tangent vector field that indicates the ruling directions. Afterward, we utilize the optimization result to extract seams that separate smooth families of rulings, and use the seams to construct the initial rulings. Finally, we further optimize the positions and orientations of the rulings to improve the alignment with the input target shape. We apply our method to a variety of freeform shapes with different topologies and complexity, demonstrating its effectiveness in approximating arbitrary shapes.
This paper introduces a method to synthesize a 3D tensor field within a constrained geometric domain represented as a tetrahedral mesh. Whereas previous techniques optimize for isotropic fields, we focus on anisotropic tensor fields that are smooth and aligned with the domain boundary or user guidance. The key ingredient of our method is a novel computational design framework, built on top of the symmetric orthogonally decomposable (odeco) tensor representation, to optimize the stretching ratios and orientations for each tensor in the domain. In contrast to past techniques designed only for isotropic tensors, we demonstrate the efficacy of our approach in generating smooth volumetric tensor fields with high anisotropy and shape conformity, especially for the domain with complex shapes. We apply these anisotropic tensor fields to various applications, such as anisotropic meshing, structural mechanics, and fabrication.
While discrete (metric) connections have become a staple of n-vector field design and analysis on simplicial meshes, the notion of torsion of a discrete connection has remained unstudied. This is all the more surprising as torsion is a crucial component in the fundamental theorem of Riemannian geometry, which introduces the existence and uniqueness of the Levi-Civita connection induced by the metric. In this paper, we extend the existing geometry processing toolbox by providing torsion control over discrete connections. Our approach consists in first introducing a new discrete Levi-Civita connection for a metric with locally-constant curvature to replace the hinge connection of a triangle mesh whose curvature is concentrated at singularities; from this reference connection, we define the discrete torsion of a connection to be the discrete dual 1-form by which a connection deviates from our discrete Levi-Civita connection. We discuss how the curvature and torsion of a discrete connection can then be controlled and assigned in a manner consistent with the continuous case. We also illustrate our approach through theoretical analysis and practical examples arising in vector and frame design.
We introduce VR-Doh, an open-source, hands-on 3D modeling system that enables intuitive creation and manipulation of elastoplastic objects in Virtual Reality (VR). By customizing the Material Point Method (MPM) for real-time simulation of hand-induced large deformations and enhancing 3D Gaussian Splatting for seamless rendering, VR-Doh provides an interactive and immersive 3D modeling experience. Users can naturally sculpt, deform, and edit objects through both contact- and gesture-based hand-object interactions. To achieve real-time performance, our system incorporates localized simulation techniques, particle-level collision handling, and the decoupling of physical and appearance representations, ensuring smooth and responsive interactions. VR-Doh supports both object creation and editing, enabling diverse modeling tasks such as designing food items, characters, and interlocking structures, all resulting in simulation-ready assets. User studies with both novice and experienced participants highlight the system's intuitive design, immersive feedback, and creative potential. Compared to existing geometric modeling tools, VR-Doh offers enhanced accessibility and natural interaction, making it a powerful tool for creative exploration in VR.
As AR/VR systems evolve to demand increasingly powerful GPUs, physically separating compute from display hardware emerges as a natural approach to enable a lightweight, comfortable form factor. Unfortunately, splitting the system into a client-server architecture leads to challenges in transporting graphical data. Simply streaming rendered images over a network suffers in terms of latency and reliability, especially given variable bandwidth. Although image-based reprojection techniques can help, they often do not support full motion parallax or disocclusion events. Instead, scene geometry can be streamed to the client, allowing local rendering of novel views. Traditionally, this has required a prohibitively large amount of interconnect bandwidth, excluding the use of practical networks. This paper presents a new quad-based geometry streaming approach that is designed with compression and the ability to adjust Quality-of-Experience (QoE) in response to target network bandwidths. Our approach advances previous work by introducing a more compact data structure and a temporal compression technique that reduces data transfer overhead by up to 15×, reducing bandwidth usage to as low as 100 Mbps. We optimized our design for hardware video codec compatibility and support an adaptive data streaming strategy that prioritizes transmitting only the most relevant geometry updates. Our approach achieves image quality comparable to, and in many cases exceeds, state-of-the-art techniques while requiring only a fraction of the bandwidth, enabling real-time geometry streaming on commodity headsets over WiFi.