Differentiation Through Black-Box Quadratic Programming Solvers

In recent years, many deep learning approaches have incorporated layers that solve optimization problems (e.g., linear, quadratic, and semidefinite programs). Integrating these optimization problems as differentiable layers requires computing the derivatives of the optimization problem's solution with respect to its objective and constraints. This has so far prevented the use of state-of-the-art black-box numerical solvers within neural networks, as they lack a differentiable interface. To address this issue for one of the most common convex optimization problems -- quadratic programming (QP) -- we introduce dQP, a modular framework that enables plug-and-play differentiation for any QP solver, allowing seamless integration into neural networks and bi-level optimization tasks. Our solution is based on the core theoretical insight that knowledge of the active constraint set at the QP optimum allows for explicit differentiation. This insight reveals a unique relationship between the computation of the solution and its derivative, enabling efficient differentiation of any solver, that only requires the primal solution. Our implementation, which will be made publicly available, interfaces with an existing framework that supports over 15 state-of-the-art QP solvers, providing each with a fully differentiable backbone for immediate use as a differentiable layer in learning setups. To demonstrate the scalability and effectiveness of dQP, we evaluate it on a large benchmark dataset of QPs with varying structures. We compare dQP with existing differentiable QP methods, demonstrating its advantages across a range of problems, from challenging small and dense problems to large-scale sparse ones, including a novel bi-level geometry optimization problem.

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.

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.

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/ .

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.

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.

Generative Escher Meshes

This paper proposes a fully-automatic, text-guided generative method for producing periodic, repeating, tile-able 2D art, such as the one seen on floors, mosaics, ceramics, and the work of M.C. Escher. In contrast to the standard concept of a seamless texture, i.e., square 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 color of a 2D mesh, in order to generate a non-square tile in the shape and appearance of the desired object, with close to no additional background details. We enable geometric optimization of tilings by our key technical contribution: an unconstrained, differentiable parameterization of the space of all possible tileable shapes for a given symmetry group. Namely, we prove that modifying the laplacian used in a 2D mesh-mapping technique - Orbifold Tutte Embedding - can achieve all possible tiling configurations for a chosen planar symmetry group. We thus consider both the mesh's tile-shape and its texture as optimizable parameters, rendering the textured mesh via a differentiable renderer. We leverage a trained image diffusion model to define a loss on the resulting image, thereby updating the mesh's parameters based on its appearance matching 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.

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.

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.

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.