High-quality textures are critical for realistic 3D content creation, yet existing generative methods are slow, rely on UV maps, and often fail to remain faithful to a reference image. To address these challenges, we propose a transformer-based framework that predicts a 3D texture field directly from a single image and a mesh, eliminating the need for UV mapping and differentiable rendering, and enabling faster texture generation. Our method integrates a triplane representation with depth-based backprojection losses, enabling efficient training and faster inference. Once trained, it generates high-fidelity textures in a single forward pass, requiring only$\sim 0.2 s$per shape. Extensive qualitative, quantitative, and user preference evaluations demonstrate that our method outperforms state-of-the-art baselines on single-image texture reconstruction in terms of both fidelity to the input image and perceptual quality, highlighting its practicality for scalable, highquality, and controllable 3D content creation.

The progression in large-scale 3D generative models has been impeded by significant resource requirements for training and challenges like inefficient representations. This paper introduces Make-A-Shape, a novel 3D generative model trained on a vast scale, using 10 million publicly-available shapes. We first innovate the wavelet-tree representation to encode high-resolution SDF shapes with minimal loss, leveraging our newly-proposed subband coefficient filtering scheme. We then design a subband coefficient packing scheme to facilitate diffusion-based generation and a subband adaptive training strategy for effective training on the large-scale dataset. Our generative framework is versatile, capable of conditioning on various input modalities such as images, point clouds, and voxels, enabling a variety of downstream applications, e.g., unconditional generation, completion, and conditional generation. Our approach clearly surpasses the existing baselines in delivering high-quality results and can efficiently generate shapes within two seconds for most conditions.

Machine learning models are known to be vulnerable to adversarial attacks, namely perturbations of the data that lead to wrong predictions despite being imperceptible. However, the existence of "universal" attacks (i.e., unique perturbations that transfer across different data points) has only been demonstrated for images to date. Part of the reason lies in the lack of a common domain, for geometric data such as graphs, meshes, and point clouds, where a universal perturbation can be defined. In this paper, we offer a change in perspective and demonstrate the existence of universal attacks for geometric data (shapes). We introduce a computational procedure that operates entirely in the spectral domain, where the attacks take the form of small perturbations to short eigenvalue sequences; the resulting geometry is then synthesized via shape-from-spectrum recovery. Our attacks are universal, in that they transfer across different shapes, different representations (meshes and point clouds), and generalize to previously unseen data.

We introduce a novel learning-based method to recover shapes from their Laplacian spectra, based on establishing and exploring connections in a learned latent space. The core of our approach consists in a cycle-consistent module that maps between a learned latent space and sequences of eigenvalues. This module provides an efficient and effective link between the shape geometry, encoded in a latent vector, and its Laplacian spectrum. Our proposed data-driven approach replaces the need for ad-hoc regularizers required by prior methods, while providing more accurate results at a fraction of the computational cost. Moreover, these latent space connections enable novel applications for both analyzing and controlling the spectral properties of deformable shapes, especially in the context of a shape collection. Our learning model and the associated analysis apply without modifications across different dimensions (2D and 3D shapes alike), representations (meshes, contours and point clouds), nature of the latent space (generated by an auto-encoder or a parametric model), as well as across different shape classes, and admits arbitrary resolution of the input spectrum without affecting complexity. The increased flexibility allows us to address notoriously difficult tasks in 3D vision and geometry processing within a unified framework, including shape generation from spectrum, latent space exploration and analysis, mesh super-resolution, shape exploration, style transfer, spectrum estimation for point clouds, segmentation transfer and non-rigid shape matching. SUPPLEMENTARY INFORMATION: The online version supplementary material available at 10.1007/s11263-021-01492-6.

We introduce the first learning-based method for recovering shapes from Laplacian spectra. Our model consists of a cycle-consistent module that maps between learned latent vectors of an auto-encoder and sequences of eigenvalues. This module provides an efficient and effective linkage between Laplacian spectrum and geometry. Our data-driven approach replaces the need for ad-hoc regularizers required by prior methods, while providing more accurate results at a fraction of the computational cost. Our learning model applies without modifications across different dimensions (2D and 3D shapes alike), representations (meshes, contours and point clouds), as well as across different shape classes, and admits arbitrary resolution of the input spectrum without affecting complexity. The increased flexibility allows us to address notoriously difficult tasks in 3D vision and geometry processing within a unified framework, including shape generation from spectrum, mesh super-resolution, shape exploration, style transfer, spectrum estimation from point clouds, segmentation transfer and point-to-point matching.

We consider the problem of localizing relevant subsets of non-rigid geometric shapes given only a partial 3D query as the input. Such problems arise in several challenging tasks in 3D vision and graphics, including partial shape similarity, retrieval, and non-rigid correspondence. We phrase the problem as one of alignment between short sequences of eigenvalues of basic differential operators, which are constructed upon a scalar function defined on the 3D surfaces. Our method therefore seeks for a scalar function that entails this alignment. Differently from existing approaches, we do not require solving for a correspondence between the query and the target, therefore greatly simplifying the optimization process; our core technique is also descriptor-free, as it is driven by the geometry of the two objects as encoded in their operator spectra. We further show that our spectral alignment algorithm provides a remarkably simple alternative to the recent shape-from-spectrum reconstruction approaches. For both applications, we demonstrate improvement over the state-of-the-art either in terms of accuracy or computational cost.

The question whether one can recover the shape of a geometric object from its Laplacian spectrum (`hear the shape of the drum') is a classical problem in spectral geometry with a broad range of implications and applications. While theoretically the answer to this question is negative (there exist examples of iso-spectral but non-isometric manifolds), little is known about the practical possibility of using the spectrum for shape reconstruction and optimization. In this paper, we introduce a numerical procedure called isospectralization, consisting of deforming one shape to make its Laplacian spectrum match that of another. We implement the isospectralization procedure using modern differentiable programming techniques and exemplify its applications in some of the classical and notoriously hard problems in geometry processing, computer vision, and graphics such as shape reconstruction, pose and style transfer, and dense deformable correspondence.