Vladimir G. Kim

Amir Barda, Matheus Gadelha, Vladimir G. Kim et al.

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.

Bo Sun, Vladimir G. Kim, Noam Aigerman et al.

This paper introduces a data-driven shape completion approach that focuses on completing geometric details of missing regions of 3D shapes. We observe that existing generative methods lack the training data and representation capacity to synthesize plausible, fine-grained details with complex geometry and topology. Our key insight is to copy and deform patches from the partial input to complete missing regions. This enables us to preserve the style of local geometric features, even if it drastically differs from the training data. Our fully automatic approach proceeds in two stages. First, we learn to retrieve candidate patches from the input shape. Second, we select and deform some of the retrieved candidates to seamlessly blend them into the complete shape. This method combines the advantages of the two most common completion methods: similarity-based single-instance completion, and completion by learning a shape space. We leverage repeating patterns by retrieving patches from the partial input, and learn global structural priors by using a neural network to guide the retrieval and deformation steps. Experimental results show our approach considerably outperforms baselines across multiple datasets and shape categories. Code and data are available at https://github.com/GitBoSun/PatchRD.

Luca Morreale, Noam Aigerman, Paul Guerrero et al.

This work is concerned with a representation of shapes that disentangles fine, local and possibly repeating geometry, from global, coarse structures. Achieving such disentanglement leads to two unrelated advantages: i) a significant compression in the number of parameters required to represent a given geometry; ii) the ability to manipulate either global geometry, or local details, without harming the other. At the core of our approach lies a novel pipeline and neural architecture, which are optimized to represent one specific atlas, representing one 3D surface. Our pipeline and architecture are designed so that disentanglement of global geometry from local details is accomplished through optimization, in a completely unsupervised manner. We show that this approach achieves better neural shape compression than the state of the art, as well as enabling manipulation and transfer of shape details. Project page at http://geometry.cs.ucl.ac.uk/projects/2022/cnnmaps/ .

Luca Morreale, Noam Aigerman, Vladimir G. Kim et al.

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.

William Gao, Noam Aigerman, Thibault Groueix et al.

We present a technique for automatically producing a deformation of an input triangle mesh, guided solely by a text prompt. Our framework is capable of deformations that produce both large, low-frequency shape changes, and small high-frequency details. Our framework relies on differentiable rendering to connect geometry to powerful pre-trained image encoders, such as CLIP and DINO. Notably, updating mesh geometry by taking gradient steps through differentiable rendering is notoriously challenging, commonly resulting in deformed meshes with significant artifacts. These difficulties are amplified by noisy and inconsistent gradients from CLIP. To overcome this limitation, we opt to represent our mesh deformation through Jacobians, which updates deformations in a global, smooth manner (rather than locally-sub-optimal steps). Our key observation is that Jacobians are a representation that favors smoother, large deformations, leading to a global relation between vertices and pixels, and avoiding localized noisy gradients. Additionally, to ensure the resulting shape is coherent from all 3D viewpoints, we encourage the deep features computed on the 2D encoding of the rendering to be consistent for a given vertex from all viewpoints. We demonstrate that our method is capable of smoothly-deforming a wide variety of source mesh and target text prompts, achieving both large modifications to, e.g., body proportions of animals, as well as adding fine semantic details, such as shoe laces on an army boot and fine details of a face.

Benjamin T. Jones, Michael Hu, Vladimir G. Kim et al.

The design of man-made objects is dominated by computer aided design (CAD) tools. Assisting design with data-driven machine learning methods is hampered by lack of labeled data in CAD's native format; the parametric boundary representation (B-Rep). Several data sets of mechanical parts in B-Rep format have recently been released for machine learning research. However, large scale databases are largely unlabeled, and labeled datasets are small. Additionally, task specific label sets are rare, and costly to annotate. This work proposes to leverage unlabeled CAD geometry on supervised learning tasks. We learn a novel, hybrid implicit/explicit surface representation for B-Rep geometry, and show that this pre-training significantly improves few-shot learning performance and also achieves state-of-the-art performance on several existing B-Rep benchmarks.

Yun-Chun Chen, Vladimir G. Kim, Noam Aigerman et al.

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.

Noam Aigerman, Kunal Gupta, Vladimir G. Kim et al.

This paper introduces a framework designed to accurately predict piecewise linear mappings of arbitrary meshes via a neural network, enabling training and evaluating over heterogeneous collections of meshes that do not share a triangulation, as well as producing highly detail-preserving maps whose accuracy exceeds current state of the art. The framework is based on reducing the neural aspect to a prediction of a matrix for a single given point, conditioned on a global shape descriptor. The field of matrices is then projected onto the tangent bundle of the given mesh, and used as candidate jacobians for the predicted map. The map is computed by a standard Poisson solve, implemented as a differentiable layer with cached pre-factorization for efficient training. This construction is agnostic to the triangulation of the input, thereby enabling applications on datasets with varying triangulations. At the same time, by operating in the intrinsic gradient domain of each individual mesh, it allows the framework to predict highly-accurate mappings. We validate these properties by conducting experiments over a broad range of scenarios, from semantic ones such as morphing, registration, and deformation transfer, to optimization-based ones, such as emulating elastic deformations and contact correction, as well as being the first work, to our knowledge, to tackle the task of learning to compute UV parameterizations of arbitrary meshes. The results exhibit the high accuracy of the method as well as its versatility, as it is readily applied to the above scenarios without any changes to the framework.

Hyunwoo Kim, Itai Lang, Noam Aigerman et al.

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.

Arman Maesumi, Paul Guerrero, Vladimir G. Kim et al.

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.

Qimin Chen, Zhiqin Chen, Vladimir G. Kim et al.

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.

Theo Deprelle, Thibault Groueix, Noam Aigerman et al.

This paper describes new techniques for learning atlas-like representations of 3D surfaces, i.e. homeomorphic transformations from a 2D domain to surfaces. Compared to prior work, we propose two major contributions. First, instead of mapping a fixed 2D domain, such as a set of square patches, to the surface, we learn a continuous 2D domain with arbitrary topology by optimizing a point sampling distribution represented as a mixture of Gaussians. Second, we learn consistent mappings in both directions: charts, from the 3D surface to 2D domain, and parametrizations, their inverse. We demonstrate that this improves the quality of the learned surface representation, as well as its consistency in a collection of related shapes. It thus leads to improvements for applications such as correspondence estimation, texture transfer, and consistent UV mapping. As an additional technical contribution, we outline that, while incorporating normal consistency has clear benefits, it leads to issues in the optimization, and that these issues can be mitigated using a simple repulsive regularization. We demonstrate that our contributions provide better surface representation than existing baselines.

Richard Liu, Noam Aigerman, Vladimir G. Kim et al.

We present a neural technique for learning to select a local sub-region around a point which can be used for mesh parameterization. The motivation for our framework is driven by interactive workflows used for decaling, texturing, or painting on surfaces. Our key idea is to incorporate segmentation probabilities as weights of a classical parameterization method, implemented as a novel differentiable parameterization layer within a neural network framework. We train a segmentation network to select 3D regions that are parameterized into 2D and penalized by the resulting distortion, giving rise to segmentations which are distortion-aware. Following training, a user can use our system to interactively select a point on the mesh and obtain a large, meaningful region around the selection which induces a low-distortion parameterization. Our code and project page are currently available.

Seungwoo Yoo, Kunho Kim, Vladimir G. Kim et al.

We present As-Plausible-as-Possible (APAP) mesh deformation technique that leverages 2D diffusion priors to preserve the plausibility of a mesh under user-controlled deformation. Our framework uses per-face Jacobians to represent mesh deformations, where mesh vertex coordinates are computed via a differentiable Poisson Solve. The deformed mesh is rendered, and the resulting 2D image is used in the Score Distillation Sampling (SDS) process, which enables extracting meaningful plausibility priors from a pretrained 2D diffusion model. To better preserve the identity of the edited mesh, we fine-tune our 2D diffusion model with LoRA. Gradients extracted by SDS and a user-prescribed handle displacement are then backpropagated to the per-face Jacobians, and we use iterative gradient descent to compute the final deformation that balances between the user edit and the output plausibility. We evaluate our method with 2D and 3D meshes and demonstrate qualitative and quantitative improvements when using plausibility priors over geometry-preservation or distortion-minimization priors used by previous techniques. Our project page is at: https://as-plausible-aspossible.github.io/

Jan Bednarik, Noam Aigerman, Vladimir G. Kim et al.

We propose a method for unsupervised reconstruction of a temporally-consistent sequence of surfaces from a sequence of time-evolving point clouds. It yields dense and semantically meaningful correspondences between frames. We represent the reconstructed surfaces as atlases computed by a neural network, which enables us to establish correspondences between frames. The key to making these correspondences semantically meaningful is to guarantee that the metric tensors computed at corresponding points are as similar as possible. We have devised an optimization strategy that makes our method robust to noise and global motions, without a priori correspondences or pre-alignment steps. As a result, our approach outperforms state-of-the-art ones on several challenging datasets. The code is available at https://github.com/bednarikjan/temporally_coherent_surface_reconstruction.

Zhiqin Chen, Vladimir G. Kim, Matthew Fisher et al.

We introduce a deep generative network for 3D shape detailization, akin to stylization with the style being geometric details. We address the challenge of creating large varieties of high-resolution and detailed 3D geometry from a small set of exemplars by treating the problem as that of geometric detail transfer. Given a low-resolution coarse voxel shape, our network refines it, via voxel upsampling, into a higher-resolution shape enriched with geometric details. The output shape preserves the overall structure (or content) of the input, while its detail generation is conditioned on an input "style code" corresponding to a detailed exemplar. Our 3D detailization via conditional refinement is realized by a generative adversarial network, coined DECOR-GAN. The network utilizes a 3D CNN generator for upsampling coarse voxels and a 3D PatchGAN discriminator to enforce local patches of the generated model to be similar to those in the training detailed shapes. During testing, a style code is fed into the generator to condition the refinement. We demonstrate that our method can refine a coarse shape into a variety of detailed shapes with different styles. The generated results are evaluated in terms of content preservation, plausibility, and diversity. Comprehensive ablation studies are conducted to validate our network designs. Code is available at https://github.com/czq142857/DECOR-GAN.

Dmitry Petrov, Pradyumn Goyal, Vikas Thamizharasan et al.

We introduce GEM3D -- a new deep, topology-aware generative model of 3D shapes. The key ingredient of our method is a neural skeleton-based representation encoding information on both shape topology and geometry. Through a denoising diffusion probabilistic model, our method first generates skeleton-based representations following the Medial Axis Transform (MAT), then generates surfaces through a skeleton-driven neural implicit formulation. The neural implicit takes into account the topological and geometric information stored in the generated skeleton representations to yield surfaces that are more topologically and geometrically accurate compared to previous neural field formulations. We discuss applications of our method in shape synthesis and point cloud reconstruction tasks, and evaluate our method both qualitatively and quantitatively. We demonstrate significantly more faithful surface reconstruction and diverse shape generation results compared to the state-of-the-art, also involving challenging scenarios of reconstructing and synthesizing structurally complex, high-genus shape surfaces from Thingi10K and ShapeNet.

Arman Maesumi, Dylan Hu, Krishi Saripalli et al.

Procedural noise is a fundamental component of computer graphics pipelines, offering a flexible way to generate textures that exhibit "natural" random variation. Many different types of noise exist, each produced by a separate algorithm. In this paper, we present a single generative model which can learn to generate multiple types of noise as well as blend between them. In addition, it is capable of producing spatially-varying noise blends despite not having access to such data for training. These features are enabled by training a denoising diffusion model using a novel combination of data augmentation and network conditioning techniques. Like procedural noise generators, the model's behavior is controllable via interpretable parameters and a source of randomness. We use our model to produce a variety of visually compelling noise textures. We also present an application of our model to improving inverse procedural material design; using our model in place of fixed-type noise nodes in a procedural material graph results in higher-fidelity material reconstructions without needing to know the type of noise in advance.

Michael Fischer, Iliyan Georgiev, Thibault Groueix et al.

Decomposing 3D assets into material parts is a common task for artists and creators, yet remains a highly manual process. In this work, we introduce Select Any Material (SAMa), a material selection approach for various 3D representations. Building on the recently introduced SAM2 video selection model, we extend its capabilities to the material domain. We leverage the model's cross-view consistency to create a 3D-consistent intermediate material-similarity representation in the form of a point cloud from a sparse set of views. Nearest-neighbour lookups in this similarity cloud allow us to efficiently reconstruct accurate continuous selection masks over objects' surfaces that can be inspected from any view. Our method is multiview-consistent by design, alleviating the need for contrastive learning or feature-field pre-processing, and performs optimization-free selection in seconds. Our approach works on arbitrary 3D representations and outperforms several strong baselines in terms of selection accuracy and multiview consistency. It enables several compelling applications, such as replacing the diffuse-textured materials on a text-to-3D output, or selecting and editing materials on NeRFs and 3D-Gaussians.

Yuezhi Yang, Qimin Chen, Vladimir G. Kim et al.

We introduce the first method for generating Vector Displacement Maps (VDMs): parameterized, detailed geometric stamps commonly used in 3D modeling. Given a single input image, our method first generates multi-view normal maps and then reconstructs a VDM from the normals via a novel reconstruction pipeline. We also propose an efficient algorithm for extracting VDMs from 3D objects, and present the first academic VDM dataset. Compared to existing 3D generative models focusing on complete shapes, we focus on generating parts that can be seamlessly attached to shape surfaces. The method gives artists rich control over adding geometric details to a 3D shape. Experiments demonstrate that our approach outperforms existing baselines. Generating VDMs offers additional benefits, such as using 2D image editing to customize and refine 3D details.

Nissim Maruani, Peiying Zhang, Siddhartha Chaudhuri et al.

We introduce Illustrator's Depth, a novel definition of depth that addresses a key challenge in digital content creation: decomposing flat images into editable, ordered layers. Inspired by an artist's compositional process, illustrator's depth infers a layer index to each pixel, forming an interpretable image decomposition through a discrete, globally consistent ordering of elements optimized for editability. We also propose and train a neural network using a curated dataset of layered vector graphics to predict layering directly from raster inputs. Our layer index inference unlocks a range of powerful downstream applications. In particular, it significantly outperforms state-of-the-art baselines for image vectorization while also enabling high-fidelity text-to-vector-graphics generation, automatic 3D relief generation from 2D images, and intuitive depth-aware editing. By reframing depth from a physical quantity to a creative abstraction, illustrator's depth prediction offers a new foundation for editable image decomposition.

Arman Maesumi, Tanish Makadia, Thibault Groueix et al.

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.

Yun-Chun Chen, Selena Ling, Zhiqin Chen et al.

We propose a novel technique for adding geometric details to an input coarse 3D mesh guided by a text prompt. Our method is composed of three stages. First, we generate a single-view RGB image conditioned on the input coarse geometry and the input text prompt. This single-view image generation step allows the user to pre-visualize the result and offers stronger conditioning for subsequent multi-view generation. Second, we use our novel multi-view normal generation architecture to jointly generate six different views of the normal images. The joint view generation reduces inconsistencies and leads to sharper details. Third, we optimize our mesh with respect to all views and generate a fine, detailed geometry as output. The resulting method produces an output within seconds and offers explicit user control over the coarse structure, pose, and desired details of the resulting 3D mesh.

Thomas W. Mitchel, Noam Aigerman, Vladimir G. Kim et al.

Möbius transformations play an important role in both geometry and spherical image processing - they are the group of conformal automorphisms of 2D surfaces and the spherical equivalent of homographies. Here we present a novel, Möbius-equivariant spherical convolution operator which we call Möbius convolution, and with it, develop the foundations for Möbius-equivariant spherical CNNs. Our approach is based on a simple observation: to achieve equivariance, we only need to consider the lower-dimensional subgroup which transforms the positions of points as seen in the frames of their neighbors. To efficiently compute Möbius convolutions at scale we derive an approximation of the action of the transformations on spherical filters, allowing us to compute our convolutions in the spectral domain with the fast Spherical Harmonic Transform. The resulting framework is both flexible and descriptive, and we demonstrate its utility by achieving promising results in both shape classification and image segmentation tasks.

Lingxiao Li, Noam Aigerman, Vladimir G. Kim et al.

Finding multiple solutions of non-convex optimization problems is a ubiquitous yet challenging task. Most past algorithms either apply single-solution optimization methods from multiple random initial guesses or search in the vicinity of found solutions using ad hoc heuristics. We present an end-to-end method to learn the proximal operator of a family of training problems so that multiple local minima can be quickly obtained from initial guesses by iterating the learned operator, emulating the proximal-point algorithm that has fast convergence. The learned proximal operator can be further generalized to recover multiple optima for unseen problems at test time, enabling applications such as object detection. The key ingredient in our formulation is a proximal regularization term, which elevates the convexity of our training loss: by applying recent theoretical results, we show that for weakly-convex objectives with Lipschitz gradients, training of the proximal operator converges globally with a practical degree of over-parameterization. We further present an exhaustive benchmark for multi-solution optimization to demonstrate the effectiveness of our method.

Benjamin Jones, Dalton Hildreth, Duowen Chen et al.

Assembly modeling is a core task of computer aided design (CAD), comprising around one third of the work in a CAD workflow. Optimizing this process therefore represents a huge opportunity in the design of a CAD system, but current research of assembly based modeling is not directly applicable to modern CAD systems because it eschews the dominant data structure of modern CAD: parametric boundary representations (BREPs). CAD assembly modeling defines assemblies as a system of pairwise constraints, called mates, between parts, which are defined relative to BREP topology rather than in world coordinates common to existing work. We propose SB-GCN, a representation learning scheme on BREPs that retains the topological structure of parts, and use these learned representations to predict CAD type mates. To train our system, we compiled the first large scale dataset of BREP CAD assemblies, which we are releasing along with benchmark mate prediction tasks. Finally, we demonstrate the compatibility of our model with an existing commercial CAD system by building a tool that assists users in mate creation by suggesting mate completions, with 72.2% accuracy.

Jan Bednarik, Vladimir G. Kim, Siddhartha Chaudhuri et al.

We propose a method for the unsupervised reconstruction of a temporally-coherent sequence of surfaces from a sequence of time-evolving point clouds, yielding dense, semantically meaningful correspondences between all keyframes. We represent the reconstructed surface as an atlas, using a neural network. Using canonical correspondences defined via the atlas, we encourage the reconstruction to be as isometric as possible across frames, leading to semantically-meaningful reconstruction. Through experiments and comparisons, we empirically show that our method achieves results that exceed that state of the art in the accuracy of unsupervised correspondences and accuracy of surface reconstruction.

Thomas W. Mitchel, Vladimir G. Kim, Michael Kazhdan

We present a novel surface convolution operator acting on vector fields that is based on a simple observation: instead of combining neighboring features with respect to a single coordinate parameterization defined at a given point, we have every neighbor describe the position of the point within its own coordinate frame. This formulation combines intrinsic spatial convolution with parallel transport in a scattering operation while placing no constraints on the filters themselves, providing a definition of convolution that commutes with the action of isometries, has increased descriptive potential, and is robust to noise and other nuisance factors. The result is a rich notion of convolution which we call field convolution, well-suited for CNNs on surfaces. Field convolutions are flexible, straight-forward to incorporate into surface learning frameworks, and their highly discriminating nature has cascading effects throughout the learning pipeline. Using simple networks constructed from residual field convolution blocks, we achieve state-of-the-art results on standard benchmarks in fundamental geometry processing tasks, such as shape classification, segmentation, correspondence, and sparse matching.

Mikaela Angelina Uy, Vladimir G. Kim, Minhyuk Sung et al.

We propose a novel technique for producing high-quality 3D models that match a given target object image or scan. Our method is based on retrieving an existing shape from a database of 3D models and then deforming its parts to match the target shape. Unlike previous approaches that independently focus on either shape retrieval or deformation, we propose a joint learning procedure that simultaneously trains the neural deformation module along with the embedding space used by the retrieval module. This enables our network to learn a deformation-aware embedding space, so that retrieved models are more amenable to match the target after an appropriate deformation. In fact, we use the embedding space to guide the shape pairs used to train the deformation module, so that it invests its capacity in learning deformations between meaningful shape pairs. Furthermore, our novel part-aware deformation module can work with inconsistent and diverse part-structures on the source shapes. We demonstrate the benefits of our joint training not only on our novel framework, but also on other state-of-the-art neural deformation modules proposed in recent years. Lastly, we also show that our jointly-trained method outperforms various non-joint baselines.

Kangxue Yin, Zhiqin Chen, Siddhartha Chaudhuri et al.

We introduce COALESCE, the first data-driven framework for component-based shape assembly which employs deep learning to synthesize part connections. To handle geometric and topological mismatches between parts, we remove the mismatched portions via erosion, and rely on a joint synthesis step, which is learned from data, to fill the gap and arrive at a natural and plausible part joint. Given a set of input parts extracted from different objects, COALESCE automatically aligns them and synthesizes plausible joints to connect the parts into a coherent 3D object represented by a mesh. The joint synthesis network, designed to focus on joint regions, reconstructs the surface between the parts by predicting an implicit shape representation that agrees with existing parts, while generating a smooth and topologically meaningful connection. We employ test-time optimization to further ensure that the synthesized joint region closely aligns with the input parts to create realistic component assemblies from diverse input parts. We demonstrate that our method significantly outperforms prior approaches including baseline deep models for 3D shape synthesis, as well as state-of-the-art methods for shape completion.

Omid Poursaeed, Tianxing Jiang, Han Qiao et al.

Point clouds provide a compact and efficient representation of 3D shapes. While deep neural networks have achieved impressive results on point cloud learning tasks, they require massive amounts of manually labeled data, which can be costly and time-consuming to collect. In this paper, we leverage 3D self-supervision for learning downstream tasks on point clouds with fewer labels. A point cloud can be rotated in infinitely many ways, which provides a rich label-free source for self-supervision. We consider the auxiliary task of predicting rotations that in turn leads to useful features for other tasks such as shape classification and 3D keypoint prediction. Using experiments on ShapeNet and ModelNet, we demonstrate that our approach outperforms the state-of-the-art. Moreover, features learned by our model are complementary to other self-supervised methods and combining them leads to further performance improvement.

Omid Poursaeed, Matthew Fisher, Noam Aigerman et al.

We propose a novel neural architecture for representing 3D surfaces, which harnesses two complementary shape representations: (i) an explicit representation via an atlas, i.e., embeddings of 2D domains into 3D; (ii) an implicit-function representation, i.e., a scalar function over the 3D volume, with its levels denoting surfaces. We make these two representations synergistic by introducing novel consistency losses that ensure that the surface created from the atlas aligns with the level-set of the implicit function. Our hybrid architecture outputs results which are superior to the output of the two equivalent single-representation networks, yielding smoother explicit surfaces with more accurate normals, and a more accurate implicit occupancy function. Additionally, our surface reconstruction step can directly leverage the explicit atlas-based representation. This process is computationally efficient, and can be directly used by differentiable rasterizers, enabling training our hybrid representation with image-based losses.

Hsueh-Ti Derek Liu, Vladimir G. Kim, Siddhartha Chaudhuri et al.

This paper introduces Neural Subdivision, a novel framework for data-driven coarse-to-fine geometry modeling. During inference, our method takes a coarse triangle mesh as input and recursively subdivides it to a finer geometry by applying the fixed topological updates of Loop Subdivision, but predicting vertex positions using a neural network conditioned on the local geometry of a patch. This approach enables us to learn complex non-linear subdivision schemes, beyond simple linear averaging used in classical techniques. One of our key contributions is a novel self-supervised training setup that only requires a set of high-resolution meshes for learning network weights. For any training shape, we stochastically generate diverse low-resolution discretizations of coarse counterparts, while maintaining a bijective mapping that prescribes the exact target position of every new vertex during the subdivision process. This leads to a very efficient and accurate loss function for conditional mesh generation, and enables us to train a method that generalizes across discretizations and favors preserving the manifold structure of the output. During training we optimize for the same set of network weights across all local mesh patches, thus providing an architecture that is not constrained to a specific input mesh, fixed genus, or category. Our network encodes patch geometry in a local frame in a rotation- and translation-invariant manner. Jointly, these design choices enable our method to generalize well, and we demonstrate that even when trained on a single high-resolution mesh our method generates reasonable subdivisions for novel shapes.

Chu Wang, Babak Samari, Vladimir G. Kim et al.

Affinity graphs are widely used in deep architectures, including graph convolutional neural networks and attention networks. Thus far, the literature has focused on abstracting features from such graphs, while the learning of the affinities themselves has been overlooked. Here we propose a principled method to directly supervise the learning of weights in affinity graphs, to exploit meaningful connections between entities in the data source. Applied to a visual attention network, our affinity supervision improves relationship recovery between objects, even without the use of manually annotated relationship labels. We further show that affinity learning between objects boosts scene categorization performance and that the supervision of affinity can also be applied to graphs built from mini-batches, for neural network training. In an image classification task we demonstrate consistent improvement over the baseline, with diverse network architectures and datasets.

Wang Yifan, Noam Aigerman, Vladimir G. Kim et al.

We propose a novel learnable representation for detail-preserving shape deformation. The goal of our method is to warp a source shape to match the general structure of a target shape, while preserving the surface details of the source. Our method extends a traditional cage-based deformation technique, where the source shape is enclosed by a coarse control mesh termed \emph{cage}, and translations prescribed on the cage vertices are interpolated to any point on the source mesh via special weight functions. The use of this sparse cage scaffolding enables preserving surface details regardless of the shape's intricacy and topology. Our key contribution is a novel neural network architecture for predicting deformations by controlling the cage. We incorporate a differentiable cage-based deformation module in our architecture, and train our network end-to-end. Our method can be trained with common collections of 3D models in an unsupervised fashion, without any cage-specific annotations. We demonstrate the utility of our method for synthesizing shape variations and deformation transfer.

Omid Poursaeed, Vladimir G. Kim, Eli Shechtman et al.

We propose a learning based method for generating new animations of a cartoon character given a few example images. Our method is designed to learn from a traditionally animated sequence, where each frame is drawn by an artist, and thus the input images lack any common structure, correspondences, or labels. We express pose changes as a deformation of a layered 2.5D template mesh, and devise a novel architecture that learns to predict mesh deformations matching the template to a target image. This enables us to extract a common low-dimensional structure from a diverse set of character poses. We combine recent advances in differentiable rendering as well as mesh-aware models to successfully align common template even if only a few character images are available during training. In addition to coarse poses, character appearance also varies due to shading, out-of-plane motions, and artistic effects. We capture these subtle changes by applying an image translation network to refine the mesh rendering, providing an end-to-end model to generate new animations of a character with high visual quality. We demonstrate that our generative model can be used to synthesize in-between frames and to create data-driven deformation. Our template fitting procedure outperforms state-of-the-art generic techniques for detecting image correspondences.

Theo Deprelle, Thibault Groueix, Matthew Fisher et al.

We propose to represent shapes as the deformation and combination of learnable elementary 3D structures, which are primitives resulting from training over a collection of shape. We demonstrate that the learned elementary 3D structures lead to clear improvements in 3D shape generation and matching. More precisely, we present two complementary approaches for learning elementary structures: (i) patch deformation learning and (ii) point translation learning. Both approaches can be extended to abstract structures of higher dimensions for improved results. We evaluate our method on two tasks: reconstructing ShapeNet objects and estimating dense correspondences between human scans (FAUST inter challenge). We show 16% improvement over surface deformation approaches for shape reconstruction and outperform FAUST inter challenge state of the art by 6%.

Thibault Groueix, Matthew Fisher, Vladimir G. Kim et al.

We propose a self-supervised approach to deep surface deformation. Given a pair of shapes, our algorithm directly predicts a parametric transformation from one shape to the other respecting correspondences. Our insight is to use cycle-consistency to define a notion of good correspondences in groups of objects and use it as a supervisory signal to train our network. Our method does not rely on a template, assume near isometric deformations or rely on point-correspondence supervision. We demonstrate the efficacy of our approach by using it to transfer segmentation across shapes. We show, on Shapenet, that our approach is competitive with comparable state-of-the-art methods when annotated training data is readily available, but outperforms them by a large margin in the few-shot segmentation scenario.

Dmitriy Smirnov, Matthew Fisher, Vladimir G. Kim et al.

Many tasks in graphics and vision demand machinery for converting shapes into consistent representations with sparse sets of parameters; these representations facilitate rendering, editing, and storage. When the source data is noisy or ambiguous, however, artists and engineers often manually construct such representations, a tedious and potentially time-consuming process. While advances in deep learning have been successfully applied to noisy geometric data, the task of generating parametric shapes has so far been difficult for these methods. Hence, we propose a new framework for predicting parametric shape primitives using deep learning. We use distance fields to transition between shape parameters like control points and input data on a pixel grid. We demonstrate efficacy on 2D and 3D tasks, including font vectorization and surface abstraction.

Chen-Hsuan Lin, Oliver Wang, Bryan C. Russell et al.

In this paper, we address the problem of 3D object mesh reconstruction from RGB videos. Our approach combines the best of multi-view geometric and data-driven methods for 3D reconstruction by optimizing object meshes for multi-view photometric consistency while constraining mesh deformations with a shape prior. We pose this as a piecewise image alignment problem for each mesh face projection. Our approach allows us to update shape parameters from the photometric error without any depth or mask information. Moreover, we show how to avoid a degeneracy of zero photometric gradients via rasterizing from a virtual viewpoint. We demonstrate 3D object mesh reconstruction results from both synthetic and real-world videos with our photometric mesh optimization, which is unachievable with either naïve mesh generation networks or traditional pipelines of surface reconstruction without heavy manual post-processing.

Hubert Lin, Melinos Averkiou, Evangelos Kalogerakis et al.

Material understanding is critical for design, geometric modeling, and analysis of functional objects. We enable material-aware 3D shape analysis by employing a projective convolutional neural network architecture to learn material- aware descriptors from view-based representations of 3D points for point-wise material classification or material- aware retrieval. Unfortunately, only a small fraction of shapes in 3D repositories are labeled with physical mate- rials, posing a challenge for learning methods. To address this challenge, we crowdsource a dataset of 3080 3D shapes with part-wise material labels. We focus on furniture models which exhibit interesting structure and material variabil- ity. In addition, we also contribute a high-quality expert- labeled benchmark of 115 shapes from Herman-Miller and IKEA for evaluation. We further apply a mesh-aware con- ditional random field, which incorporates rotational and reflective symmetries, to smooth our local material predic- tions across neighboring surface patches. We demonstrate the effectiveness of our learned descriptors for automatic texturing, material-aware retrieval, and physical simulation. The dataset and code will be publicly available.

Thibault Groueix, Matthew Fisher, Vladimir G. Kim et al.

We present a new deep learning approach for matching deformable shapes by introducing {\it Shape Deformation Networks} which jointly encode 3D shapes and correspondences. This is achieved by factoring the surface representation into (i) a template, that parameterizes the surface, and (ii) a learnt global feature vector that parameterizes the transformation of the template into the input surface. By predicting this feature for a new shape, we implicitly predict correspondences between this shape and the template. We show that these correspondences can be improved by an additional step which improves the shape feature by minimizing the Chamfer distance between the input and transformed template. We demonstrate that our simple approach improves on state-of-the-art results on the difficult FAUST-inter challenge, with an average correspondence error of 2.88cm. We show, on the TOSCA dataset, that our method is robust to many types of perturbations, and generalizes to non-human shapes. This robustness allows it to perform well on real unclean, meshes from the the SCAPE dataset.

Thibault Groueix, Matthew Fisher, Vladimir G. Kim et al.

We introduce a method for learning to generate the surface of 3D shapes. Our approach represents a 3D shape as a collection of parametric surface elements and, in contrast to methods generating voxel grids or point clouds, naturally infers a surface representation of the shape. Beyond its novelty, our new shape generation framework, AtlasNet, comes with significant advantages, such as improved precision and generalization capabilities, and the possibility to generate a shape of arbitrary resolution without memory issues. We demonstrate these benefits and compare to strong baselines on the ShapeNet benchmark for two applications: (i) auto-encoding shapes, and (ii) single-view reconstruction from a still image. We also provide results showing its potential for other applications, such as morphing, parametrization, super-resolution, matching, and co-segmentation.

Sanjeev Muralikrishnan, Vladimir G. Kim, Siddhartha Chaudhuri

We propose a novel method for discovering shape regions that strongly correlate with user-prescribed tags. For example, given a collection of chairs tagged as either "has armrest" or "lacks armrest", our system correctly highlights the armrest regions as the main distinctive parts between the two chair types. To obtain point-wise predictions from shape-wise tags we develop a novel neural network architecture that is trained with tag classification loss, but is designed to rely on segmentation to predict the tag. Our network is inspired by U-Net, but we replicate shallow U structures several times with new skip connections and pooling layers, and call the resulting architecture "WU-Net". We test our method on segmentation benchmarks and show that even with weak supervision of whole shape tags, our method can infer meaningful semantic regions, without ever observing shape segmentations. Further, once trained, the model can process shapes for which the tag is entirely unknown. As a bonus, our architecture is directly operational under full supervision and performs strongly on standard benchmarks. We validate our method through experiments with many variant architectures and prior baselines, and demonstrate several applications.

Haibin Huang, Evangelos Kalogerakis, Siddhartha Chaudhuri et al.

We present a new local descriptor for 3D shapes, directly applicable to a wide range of shape analysis problems such as point correspondences, semantic segmentation, affordance prediction, and shape-to-scan matching. The descriptor is produced by a convolutional network that is trained to embed geometrically and semantically similar points close to one another in descriptor space. The network processes surface neighborhoods around points on a shape that are captured at multiple scales by a succession of progressively zoomed out views, taken from carefully selected camera positions. We leverage two extremely large sources of data to train our network. First, since our network processes rendered views in the form of 2D images, we repurpose architectures pre-trained on massive image datasets. Second, we automatically generate a synthetic dense point correspondence dataset by non-rigid alignment of corresponding shape parts in a large collection of segmented 3D models. As a result of these design choices, our network effectively encodes multi-scale local context and fine-grained surface detail. Our network can be trained to produce either category-specific descriptors or more generic descriptors by learning from multiple shape categories. Once trained, at test time, the network extracts local descriptors for shapes without requiring any part segmentation as input. Our method can produce effective local descriptors even for shapes whose category is unknown or different from the ones used while training. We demonstrate through several experiments that our learned local descriptors are more discriminative compared to state of the art alternatives, and are effective in a variety of shape analysis applications.