Maks Ovsjanikov

Mingze Sun, Shiwei Mao, Puhua Jiang et al.

Cycle consistency has long been exploited as a powerful prior for jointly optimizing maps within a collection of shapes. In this paper, we investigate its utility in the approaches of Deep Functional Maps, which are considered state-of-the-art in non-rigid shape matching. We first justify that under certain conditions, the learned maps, when represented in the spectral domain, are already cycle consistent. Furthermore, we identify the discrepancy that spectrally consistent maps are not necessarily spatially, or point-wise, consistent. In light of this, we present a novel design of unsupervised Deep Functional Maps, which effectively enforces the harmony of learned maps under the spectral and the point-wise representation. By taking advantage of cycle consistency, our framework produces state-of-the-art results in mapping shapes even under significant distortions. Beyond that, by independently estimating maps in both spectral and spatial domains, our method naturally alleviates over-fitting in network training, yielding superior generalization performance and accuracy within an array of challenging tests for both near-isometric and non-isometric datasets. Codes are available at https://github.com/rqhuang88/Spatiallyand-Spectrally-Consistent-Deep-Functional-Maps.

Souhaib Attaiki, Maks Ovsjanikov

Deep functional maps have recently emerged as a successful paradigm for non-rigid 3D shape correspondence tasks. An essential step in this pipeline consists in learning feature functions that are used as constraints to solve for a functional map inside the network. However, the precise nature of the information learned and stored in these functions is not yet well understood. Specifically, a major question is whether these features can be used for any other objective, apart from their purely algebraic role in solving for functional map matrices. In this paper, we show that under some mild conditions, the features learned within deep functional map approaches can be used as point-wise descriptors and thus are directly comparable across different shapes, even without the necessity of solving for a functional map at test time. Furthermore, informed by our analysis, we propose effective modifications to the standard deep functional map pipeline, which promote structural properties of learned features, significantly improving the matching results. Finally, we demonstrate that previously unsuccessful attempts at using extrinsic architectures for deep functional map feature extraction can be remedied via simple architectural changes, which encourage the theoretical properties suggested by our analysis. We thus bridge the gap between intrinsic and extrinsic surface-based learning, suggesting the necessary and sufficient conditions for successful shape matching. Our code is available at https://github.com/pvnieo/clover.

Ramana Sundararaman, Riccardo Marin, Emanuele Rodola et al.

In this work we present a novel approach for computing correspondences between non-rigid objects, by exploiting a reduced representation of deformation fields. Different from existing works that represent deformation fields by training a general-purpose neural network, we advocate for an approximation based on mesh-free methods. By letting the network learn deformation parameters at a sparse set of positions in space (nodes), we reconstruct the continuous deformation field in a closed-form with guaranteed smoothness. With this reduction in degrees of freedom, we show significant improvement in terms of data-efficiency thus enabling limited supervision. Furthermore, our approximation provides direct access to first-order derivatives of deformation fields, which facilitates enforcing desirable regularization effectively. Our resulting model has high expressive power and is able to capture complex deformations. We illustrate its effectiveness through state-of-the-art results across multiple deformable shape matching benchmarks. Our code and data are publicly available at: https://github.com/Sentient07/DeformationBasis.

Panos Achlioptas, Maks Ovsjanikov, Leonidas Guibas et al.

In this work, we explore the emotional reactions that real-world images tend to induce by using natural language as the medium to express the rationale behind an affective response to a given visual stimulus. To embark on this journey, we introduce and share with the research community a large-scale dataset that contains emotional reactions and free-form textual explanations for 85,007 publicly available images, analyzed by 6,283 annotators who were asked to indicate and explain how and why they felt in a particular way when observing a specific image, producing a total of 526,749 responses. Even though emotional reactions are subjective and sensitive to context (personal mood, social status, past experiences) - we show that there is significant common ground to capture potentially plausible emotional responses with a large support in the subject population. In light of this crucial observation, we ask the following questions: i) Can we develop multi-modal neural networks that provide reasonable affective responses to real-world visual data, explained with language? ii) Can we steer such methods towards producing explanations with varying degrees of pragmatic language or justifying different emotional reactions while adapting to the underlying visual stimulus? Finally, iii) How can we evaluate the performance of such methods for this novel task? With this work, we take the first steps in addressing all of these questions, thus paving the way for richer, more human-centric, and emotionally-aware image analysis systems. Our introduced dataset and all developed methods are available on https://affective-explanations.org

Ahmed Abdelreheem, Ivan Skorokhodov, Maks Ovsjanikov et al.

We explore the task of zero-shot semantic segmentation of 3D shapes by using large-scale off-the-shelf 2D image recognition models. Surprisingly, we find that modern zero-shot 2D object detectors are better suited for this task than contemporary text/image similarity predictors or even zero-shot 2D segmentation networks. Our key finding is that it is possible to extract accurate 3D segmentation maps from multi-view bounding box predictions by using the topological properties of the underlying surface. For this, we develop the Segmentation Assignment with Topological Reweighting (SATR) algorithm and evaluate it on ShapeNetPart and our proposed FAUST benchmarks. SATR achieves state-of-the-art performance and outperforms a baseline algorithm by 1.3% and 4% average mIoU on the FAUST coarse and fine-grained benchmarks, respectively, and by 5.2% average mIoU on the ShapeNetPart benchmark. Our source code and data will be publicly released. Project webpage: https://samir55.github.io/SATR/.

Robin Magnet, Jing Ren, Olga Sorkine-Hornung et al.

We introduce pointwise map smoothness via the Dirichlet energy into the functional map pipeline, and propose an algorithm for optimizing it efficiently, which leads to high-quality results in challenging settings. Specifically, we first formulate the Dirichlet energy of the pulled-back shape coordinates, as a way to evaluate smoothness of a pointwise map across discrete surfaces. We then extend the recently proposed discrete solver and show how a strategy based on auxiliary variable reformulation allows us to optimize pointwise map smoothness alongside desirable functional map properties such as bijectivity. This leads to an efficient map refinement strategy that simultaneously improves functional and point-to-point correspondences, obtaining smooth maps even on non-isometric shape pairs. Moreover, we demonstrate that several previously proposed methods for computing smooth maps can be reformulated as variants of our approach, which allows us to compare different formulations in a consistent framework. Finally, we compare these methods both on existing benchmarks and on a new rich dataset that we introduce, which contains non-rigid, non-isometric shape pairs with inter-category and cross-category correspondences. Our work leads to a general framework for optimizing and analyzing map smoothness both conceptually and in challenging practical settings.

Ahmed Abdelreheem, Abdelrahman Eldesokey, Maks Ovsjanikov et al.

We propose a novel zero-shot approach to computing correspondences between 3D shapes. Existing approaches mainly focus on isometric and near-isometric shape pairs (e.g., human vs. human), but less attention has been given to strongly non-isometric and inter-class shape matching (e.g., human vs. cow). To this end, we introduce a fully automatic method that exploits the exceptional reasoning capabilities of recent foundation models in language and vision to tackle difficult shape correspondence problems. Our approach comprises multiple stages. First, we classify the 3D shapes in a zero-shot manner by feeding rendered shape views to a language-vision model (e.g., BLIP2) to generate a list of class proposals per shape. These proposals are unified into a single class per shape by employing the reasoning capabilities of ChatGPT. Second, we attempt to segment the two shapes in a zero-shot manner, but in contrast to the co-segmentation problem, we do not require a mutual set of semantic regions. Instead, we propose to exploit the in-context learning capabilities of ChatGPT to generate two different sets of semantic regions for each shape and a semantic mapping between them. This enables our approach to match strongly non-isometric shapes with significant differences in geometric structure. Finally, we employ the generated semantic mapping to produce coarse correspondences that can further be refined by the functional maps framework to produce dense point-to-point maps. Our approach, despite its simplicity, produces highly plausible results in a zero-shot manner, especially between strongly non-isometric shapes. Project webpage: https://samir55.github.io/3dshapematch/.

Nicolas Donati, Etienne Corman, Maks Ovsjanikov

State-of-the-art fully intrinsic networks for non-rigid shape matching often struggle to disambiguate the symmetries of the shapes leading to unstable correspondence predictions. Meanwhile, recent advances in the functional map framework allow to enforce orientation preservation using a functional representation for tangent vector field transfer, through so-called complex functional maps. Using this representation, we propose a new deep learning approach to learn orientation-aware features in a fully unsupervised setting. Our architecture is built on top of DiffusionNet, making it robust to discretization changes. Additionally, we introduce a vector field-based loss, which promotes orientation preservation without using (often unstable) extrinsic descriptors.

Lei Li, Nicolas Donati, Maks Ovsjanikov

In this work, we present a novel non-rigid shape matching framework based on multi-resolution functional maps with spectral attention. Existing functional map learning methods all rely on the critical choice of the spectral resolution hyperparameter, which can severely affect the overall accuracy or lead to overfitting, if not chosen carefully. In this paper, we show that spectral resolution tuning can be alleviated by introducing spectral attention. Our framework is applicable in both supervised and unsupervised settings, and we show that it is possible to train the network so that it can adapt the spectral resolution, depending on the given shape input. More specifically, we propose to compute multi-resolution functional maps that characterize correspondence across a range of spectral resolutions, and introduce a spectral attention network that helps to combine this representation into a single coherent final correspondence. Our approach is not only accurate with near-isometric input, for which a high spectral resolution is typically preferred, but also robust and able to produce reasonable matching even in the presence of significant non-isometric distortion, which poses great challenges to existing methods. We demonstrate the superior performance of our approach through experiments on a suite of challenging near-isometric and non-isometric shape matching benchmarks.

Mikhail Panine, Maxime Kirgo, Maks Ovsjanikov

We propose a principled approach for non-isometric landmark-preserving non-rigid shape matching. Our method is based on the functional maps framework, but rather than promoting isometries we focus instead on near-conformal maps that preserve landmarks exactly. We achieve this, first, by introducing a novel landmark-adapted basis using an intrinsic Dirichlet-Steklov eigenproblem. Second, we establish the functional decomposition of conformal maps expressed in this basis. Finally, we formulate a conformally-invariant energy that promotes high-quality landmark-preserving maps, and show how it can be solved via a variant of the recently proposed ZoomOut method that we extend to our setting. Our method is descriptor-free, efficient and robust to significant mesh variability. We evaluate our approach on a range of benchmark datasets and demonstrate state-of-the-art performance on non-isometric benchmarks and near state-of-the-art performance on isometric ones.

Ramana Sundararaman, Gautam Pai, Maks Ovsjanikov

Establishing a correspondence between two non-rigidly deforming shapes is one of the most fundamental problems in visual computing. Existing methods often show weak resilience when presented with challenges innate to real-world data such as noise, outliers, self-occlusion etc. On the other hand, auto-decoders have demonstrated strong expressive power in learning geometrically meaningful latent embeddings. However, their use in \emph{shape analysis} has been limited. In this paper, we introduce an approach based on an auto-decoder framework, that learns a continuous shape-wise deformation field over a fixed template. By supervising the deformation field for points on-surface and regularising for points off-surface through a novel \emph{Signed Distance Regularisation} (SDR), we learn an alignment between the template and shape \emph{volumes}. Trained on clean water-tight meshes, \emph{without} any data-augmentation, we demonstrate compelling performance on compromised data and real-world scans.

Maysam Behmanesh, Maximilian Krahn, Maks Ovsjanikov

A prominent paradigm for graph neural networks is based on the message-passing framework. In this framework, information communication is realized only between neighboring nodes. The challenge of approaches that use this paradigm is to ensure efficient and accurate long-distance communication between nodes, as deep convolutional networks are prone to oversmoothing. In this paper, we present a novel method based on time derivative graph diffusion (TIDE) to overcome these structural limitations of the message-passing framework. Our approach allows for optimizing the spatial extent of diffusion across various tasks and network channels, thus enabling medium and long-distance communication efficiently. Furthermore, we show that our architecture design also enables local message-passing and thus inherits from the capabilities of local message-passing approaches. We show that on both widely used graph benchmarks and synthetic mesh and graph datasets, the proposed framework outperforms state-of-the-art methods by a significant margin

Adrien Poulenard, Maks Ovsjanikov, Leonidas J. Guibas

A wide range of techniques have been proposed in recent years for designing neural networks for 3D data that are equivariant under rotation and translation of the input. Most approaches for equivariance under the Euclidean group $\mathrm{SE}(3)$ of rotations and translations fall within one of the two major categories. The first category consists of methods that use $\mathrm{SE}(3)$-convolution which generalizes classical $\mathbb{R}^3$-convolution on signals over $\mathrm{SE}(3)$. Alternatively, it is possible to use \textit{steerable convolution} which achieves $\mathrm{SE}(3)$-equivariance by imposing constraints on $\mathbb{R}^3$-convolution of tensor fields. It is known by specialists in the field that the two approaches are equivalent, with steerable convolution being the Fourier transform of $\mathrm{SE}(3)$ convolution. Unfortunately, these results are not widely known and moreover the exact relations between deep learning architectures built upon these two approaches have not been precisely described in the literature on equivariant deep learning. In this work we provide an in-depth analysis of both methods and their equivalence and relate the two constructions to multiview convolutional networks. Furthermore, we provide theoretical justifications of separability of $\mathrm{SE}(3)$ group convolution, which explain the applicability and success of some recent approaches. Finally, we express different methods using a single coherent formalism and provide explicit formulas that relate the kernels learned by different methods. In this way, our work helps to unify different previously-proposed techniques for achieving roto-translational equivariance, and helps to shed light on both the utility and precise differences between various alternatives. We also derive new TFN non-linearities from our equivalence principle and test them on practical benchmark datasets.

Lei Li, Souhaib Attaiki, Maks Ovsjanikov

In this work, we present a novel learning-based framework that combines the local accuracy of contrastive learning with the global consistency of geometric approaches, for robust non-rigid matching. We first observe that while contrastive learning can lead to powerful point-wise features, the learned correspondences commonly lack smoothness and consistency, owing to the purely combinatorial nature of the standard contrastive losses. To overcome this limitation we propose to boost contrastive feature learning with two types of smoothness regularization that inject geometric information into correspondence learning. With this novel combination in hand, the resulting features are both highly discriminative across individual points, and, at the same time, lead to robust and consistent correspondences, through simple proximity queries. Our framework is general and is applicable to local feature learning in both the 3D and 2D domains. We demonstrate the superiority of our approach through extensive experiments on a wide range of challenging matching benchmarks, including 3D non-rigid shape correspondence and 2D image keypoint matching.

Sara Hahner, Souhaib Attaiki, Jochen Garcke et al.

We introduce a novel learning-based method for encoding and manipulating 3D surface meshes. Our method is specifically designed to create an interpretable embedding space for deformable shape collections. Unlike previous 3D mesh autoencoders that require meshes to be in a 1-to-1 correspondence, our approach is trained on diverse meshes in an unsupervised manner. Central to our method is a spectral pooling technique that establishes a universal latent space, breaking free from traditional constraints of mesh connectivity and shape categories. The entire process consists of two stages. In the first stage, we employ the functional map paradigm to extract point-to-point (p2p) maps between a collection of shapes in an unsupervised manner. These p2p maps are then utilized to construct a common latent space, which ensures straightforward interpretation and independence from mesh connectivity and shape category. Through extensive experiments, we demonstrate that our method achieves excellent reconstructions and produces more realistic and smoother interpolations than baseline approaches.

Souhaib Attaiki, Maks Ovsjanikov

We present Shape Non-rigid Kinematics (SNK), a novel zero-shot method for non-rigid shape matching that eliminates the need for extensive training or ground truth data. SNK operates on a single pair of shapes, and employs a reconstruction-based strategy using an encoder-decoder architecture, which deforms the source shape to closely match the target shape. During the process, an unsupervised functional map is predicted and converted into a point-to-point map, serving as a supervisory mechanism for the reconstruction. To aid in training, we have designed a new decoder architecture that generates smooth, realistic deformations. SNK demonstrates competitive results on traditional benchmarks, simplifying the shape-matching process without compromising accuracy. Our code can be found online: https://github.com/pvnieo/SNK

Souhail Hadgi, Luca Moschella, Andrea Santilli et al.

Recent works have shown that, when trained at scale, uni-modal 2D vision and text encoders converge to learned features that share remarkable structural properties, despite arising from different representations. However, the role of 3D encoders with respect to other modalities remains unexplored. Furthermore, existing 3D foundation models that leverage large datasets are typically trained with explicit alignment objectives with respect to frozen encoders from other representations. In this work, we investigate the possibility of a posteriori alignment of representations obtained from uni-modal 3D encoders compared to text-based feature spaces. We show that naive post-training feature alignment of uni-modal text and 3D encoders results in limited performance. We then focus on extracting subspaces of the corresponding feature spaces and discover that by projecting learned representations onto well-chosen lower-dimensional subspaces the quality of alignment becomes significantly higher, leading to improved accuracy on matching and retrieval tasks. Our analysis further sheds light on the nature of these shared subspaces, which roughly separate between semantic and geometric data representations. Overall, ours is the first work that helps to establish a baseline for post-training alignment of 3D uni-modal and text feature spaces, and helps to highlight both the shared and unique properties of 3D data compared to other representations. Our code and weights are available at https://github.com/Souhail-01/3d-text-alignment

Emery Pierson, Lei Li, Angela Dai et al.

Deep functional maps have recently emerged as a powerful tool for solving non-rigid shape correspondence tasks. Methods that use this approach combine the power and flexibility of the functional map framework, with data-driven learning for improved accuracy and generality. However, most existing methods in this area restrict the learning aspect only to the feature functions and still rely on axiomatic modeling for formulating the training loss or for functional map regularization inside the networks. This limits both the accuracy and the applicability of the resulting approaches only to scenarios where assumptions of the axiomatic models hold. In this work, we show, for the first time, that both in-network regularization and functional map training can be replaced with data-driven methods. For this, we first train a generative model of functional maps in the spectral domain using score-based generative modeling, built from a large collection of high-quality maps. We then exploit the resulting model to promote the structural properties of ground truth functional maps on new shape collections. Remarkably, we demonstrate that the learned models are category-agnostic, and can fully replace commonly used strategies such as enforcing Laplacian commutativity or orthogonality of functional maps. Our key technical contribution is a novel distillation strategy from diffusion models in the spectral domain. Experiments demonstrate that our learned regularization leads to better results than axiomatic approaches for zero-shot non-rigid shape matching. Our code is available at: https://github.com/daidedou/diffumatch/

Souhaib Attaiki, Lei Li, Maks Ovsjanikov

Transfer learning is fundamental for addressing problems in settings with little training data. While several transfer learning approaches have been proposed in 3D, unfortunately, these solutions typically operate on an entire 3D object or even scene-level and thus, as we show, fail to generalize to new classes, such as deformable organic shapes. In addition, there is currently a lack of understanding of what makes pre-trained features transferable across significantly different 3D shape categories. In this paper, we make a step toward addressing these challenges. First, we analyze the link between feature locality and transferability in tasks involving deformable 3D objects, while also comparing different backbones and losses for local feature pre-training. We observe that with proper training, learned features can be useful in such tasks, but, crucially, only with an appropriate choice of the receptive field size. We then propose a differentiable method for optimizing the receptive field within 3D transfer learning. Jointly, this leads to the first learnable features that can successfully generalize to unseen classes of 3D shapes such as humans and animals. Our extensive experiments show that this approach leads to state-of-the-art results on several downstream tasks such as segmentation, shape correspondence, and classification. Our code is available at \url{https://github.com/pvnieo/vader}.

Souhaib Attaiki, Maks Ovsjanikov

We present Neural Correspondence Prior (NCP), a new paradigm for computing correspondences between 3D shapes. Our approach is fully unsupervised and can lead to high-quality correspondences even in challenging cases such as sparse point clouds or non-isometric meshes, where current methods fail. Our first key observation is that, in line with neural priors observed in other domains, recent network architectures on 3D data, even without training, tend to produce pointwise features that induce plausible maps between rigid or non-rigid shapes. Secondly, we show that given a noisy map as input, training a feature extraction network with the input map as supervision tends to remove artifacts from the input and can act as a powerful correspondence denoising mechanism, both between individual pairs and within a collection. With these observations in hand, we propose a two-stage unsupervised paradigm for shape matching by (i) performing unsupervised training by adapting an existing approach to obtain an initial set of noisy matches, and (ii) using these matches to train a network in a supervised manner. We demonstrate that this approach significantly improves the accuracy of the maps, especially when trained within a collection. We show that NCP is data-efficient, fast, and achieves state-of-the-art results on many tasks. Our code can be found online: https://github.com/pvnieo/NCP.

Souhaib Attaiki, Gautam Pai, Maks Ovsjanikov

We consider the problem of computing dense correspondences between non-rigid shapes with potentially significant partiality. Existing formulations tackle this problem through heavy manifold optimization in the spectral domain, given hand-crafted shape descriptors. In this paper, we propose the first learning method aimed directly at partial non-rigid shape correspondence. Our approach uses the functional map framework, can be trained in a supervised or unsupervised manner, and learns descriptors directly from the data, thus both improving robustness and accuracy in challenging cases. Furthermore, unlike existing techniques, our method is also applicable to partial-to-partial non-rigid matching, in which the common regions on both shapes are unknown a priori. We demonstrate that the resulting method is data-efficient, and achieves state-of-the-art results on several benchmark datasets. Our code and data can be found online: https://github.com/pvnieo/DPFM

Marie-Julie Rakotosaona, Noam Aigerman, Niloy Mitra et al.

Triangle meshes remain the most popular data representation for surface geometry. This ubiquitous representation is essentially a hybrid one that decouples continuous vertex locations from the discrete topological triangulation. Unfortunately, the combinatorial nature of the triangulation prevents taking derivatives over the space of possible meshings of any given surface. As a result, to date, mesh processing and optimization techniques have been unable to truly take advantage of modular gradient descent components of modern optimization frameworks. In this work, we present a differentiable surface triangulation that enables optimization for any per-vertex or per-face differentiable objective function over the space of underlying surface triangulations. Our method builds on the result that any 2D triangulation can be achieved by a suitably perturbed weighted Delaunay triangulation. We translate this result into a computational algorithm by proposing a soft relaxation of the classical weighted Delaunay triangulation and optimizing over vertex weights and vertex locations. We extend the algorithm to 3D by decomposing shapes into developable sets and differentiably meshing each set with suitable boundary constraints. We demonstrate the efficacy of our method on various planar and surface meshes on a range of difficult-to-optimize objective functions. Our code can be found online: https://github.com/mrakotosaon/diff-surface-triangulation.

Marie-Julie Rakotosaona, Paul Guerrero, Noam Aigerman et al.

We present a method for reconstructing triangle meshes from point clouds. Existing learning-based methods for mesh reconstruction mostly generate triangles individually, making it hard to create manifold meshes. We leverage the properties of 2D Delaunay triangulations to construct a mesh from manifold surface elements. Our method first estimates local geodesic neighborhoods around each point. We then perform a 2D projection of these neighborhoods using a learned logarithmic map. A Delaunay triangulation in this 2D domain is guaranteed to produce a manifold patch, which we call a Delaunay surface element. We synchronize the local 2D projections of neighboring elements to maximize the manifoldness of the reconstructed mesh. Our results show that we achieve better overall manifoldness of our reconstructed meshes than current methods to reconstruct meshes with arbitrary topology. Our code, data and pretrained models can be found online: https://github.com/mrakotosaon/dse-meshing

Abhishek Sharma, Maks Ovsjanikov

We propose a totally functional view of geometric matrix completion problem. Differently from existing work, we propose a novel regularization inspired from the functional map literature that is more interpretable and theoretically sound. On synthetic tasks with strong underlying geometric structure, our framework outperforms state of the art by a huge margin (two order of magnitude) demonstrating the potential of our approach. On real datasets, we achieve state-of-the-art results at a fraction of the computational effort of previous methods. Our code is publicly available at https://github.com/Not-IITian/functional-matrix-completion

Abhishek Sharma, Maks Ovsjanikov

A variety of deep functional maps have been proposed recently, from fully supervised to totally unsupervised, with a range of loss functions as well as different regularization terms. However, it is still not clear what are minimum ingredients of a deep functional map pipeline and whether such ingredients unify or generalize all recent work on deep functional maps. We show empirically minimum components for obtaining state of the art results with different loss functions, supervised as well as unsupervised. Furthermore, we propose a novel framework designed for both full-to-full as well as partial to full shape matching that achieves state of the art results on several benchmark datasets outperforming even the fully supervised methods by a significant margin. Our code is publicly available at https://github.com/Not-IITian/Weakly-supervised-Functional-map

Nicolas Donati, Abhishek Sharma, Maks Ovsjanikov

We present a novel learning-based approach for computing correspondences between non-rigid 3D shapes. Unlike previous methods that either require extensive training data or operate on handcrafted input descriptors and thus generalize poorly across diverse datasets, our approach is both accurate and robust to changes in shape structure. Key to our method is a feature-extraction network that learns directly from raw shape geometry, combined with a novel regularized map extraction layer and loss, based on the functional map representation. We demonstrate through extensive experiments in challenging shape matching scenarios that our method can learn from less training data than existing supervised approaches and generalizes significantly better than current descriptor-based learning methods. Our source code is available at: https://github.com/LIX-shape-analysis/GeomFmaps.

Bingchen Gong, Diego Gomez, Abdullah Hamdi et al.

We propose a novel zero-shot approach for keypoint detection on 3D shapes. Point-level reasoning on visual data is challenging as it requires precise localization capability, posing problems even for powerful models like DINO or CLIP. Traditional methods for 3D keypoint detection rely heavily on annotated 3D datasets and extensive supervised training, limiting their scalability and applicability to new categories or domains. In contrast, our method utilizes the rich knowledge embedded within Multi-Modal Large Language Models (MLLMs). Specifically, we demonstrate, for the first time, that pixel-level annotations used to train recent MLLMs can be exploited for both extracting and naming salient keypoints on 3D models without any ground truth labels or supervision. Experimental evaluations demonstrate that our approach achieves competitive performance on standard benchmarks compared to supervised methods, despite not requiring any 3D keypoint annotations during training. Our results highlight the potential of integrating language models for localized 3D shape understanding. This work opens new avenues for cross-modal learning and underscores the effectiveness of MLLMs in contributing to 3D computer vision challenges.

Erkan Turan, Aristotelis Siozopoulos, Louis Martinez et al.

Continuous Normalizing Flows (CNFs) enable elegant generative modeling but remain bottlenecked by slow sampling: producing a single sample requires solving a nonlinear ODE with hundreds of function evaluations. Recent approaches such as Rectified Flow and OT-CFM accelerate sampling by straightening trajectories, yet the learned dynamics remain nonlinear black boxes, limiting both efficiency and interpretability. We propose a fundamentally different perspective: globally linearizing flow dynamics via Koopman theory. By lifting Conditional Flow Matching (CFM) into a higher-dimensional Koopman space, we represent its evolution with a single linear operator. This yields two key benefits. First, sampling becomes one-step and parallelizable, computed in closed form via the matrix exponential. Second, the Koopman operator provides a spectral blueprint of generation, enabling novel interpretability through its eigenvalues and modes. We derive a practical, simulation-free training objective that enforces infinitesimal consistency with the teacher's dynamics and show that this alignment preserves fidelity along the full generative path, distinguishing our method from boundary-only distillation. Empirically, our approach achieves competitive sample quality with dramatic speedups, while uniquely enabling spectral analysis of generative flows.

Diego Gomez, Bingchen Gong, Maks Ovsjanikov

In this work, we introduce FourieRF, a novel approach for achieving fast and high-quality reconstruction in the few-shot setting. Our method effectively parameterizes features through an explicit curriculum training procedure, incrementally increasing scene complexity during optimization. Experimental results show that the prior induced by our approach is both robust and adaptable across a wide variety of scenes, establishing FourieRF as a strong and versatile baseline for the few-shot rendering problem. While our approach significantly reduces artifacts, it may still lead to reconstruction errors in severely under-constrained scenarios, particularly where view occlusion leaves parts of the shape uncovered. In the future, our method could be enhanced by integrating foundation models to complete missing parts using large data-driven priors.

Souhaib Attaiki, Paul Guerrero, Duygu Ceylan et al.

We train a feed-forward text-to-3D diffusion generator for human characters using only single-view 2D data for supervision. Existing 3D generative models cannot yet match the fidelity of image or video generative models. State-of-the-art 3D generators are either trained with explicit 3D supervision and are thus limited by the volume and diversity of existing 3D data. Meanwhile, generators that can be trained with only 2D data as supervision typically produce coarser results, cannot be text-conditioned, or must revert to test-time optimization. We observe that GAN- and diffusion-based generators have complementary qualities: GANs can be trained efficiently with 2D supervision to produce high-quality 3D objects but are hard to condition on text. In contrast, denoising diffusion models can be conditioned efficiently but tend to be hard to train with only 2D supervision. We introduce GANFusion, which starts by generating unconditional triplane features for 3D data using a GAN architecture trained with only single-view 2D data. We then generate random samples from the GAN, caption them, and train a text-conditioned diffusion model that directly learns to sample from the space of good triplane features that can be decoded into 3D objects.

Maysam Behmanesh, Erkan Turan, Maks Ovsjanikov

Graph alignment, the problem of identifying corresponding nodes across multiple graphs, is fundamental to numerous applications. Most existing unsupervised methods embed node features into latent representations to enable cross-graph comparison without ground-truth correspondences. However, these methods suffer from two critical limitations: the degradation of node distinctiveness due to oversmoothing in GNN-based embeddings, and the misalignment of latent spaces across graphs caused by structural noise, feature heterogeneity, and training instability, ultimately leading to unreliable node correspondences. We propose a novel graph alignment framework that simultaneously enhances node distinctiveness and enforces geometric consistency across latent spaces. Our approach introduces a dual-pass encoder that combines low-pass and high-pass spectral filters to generate embeddings that are both structure-aware and highly discriminative. To address latent space misalignment, we incorporate a geometry-aware functional map module that learns bijective and isometric transformations between graph embeddings, ensuring consistent geometric relationships across different representations. Extensive experiments on graph benchmarks demonstrate that our method consistently outperforms existing unsupervised alignment baselines, exhibiting superior robustness to structural inconsistencies and challenging alignment scenarios. Additionally, comprehensive evaluation on vision-language benchmarks using diverse pretrained models shows that our framework effectively generalizes beyond graph domains, enabling unsupervised alignment of vision and language representations.

Souhail Hadgi, Lei Li, Maks Ovsjanikov

Transfer learning has long been a key factor in the advancement of many fields including 2D image analysis. Unfortunately, its applicability in 3D data processing has been relatively limited. While several approaches for point cloud transfer learning have been proposed in recent literature, with contrastive learning gaining particular prominence, most existing methods in this domain have only been studied and evaluated in limited scenarios. Most importantly, there is currently a lack of principled understanding of both when and why point cloud transfer learning methods are applicable. Remarkably, even the applicability of standard supervised pre-training is poorly understood. In this work, we conduct the first in-depth quantitative and qualitative investigation of supervised and contrastive pre-training strategies and their utility in downstream 3D tasks. We demonstrate that layer-wise analysis of learned features provides significant insight into the downstream utility of trained networks. Informed by this analysis, we propose a simple geometric regularization strategy, which improves the transferability of supervised pre-training. Our work thus sheds light onto both the specific challenges of point cloud transfer learning, as well as strategies to overcome them.

Nissim Maruani, Maks Ovsjanikov, Pierre Alliez et al.

Although polygon meshes have been a standard representation in geometry processing, their irregular and combinatorial nature hinders their suitability for learning-based applications. In this work, we introduce a novel learnable mesh representation through a set of local 3D sample Points and their associated Normals and Quadric error metrics (QEM) w.r.t. the underlying shape, which we denote PoNQ. A global mesh is directly derived from PoNQ by efficiently leveraging the knowledge of the local quadric errors. Besides marking the first use of QEM within a neural shape representation, our contribution guarantees both topological and geometrical properties by ensuring that a PoNQ mesh does not self-intersect and is always the boundary of a volume. Notably, our representation does not rely on a regular grid, is supervised directly by the target surface alone, and also handles open surfaces with boundaries and/or sharp features. We demonstrate the efficacy of PoNQ through a learning-based mesh prediction from SDF grids and show that our method surpasses recent state-of-the-art techniques in terms of both surface and edge-based metrics.

Maysam Behmanesh, Maks Ovsjanikov

Graph contrastive learning (GCL) aligns node representations by classifying node pairs into positives and negatives using a selection process that typically relies on establishing correspondences within two augmented graphs. The conventional GCL approaches incorporate negative samples uniformly in the contrastive loss, resulting in the equal treatment of negative nodes, regardless of their proximity to the true positive. In this paper, we present a Smoothed Graph Contrastive Learning model (SGCL), which leverages the geometric structure of augmented graphs to inject proximity information associated with positive/negative pairs in the contrastive loss, thus significantly regularizing the learning process. The proposed SGCL adjusts the penalties associated with node pairs in contrastive loss by incorporating three distinct smoothing techniques that result in proximity-aware positives and negatives. To enhance scalability for large-scale graphs, the proposed framework incorporates a graph batch-generating strategy that partitions the given graphs into multiple subgraphs, facilitating efficient training in separate batches. Through extensive experimentation in the unsupervised setting on various benchmarks, particularly those of large scale, we demonstrate the superiority of our proposed framework against recent baselines.

Nissim Maruani, Roman Klokov, Maks Ovsjanikov et al.

In stark contrast to the case of images, finding a concise, learnable discrete representation of 3D surfaces remains a challenge. In particular, while polygon meshes are arguably the most common surface representation used in geometry processing, their irregular and combinatorial structure often make them unsuitable for learning-based applications. In this work, we present VoroMesh, a novel and differentiable Voronoi-based representation of watertight 3D shape surfaces. From a set of 3D points (called generators) and their associated occupancy, we define our boundary representation through the Voronoi diagram of the generators as the subset of Voronoi faces whose two associated (equidistant) generators are of opposite occupancy: the resulting polygon mesh forms a watertight approximation of the target shape's boundary. To learn the position of the generators, we propose a novel loss function, dubbed VoroLoss, that minimizes the distance from ground truth surface samples to the closest faces of the Voronoi diagram which does not require an explicit construction of the entire Voronoi diagram. A direct optimization of the Voroloss to obtain generators on the Thingi32 dataset demonstrates the geometric efficiency of our representation compared to axiomatic meshing algorithms and recent learning-based mesh representations. We further use VoroMesh in a learning-based mesh prediction task from input SDF grids on the ABC dataset, and show comparable performance to state-of-the-art methods while guaranteeing closed output surfaces free of self-intersections.

Nicolas Donati, Etienne Corman, Simone Melzi et al.

In this paper, we introduce complex functional maps, which extend the functional map framework to conformal maps between tangent vector fields on surfaces. A key property of these maps is their orientation awareness. More specifically, we demonstrate that unlike regular functional maps that link functional spaces of two manifolds, our complex functional maps establish a link between oriented tangent bundles, thus permitting robust and efficient transfer of tangent vector fields. By first endowing and then exploiting the tangent bundle of each shape with a complex structure, the resulting operations become naturally orientationaware, thus favoring orientation and angle preserving correspondence across shapes, without relying on descriptors or extra regularization. Finally, and perhaps more importantly, we demonstrate how these objects enable several practical applications within the functional map framework. We show that functional maps and their complex counterparts can be estimated jointly to promote orientation preservation, regularizing pipelines that previously suffered from orientation-reversing symmetry errors.

Riccardo Marin, Souhaib Attaiki, Simone Melzi et al.

Many innovative applications require establishing correspondences among 3D geometric objects. However, the countless possible deformations of smooth surfaces make shape matching a challenging task. Finding an embedding to represent the different shapes in high-dimensional space where the matching is easier to solve is a well-trodden path that has given many outstanding solutions. Recently, a new trend has shown advantages in learning such representations. This novel idea motivated us to investigate which properties differentiate these data-driven embeddings and which ones promote state-of-the-art results. In this study, we analyze, for the first time, properties that arise in data-driven learned embedding and their relation to the shape-matching task. Our discoveries highlight the close link between matching and smoothness, which naturally emerge from training. Also, we demonstrate the relation between the orthogonality of the embedding and the bijectivity of the correspondence. Our experiments show exciting results, overcoming well-established alternatives and shedding a different light on relevant contexts and properties for learned embeddings.

Abhishek Sharma, Maks Ovsjanikov

Despite the success of deep functional maps in non-rigid 3D shape matching, there exists no learning framework that models both self-symmetry and shape matching simultaneously. This is despite the fact that errors due to symmetry mismatch are a major challenge in non-rigid shape matching. In this paper, we propose a novel framework that simultaneously learns both self symmetry as well as a pairwise map between a pair of shapes. Our key idea is to couple a self symmetry map and a pairwise map through a regularization term that provides a joint constraint on both of them, thereby, leading to more accurate maps. We validate our method on several benchmarks where it outperforms many competitive baselines on both tasks.

Abhishek Sharma, Maks Ovsjanikov

This paper provides a novel framework that learns canonical embeddings for non-rigid shape matching. In contrast to prior work in this direction, our framework is trained end-to-end and thus avoids instabilities and constraints associated with the commonly-used Laplace-Beltrami basis or sequential optimization schemes. On multiple datasets, we demonstrate that learning self symmetry maps with a deep functional map projects 3D shapes into a low dimensional canonical embedding that facilitates non-rigid shape correspondence via a simple nearest neighbor search. Our framework outperforms multiple recent learning based methods on FAUST and SHREC benchmarks while being computationally cheaper, data-efficient, and robust.

Lei Li, Hongbo Fu, Maks Ovsjanikov

In this work, we present a novel method called WSDesc to learn 3D local descriptors in a weakly supervised manner for robust point cloud registration. Our work builds upon recent 3D CNN-based descriptor extractors, which leverage a voxel-based representation to parameterize local geometry of 3D points. Instead of using a predefined fixed-size local support in voxelization, we propose to learn the optimal support in a data-driven manner. To this end, we design a novel differentiable voxelization layer that can back-propagate the gradient to the support size optimization. To train the extracted descriptors, we propose a novel registration loss based on the deviation from rigidity of 3D transformations, and the loss is weakly supervised by the prior knowledge that the input point clouds have partial overlap, without requiring ground-truth alignment information. Through extensive experiments, we show that our learned descriptors yield superior performance on existing geometric registration benchmarks.

Luca Moschella, Simone Melzi, Luca Cosmo et al.

Spectral geometric methods have brought revolutionary changes to the field of geometry processing. Of particular interest is the study of the Laplacian spectrum as a compact, isometry and permutation-invariant representation of a shape. Some recent works show how the intrinsic geometry of a full shape can be recovered from its spectrum, but there are approaches that consider the more challenging problem of recovering the geometry from the spectral information of partial shapes. In this paper, we propose a possible way to fill this gap. We introduce a learning-based method to estimate the Laplacian spectrum of the union of partial non-rigid 3D shapes, without actually computing the 3D geometry of the union or any correspondence between those partial shapes. We do so by operating purely in the spectral domain and by defining the union operation between short sequences of eigenvalues. We show that the approximated union spectrum can be used as-is to reconstruct the complete geometry [MRC*19], perform region localization on a template [RTO*19] and retrieve shapes from a database, generalizing ShapeDNA [RWP06] to work with partialities. Working with eigenvalues allows us to deal with unknown correspondence, different sampling, and different discretizations (point clouds and meshes alike), making this operation especially robust and general. Our approach is data-driven and can generalize to isometric and non-isometric deformations of the surface, as long as these stay within the same semantic class (e.g., human bodies or horses), as well as to partiality artifacts not seen at training time.

Abhishek Sharma, Maks Ovsjanikov

We propose a functional view of matrix decomposition problems on graphs such as geometric matrix completion and graph regularized dimensionality reduction. Our unifying framework is based on the key idea that using a reduced basis to represent functions on the product space is sufficient to recover a low rank matrix approximation even from a sparse signal. We validate our framework on several real and synthetic benchmarks (for both problems) where it either outperforms state of the art or achieves competitive results at a fraction of the computational effort of prior work.

Panos Achlioptas, Maks Ovsjanikov, Kilichbek Haydarov et al.

We present a novel large-scale dataset and accompanying machine learning models aimed at providing a detailed understanding of the interplay between visual content, its emotional effect, and explanations for the latter in language. In contrast to most existing annotation datasets in computer vision, we focus on the affective experience triggered by visual artworks and ask the annotators to indicate the dominant emotion they feel for a given image and, crucially, to also provide a grounded verbal explanation for their emotion choice. As we demonstrate below, this leads to a rich set of signals for both the objective content and the affective impact of an image, creating associations with abstract concepts (e.g., "freedom" or "love"), or references that go beyond what is directly visible, including visual similes and metaphors, or subjective references to personal experiences. We focus on visual art (e.g., paintings, artistic photographs) as it is a prime example of imagery created to elicit emotional responses from its viewers. Our dataset, termed ArtEmis, contains 439K emotion attributions and explanations from humans, on 81K artworks from WikiArt. Building on this data, we train and demonstrate a series of captioning systems capable of expressing and explaining emotions from visual stimuli. Remarkably, the captions produced by these systems often succeed in reflecting the semantic and abstract content of the image, going well beyond systems trained on existing datasets. The collected dataset and developed methods are available at https://artemisdataset.org.

Nicholas Sharp, Souhaib Attaiki, Keenan Crane et al.

We introduce a new general-purpose approach to deep learning on 3D surfaces, based on the insight that a simple diffusion layer is highly effective for spatial communication. The resulting networks are automatically robust to changes in resolution and sampling of a surface -- a basic property which is crucial for practical applications. Our networks can be discretized on various geometric representations such as triangle meshes or point clouds, and can even be trained on one representation then applied to another. We optimize the spatial support of diffusion as a continuous network parameter ranging from purely local to totally global, removing the burden of manually choosing neighborhood sizes. The only other ingredients in the method are a multi-layer perceptron applied independently at each point, and spatial gradient features to support directional filters. The resulting networks are simple, robust, and efficient. Here, we focus primarily on triangle mesh surfaces, and demonstrate state-of-the-art results for a variety of tasks including surface classification, segmentation, and non-rigid correspondence.

Riccardo Marin, Marie-Julie Rakotosaona, Simone Melzi et al.

In this paper, we propose a fully differentiable pipeline for estimating accurate dense correspondences between 3D point clouds. The proposed pipeline is an extension and a generalization of the functional maps framework. However, instead of using the Laplace-Beltrami eigenfunctions as done in virtually all previous works in this domain, we demonstrate that learning the basis from data can both improve robustness and lead to better accuracy in challenging settings. We interpret the basis as a learned embedding into a higher dimensional space. Following the functional map paradigm the optimal transformation in this embedding space must be linear and we propose a separate architecture aimed at estimating the transformation by learning optimal descriptor functions. This leads to the first end-to-end trainable functional map-based correspondence approach in which both the basis and the descriptors are learned from data. Interestingly, we also observe that learning a \emph{canonical} embedding leads to worse results, suggesting that leaving an extra linear degree of freedom to the embedding network gives it more robustness, thereby also shedding light onto the success of previous methods. Finally, we demonstrate that our approach achieves state-of-the-art results in challenging non-rigid 3D point cloud correspondence applications.

Nicholas Sharp, Maks Ovsjanikov

This work considers a new task in geometric deep learning: generating a triangulation among a set of points in 3D space. We present PointTriNet, a differentiable and scalable approach enabling point set triangulation as a layer in 3D learning pipelines. The method iteratively applies two neural networks: a classification network predicts whether a candidate triangle should appear in the triangulation, while a proposal network suggests additional candidates. Both networks are structured as PointNets over nearby points and triangles, using a novel triangle-relative input encoding. Since these learning problems operate on local geometric data, our method is efficient and scalable, and generalizes to unseen shape categories. Our networks are trained in an unsupervised manner from a collection of shapes represented as point clouds. We demonstrate the effectiveness of this approach for classical meshing tasks, robustness to outliers, and as a component in end-to-end learning systems.

Marie-Julie Rakotosaona, Maks Ovsjanikov

We present a learning-based method for interpolating and manipulating 3D shapes represented as point clouds, that is explicitly designed to preserve intrinsic shape properties. Our approach is based on constructing a dual encoding space that enables shape synthesis and, at the same time, provides links to the intrinsic shape information, which is typically not available on point cloud data. Our method works in a single pass and avoids expensive optimization, employed by existing techniques. Furthermore, the strong regularization provided by our dual latent space approach also helps to improve shape recovery in challenging settings from noisy point clouds across different datasets. Extensive experiments show that our method results in more realistic and smoother interpolations compared to baselines.

Riccardo Marin, Arianna Rampini, Umberto Castellani et al.

We introduce the first learning-based method for recovering shapes from Laplacian spectra. Given an auto-encoder, our model takes the form of a cycle-consistent module to map latent vectors to sequences of eigenvalues. This module provides an efficient and effective linkage between spectrum and geometry of a given shape. 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 provide a proxy to differentiable eigendecomposition and 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.

Adrien Poulenard, Marie-Julie Rakotosaona, Yann Ponty et al.

We present a novel rotation invariant architecture operating directly on point cloud data. We demonstrate how rotation invariance can be injected into a recently proposed point-based PCNN architecture, at all layers of the network, achieving invariance to both global shape transformations, and to local rotations on the level of patches or parts, useful when dealing with non-rigid objects. We achieve this by employing a spherical harmonics based kernel at different layers of the network, which is guaranteed to be invariant to rigid motions. We also introduce a more efficient pooling operation for PCNN using space-partitioning data-structures. This results in a flexible, simple and efficient architecture that achieves accurate results on challenging shape analysis tasks including classification and segmentation, without requiring data-augmentation, typically employed by non-invariant approaches.

Ruqi Huang, Marie-Julie Rakotosaona, Panos Achlioptas et al.

This paper proposes a learning-based framework for reconstructing 3D shapes from functional operators, compactly encoded as small-sized matrices. To this end we introduce a novel neural architecture, called OperatorNet, which takes as input a set of linear operators representing a shape and produces its 3D embedding. We demonstrate that this approach significantly outperforms previous purely geometric methods for the same problem. Furthermore, we introduce a novel functional operator, which encodes the extrinsic or pose-dependent shape information, and thus complements purely intrinsic pose-oblivious operators, such as the classical Laplacian. Coupled with this novel operator, our reconstruction network achieves very high reconstruction accuracy, even in the presence of incomplete information about a shape, given a soft or functional map expressed in a reduced basis. Finally, we demonstrate that the multiplicative functional algebra enjoyed by these operators can be used to synthesize entirely new unseen shapes, in the context of shape interpolation and shape analogy applications.