arXiv subjects

Noam Aigerman

Publications and source records attributed to Noam Aigerman.

At least 19 recordsLinked to original sources

arXiv2026

Intrinsic and Triangulation-Agnostic Attention: A Simple and Powerful Approach for Learning on Meshes

This work proposes an adaptation of the attention mechanism for triangle meshes. The core observation is that endowing the attention mechanism with critical properties for learning over meshes -- intrinsicality and triangulation-agnosticism -- enables it to attain state-of-the-art results over several learning-based tasks in geometry-processing. The above is achieved by modifying the attention mechanism from the bottom up based on simple principles from geometry-processing. Namely, the quantities used within attention -- queries, keys and values -- are created by an intrinsic, triangulation-agnostic network, and treated as discretizations of continuous functions. From that, we devise an appropriate attention mechanism that operates over triangle meshes through standard FEM discretization of the resulting integrals of the above functions. Surprisingly, as far as we know, this straightforward approach has not been utilized for learning over meshes. Experiments show our method exceeds current state of the art, including both mesh-based architectures as well as point cloud transformers. Namely, we show significant improvements on several common benchmarks and tasks -- predicting canonical high-frequency signals; predicting deformations; computing dense correspondences, both between full shapes and partial ones; and predicting feature descriptors.

cs.GR↗

arXiv2026

Mat\'ern Noise for Triangulation-Agnostic Flow Matching on Meshes

This paper tackles the task of learning to generate signals over triangle meshes in a triangulation-agnostic manner, meaning the trained model can be applied to different meshes and triangulations effectively. Practically, the paper adapts the flow matching (FM) paradigm to a mesh-based, triangulation-agnostic setting. Theoretically, it proposes a specific noise distribution which is triangulation agnostic, to be used inside the FM model's denoising process. While noise distributions are usually trivial to devise for, e.g., images, devising a triangulation-agnostic distribution proves to be a much more difficult task. We formulate a mathematical definition of triangulation agnosticism of distributions, via their spectrum. We then show that a discretization of a specific Gaussian random field called a Mat\'ern process holds these desired properties, and provides a simple and efficient sampling algorithm. We use it as our noise model, and adapt FM to the triangulation-agnostic setting by using a state-of-the-art approach for learning signals on meshes in the gradient domain -- PoissonNet -- as the denoiser. We conduct experiments on elaborate tasks such as sampling elastic rest states, and generating poses of humanoids. Our method is shown to be capable of producing highly realistic results for meshes of over one million triangles, significantly exceeding the state-of-the-art in quality and diversity.

cs.GR↗

arXiv2025

PoissonNet: A Local-Global Approach for Learning on Surfaces

Many network architectures exist for learning on meshes, yet their constructions entail delicate trade-offs between difficulty learning high-frequency features, insufficient receptive field, sensitivity to discretization, and inefficient computational overhead. Drawing from classic local-global approaches in mesh processing, we introduce PoissonNet, a novel neural architecture that overcomes all of these deficiencies by formulating a local-global learning scheme, which uses Poisson's equation as the primary mechanism for feature propagation. Our core network block is simple; we apply learned local feature transformations in the gradient domain of the mesh, then solve a Poisson system to propagate scalar feature updates across the surface globally. Our local-global learning framework preserves the features's full frequency spectrum and provides a truly global receptive field, while remaining agnostic to mesh triangulation. Our construction is efficient, requiring far less compute overhead than comparable methods, which enables scalability -- both in the size of our datasets, and the size of individual training samples. These qualities are validated on various experiments where, compared to previous intrinsic architectures, we attain state-of-the-art performance on semantic segmentation and parameterizing highly-detailed animated surfaces. Finally, as a central application of PoissonNet, we show its ability to learn deformations, significantly outperforming state-of-the-art architectures that learn on surfaces.

cs.GR↗

arXiv2025

Neural Kinematic Bases for Fluids

We propose mesh-free fluid simulations that exploit a kinematic neural basis for velocity fields represented by an MLP. We design a set of losses that ensures that these neural bases approximate fundamental physical properties such as orthogonality, divergence-free, boundary alignment, and smoothness. Our neural bases can then be used to fit an input sketch of a flow, which will inherit the same fundamental properties from the bases. We then can animate such flow in real-time using standard time integrators. Our neural bases can accommodate different domains, moving boundaries, and naturally extend to three dimensions.

cs.GR↗

arXiv2025

View-Dependent Deformation Fields for 2D Editing of 3D Models

We propose a method for authoring non-realistic 3D objects (represented as either 3D Gaussian Splats or meshes), that comply with 2D edits from specific viewpoints. Namely, given a 3D object, a user chooses different viewpoints and interactively deforms the object in the 2D image plane of each view. The method then produces a "deformation field" - an interpolation between those 2D deformations in a smooth manner as the viewpoint changes. Our core observation is that the 2D deformations do not need to be tied to an underlying object, nor share the same deformation space. We use this observation to devise a method for authoring view-dependent deformations, holding several technical contributions: first, a novel way to compositionality-blend between the 2D deformations after lifting them to 3D - this enables the user to "stack" the deformations similarly to layers in an editing software, each deformation operating on the results of the previous; second, a novel method to apply the 3D deformation to 3D Gaussian Splats; third, an approach to author the 2D deformations, by deforming a 2D mesh encapsulating a rendered image of the object. We show the versatility and efficacy of our method by adding cartoonish effects to objects, providing means to modify human characters, fitting 3D models to given 2D sketches and caricatures, resolving occlusions, and recreating classic non-realistic paintings as 3D models.

cs.GR↗

arXiv2024

Instant3dit: Multiview Inpainting for Fast Editing of 3D Objects

We propose a generative technique to edit 3D shapes, represented as meshes, NeRFs, or Gaussian Splats, in approximately 3 seconds, without the need for running an SDS type of optimization. Our key insight is to cast 3D editing as a multiview image inpainting problem, as this representation is generic and can be mapped back to any 3D representation using the bank of available Large Reconstruction Models. We explore different fine-tuning strategies to obtain both multiview generation and inpainting capabilities within the same diffusion model. In particular, the design of the inpainting mask is an important factor of training an inpainting model, and we propose several masking strategies to mimic the types of edits a user would perform on a 3D shape. Our approach takes 3D generative editing from hours to seconds and produces higher-quality results compared to previous works.

cs.CV↗

arXiv2024

Sketch-guided Cage-based 3D Gaussian Splatting Deformation

3D Gaussian Splatting (GS) is one of the most promising novel 3D representations that has received great interest in computer graphics and computer vision. While various systems have introduced editing capabilities for 3D GS, such as those guided by text prompts, fine-grained control over deformation remains an open challenge. In this work, we present a novel sketch-guided 3D GS deformation system that allows users to intuitively modify the geometry of a 3D GS model by drawing a silhouette sketch from a single viewpoint. Our approach introduces a new deformation method that combines cage-based deformations with a variant of Neural Jacobian Fields, enabling precise, fine-grained control. Additionally, it leverages large-scale 2D diffusion priors and ControlNet to ensure the generated deformations are semantically plausible. Through a series of experiments, we demonstrate the effectiveness of our method and showcase its ability to animate static 3D GS models as one of its key applications.

cs.CV↗

arXiv2024

Differentiation Through Black-Box Quadratic Programming Solvers

Differentiable optimization has attracted significant research interest, particularly for quadratic programming (QP). Existing approaches for differentiating the solution of a QP with respect to its defining parameters often rely on specific integrated solvers. This integration limits their applicability, including their use in neural network architectures and bi-level optimization tasks, restricting users to a narrow selection of solver choices. To address this limitation, we introduce dQP, a modular and solver-agnostic framework for plug-and-play differentiation of virtually any QP solver. A key insight we leverage to achieve modularity is that, once the active set of inequality constraints is known, both the solution and its derivative can be expressed using simplified linear systems that share the same matrix. This formulation fully decouples the computation of the QP solution from its differentiation. Building on this result, we provide a minimal-overhead, open-source implementation ( https://github.com/cwmagoon/dQP ) that seamlessly integrates with over 15 state-of-the-art solvers. Comprehensive benchmark experiments demonstrate dQP's robustness and scalability, particularly highlighting its advantages in large-scale sparse problems.

cs.LG↗

arXiv2024

DECOLLAGE: 3D Detailization by Controllable, Localized, and Learned Geometry Enhancement

We present a 3D modeling method which enables end-users to refine or detailize 3D shapes using machine learning, expanding the capabilities of AI-assisted 3D content creation. Given a coarse voxel shape (e.g., one produced with a simple box extrusion tool or via generative modeling), a user can directly "paint" desired target styles representing compelling geometric details, from input exemplar shapes, over different regions of the coarse shape. These regions are then up-sampled into high-resolution geometries which adhere with the painted styles. To achieve such controllable and localized 3D detailization, we build on top of a Pyramid GAN by making it masking-aware. We devise novel structural losses and priors to ensure that our method preserves both desired coarse structures and fine-grained features even if the painted styles are borrowed from diverse sources, e.g., different semantic parts and even different shape categories. Through extensive experiments, we show that our ability to localize details enables novel interactive creative workflows and applications. Our experiments further demonstrate that in comparison to prior techniques built on global detailization, our method generates structure-preserving, high-resolution stylized geometries with more coherent shape details and style transitions.

cs.CV↗

arXiv2024

MeshUp: Multi-Target Mesh Deformation via Blended Score Distillation

We propose MeshUp, a technique that deforms a 3D mesh towards multiple target concepts, and intuitively controls the region where each concept is expressed. Conveniently, the concepts can be defined as either text queries, e.g., "a dog" and "a turtle," or inspirational images, and the local regions can be selected as any number of vertices on the mesh. We can effectively control the influence of the concepts and mix them together using a novel score distillation approach, referred to as the Blended Score Distillation (BSD). BSD operates on each attention layer of the denoising U-Net of a diffusion model as it extracts and injects the per-objective activations into a unified denoising pipeline from which the deformation gradients are calculated. To localize the expression of these activations, we create a probabilistic Region of Interest (ROI) map on the surface of the mesh, and turn it into 3D-consistent masks that we use to control the expression of these activations. We demonstrate the effectiveness of BSD empirically and show that it can deform various meshes towards multiple objectives. Our project page is at https://threedle.github.io/MeshUp.

cs.CV↗

arXiv2024

Temporal Residual Jacobians For Rig-free Motion Transfer

We introduce Temporal Residual Jacobians as a novel representation to enable data-driven motion transfer. Our approach does not assume access to any rigging or intermediate shape keyframes, produces geometrically and temporally consistent motions, and can be used to transfer long motion sequences. Central to our approach are two coupled neural networks that individually predict local geometric and temporal changes that are subsequently integrated, spatially and temporally, to produce the final animated meshes. The two networks are jointly trained, complement each other in producing spatial and temporal signals, and are supervised directly with 3D positional information. During inference, in the absence of keyframes, our method essentially solves a motion extrapolation problem. We test our setup on diverse meshes (synthetic and scanned shapes) to demonstrate its superiority in generating realistic and natural-looking animations on unseen body shapes against SoTA alternatives. Supplemental video and code are available at https://temporaljacobians.github.io/ .

cs.CV↗

arXiv2024

TutteNet: Injective 3D Deformations by Composition of 2D Mesh Deformations

This work proposes a novel representation of injective deformations of 3D space, which overcomes existing limitations of injective methods: inaccuracy, lack of robustness, and incompatibility with general learning and optimization frameworks. The core idea is to reduce the problem to a deep composition of multiple 2D mesh-based piecewise-linear maps. Namely, we build differentiable layers that produce mesh deformations through Tutte's embedding (guaranteed to be injective in 2D), and compose these layers over different planes to create complex 3D injective deformations of the 3D volume. We show our method provides the ability to efficiently and accurately optimize and learn complex deformations, outperforming other injective approaches. As a main application, we produce complex and artifact-free NeRF and SDF deformations.

cs.CV↗

arXiv2024

MagicClay: Sculpting Meshes With Generative Neural Fields

The recent developments in neural fields have brought phenomenal capabilities to the field of shape generation, but they lack crucial properties, such as incremental control - a fundamental requirement for artistic work. Triangular meshes, on the other hand, are the representation of choice for most geometry related tasks, offering efficiency and intuitive control, but do not lend themselves to neural optimization. To support downstream tasks, previous art typically proposes a two-step approach, where first a shape is generated using neural fields, and then a mesh is extracted for further processing. Instead, in this paper we introduce a hybrid approach that maintains both a mesh and a Signed Distance Field (SDF) representations consistently. Using this representation, we introduce MagicClay - an artist friendly tool for sculpting regions of a mesh according to textual prompts while keeping other regions untouched. Our framework carefully and efficiently balances consistency between the representations and regularizations in every step of the shape optimization; Relying on the mesh representation, we show how to render the SDF at higher resolutions and faster. In addition, we employ recent work in differentiable mesh reconstruction to adaptively allocate triangles in the mesh where required, as indicated by the SDF. Using an implemented prototype, we demonstrate superior generated geometry compared to the state-of-the-art, and novel consistent control, allowing sequential prompt-based edits to the same mesh for the first time.

cs.GR↗

arXiv2023

Explorable Mesh Deformation Subspaces from Unstructured Generative Models

Exploring variations of 3D shapes is a time-consuming process in traditional 3D modeling tools. Deep generative models of 3D shapes often feature continuous latent spaces that can, in principle, be used to explore potential variations starting from a set of input shapes. In practice, doing so can be problematic: latent spaces are high dimensional and hard to visualize, contain shapes that are not relevant to the input shapes, and linear paths through them often lead to sub-optimal shape transitions. Furthermore, one would ideally be able to explore variations in the original high-quality meshes used to train the generative model, not its lower-quality output geometry. In this paper, we present a method to explore variations among a given set of landmark shapes by constructing a mapping from an easily-navigable 2D exploration space to a subspace of a pre-trained generative model. We first describe how to find a mapping that spans the set of input landmark shapes and exhibits smooth variations between them. We then show how to turn the variations in this subspace into deformation fields, to transfer those variations to high-quality meshes for the landmark shapes. Our results show that our method can produce visually-pleasing and easily-navigable 2D exploration spaces for several different shape categories, especially as compared to prior work on learning deformation spaces for 3D shapes.

cs.GR↗

arXiv2023

Generative Escher Meshes

This paper proposes a fully-automatic, text-guided generative method for producing perfectly-repeating, periodic, tile-able 2D imagery, such as the one seen on floors, mosaics, ceramics, and the work of M.C. Escher. In contrast to square texture images that are seamless when tiled, our method generates non-square tilings which comprise solely of repeating copies of the same object. It achieves this by optimizing both geometry and texture of a 2D mesh, yielding a non-square tile in the shape and appearance of the desired object, with close to no additional background details, that can tile the plane without gaps nor overlaps. We enable optimization of the tile's shape by an unconstrained, differentiable parameterization of the space of all valid tileable meshes for given boundary conditions stemming from a symmetry group. Namely, we construct a differentiable family of linear systems derived from a 2D mesh-mapping technique - Orbifold Tutte Embedding - by considering the mesh's Laplacian matrix as differentiable parameters. We prove that the solution space of these linear systems is exactly all possible valid tiling configurations, thereby providing an end-to-end differentiable representation for the entire space of valid tiles. We render the textured mesh via a differentiable renderer, and leverage a pre-trained image diffusion model to induce a loss on the resulting image, updating the mesh's parameters so as to make its appearance match the text prompt. We show our method is able to produce plausible, appealing results, with non-trivial tiles, for a variety of different periodic tiling patterns.

cs.CV↗

arXiv2023

Neural Semantic Surface Maps

We present an automated technique for computing a map between two genus-zero shapes, which matches semantically corresponding regions to one another. Lack of annotated data prohibits direct inference of 3D semantic priors; instead, current State-of-the-art methods predominantly optimize geometric properties or require varying amounts of manual annotation. To overcome the lack of annotated training data, we distill semantic matches from pre-trained vision models: our method renders the pair of 3D shapes from multiple viewpoints; the resulting renders are then fed into an off-the-shelf image-matching method which leverages a pretrained visual model to produce feature points. This yields semantic correspondences, which can be projected back to the 3D shapes, producing a raw matching that is inaccurate and inconsistent between different viewpoints. These correspondences are refined and distilled into an inter-surface map by a dedicated optimization scheme, which promotes bijectivity and continuity of the output map. We illustrate that our approach can generate semantic surface-to-surface maps, eliminating manual annotations or any 3D training data requirement. Furthermore, it proves effective in scenarios with high semantic complexity, where objects are non-isometrically related, as well as in situations where they are nearly isometric.

cs.CV↗

arXiv2023

Neural Progressive Meshes

The recent proliferation of 3D content that can be consumed on hand-held devices necessitates efficient tools for transmitting large geometric data, e.g., 3D meshes, over the Internet. Detailed high-resolution assets can pose a challenge to storage as well as transmission bandwidth, and level-of-detail techniques are often used to transmit an asset using an appropriate bandwidth budget. It is especially desirable for these methods to transmit data progressively, improving the quality of the geometry with more data. Our key insight is that the geometric details of 3D meshes often exhibit similar local patterns even across different shapes, and thus can be effectively represented with a shared learned generative space. We learn this space using a subdivision-based encoder-decoder architecture trained in advance on a large collection of surfaces. We further observe that additional residual features can be transmitted progressively between intermediate levels of subdivision that enable the client to control the tradeoff between bandwidth cost and quality of reconstruction, providing a neural progressive mesh representation. We evaluate our method on a diverse set of complex 3D shapes and demonstrate that it outperforms baselines in terms of compression ratio and reconstruction quality.

cs.CV↗

arXiv2023

Neural Face Rigging for Animating and Retargeting Facial Meshes in the Wild

We propose an end-to-end deep-learning approach for automatic rigging and retargeting of 3D models of human faces in the wild. Our approach, called Neural Face Rigging (NFR), holds three key properties: (i) NFR's expression space maintains human-interpretable editing parameters for artistic controls; (ii) NFR is readily applicable to arbitrary facial meshes with different connectivity and expressions; (iii) NFR can encode and produce fine-grained details of complex expressions performed by arbitrary subjects. To the best of our knowledge, NFR is the first approach to provide realistic and controllable deformations of in-the-wild facial meshes, without the manual creation of blendshapes or correspondence. We design a deformation autoencoder and train it through a multi-dataset training scheme, which benefits from the unique advantages of two data sources: a linear 3DMM with interpretable control parameters as in FACS, and 4D captures of real faces with fine-grained details. Through various experiments, we show NFR's ability to automatically produce realistic and accurate facial deformations across a wide range of existing datasets as well as noisy facial scans in-the-wild, while providing artist-controlled, editable parameters.

cs.GR↗