Creating human avatars is a highly desirable yet challenging task. Recent advancements in radiance field rendering have achieved unprecedented photorealism and realtime performance for personalized dynamic human avatars. However, these approaches are typically limited to personspecific rendering models trained on multi-view video data for a single individual, limiting their ability to generalize across different identities. On the other hand, generative approaches leveraging prior knowledge from pre-trained 2D diffusion models can produce cartoonish, static human avatars, which are animated through simple skeleton-based articulation. Therefore, the avatars generated by these methods suffer from lower rendering quality compared to person-specific rendering methods and fail to capture pose- dependent deformations such as cloth wrinkles. In this paper, we propose a novel approach that unites the strengths of person-specific rendering and diffusion-based generative modeling to enable dynamic human avatar generation with both high photorealism and realistic pose-dependent deformations. Our method follows a two-stage pipeline: first, we optimize a set of person-specific UNets, with each network representing a dynamic human avatar that captures intricate pose-dependent deformations. In the second stage, we train a hyper diffusion model over the optimized network weights. During inference, our method generates network weights for real-time, controllable rendering of dynamic human avatars. Using a large-scale, cross-identity, multi-view video dataset, we demonstrate that our approach outperforms state-of-the-art human avatar generation methods.

The task of establishing correspondences between two 3D shapes is a long-standing challenge in computer vision. While numerous studies address full-full and partial-full 3D shape matching, only a limited number of works have explored the partial-partial setting, very likely due to its unique challenges: we must compute accurate correspondences while at the same time find the unknown overlapping region. Nevertheless, partial-partial 3D shape matching reflects the most realistic setting, as in many real-world cases, such as 3D scanning, shapes are only partially observable. In this work, we introduce the first integer linear programming approach specifically designed to address the distinctive challenges of partial-partial shape matching. Our method leverages geometric consistency as a strong prior, enabling both robust estimation of the overlapping region and computation of neighbourhood-preserving correspondences. We empirically demonstrate that our approach achieves high-quality matching results both in terms of matching error and smoothness. Moreover, we show that our method is more scalable than previous formalisms. Our code is publicly available at https://github.com/vikiehm/partial-geco.

Recovering a 4D motion from sparse visual information (such as two temporal frames of a subject) is a significant challenge. While humans are able to hallucinate the missing information in a plausible way, generative AI struggles due to a lack of high-quality training data and heavy computing requirements. To overcome these limitations, we propose TwoSquared, a method that obtains a 4D plausible sequence from just two 2D RGB images corresponding to the beginning and the end of the action. We propose to solve the problem in two steps: 1) first, obtaining a 3D reconstruction of the initial and final status, and 2) model the intermediate sequence as a physically plausible deformation. Our method does not require templates or class-specific prior knowledge, and can operate with arbitrary in-the-wild examples. We demonstrate our capabilities in a number of different objects, diverse in terms of nature, class, and deformation, surpassing video-based alternatives, which cannot achieve the same level of consistency.

Matching a 2D contour to a non-rigidly deformed 3D mesh is a challenging problem due to ambiguities arising from dimensionality differences. In the past, product graph based methods were only able to either produce fast but noisy solutions, or smooth but slow solutions (the latter enabled by higher-order costs computed in the conjugate product graph). In this work, we propose an approximation of these higher-order costs so that they can be computed in the ordinary product graph. This leads to an efficient algorithm for high-quality 2D-3D shape matching and enables novel applications, like an interactive user interface which allows to refine the solution gradually. We show theoretically that our method is efficient, and we experimentally validate that the accuracy gap of our approximation to the optimum is small in practice. Our code is available.11https://github.com/christophpetzsch/sm-2D3D-approx

Multi-graph matching is an important problem in computer vision. Our task comes from bioimaging, where a set of 100 3D-microscopic images of worms have to be brought into correspondence. Surprisingly, virtually all existing methods are not applicable to this large-scale, real-world problem since they either assume a complete or dense problem setting, and they have so far only been applied to small-scale, toy or synthetic problems. Despite claims in literature that methods addressing complete multi-graph matching are applicable in an incomplete setting, our first contribution is to prove that their runtime would be excessive and impractical. Our second contribution is a new method for incomplete multi-graph matching that applies to real-world, larger-scale problems. We experimentally show that for our bioimaging application we are able to attain results in less than two minutes, whereas the only competing approach requires at least half an hour while producing far worse results. Furthermore, even for small-scale, dense or complete problem instances we achieve results that are at least on par with the leading methods, but an order of magnitude faster.

In this work we address various shape matching problems that can be cast as finding cyclic paths in a product graph. This involves for example 2D-3D shape matching, 3D shape matching, or the matching of a contour to a graph. In this context, matchings are typically obtained as the minimum cost cycle in the product graph. Instead, inspired by related works on model-based image segmentation [68], we consider minimum ratio cycles, which we combine with the recently introduced conjugate product graph in order to allow for higher-order matching costs. With that, on the one hand we avoid the bias of obtaining matchings that involve fewer/shorter edges, while on the other hand we are able to impose powerful geometric regularisation, e.g. to avoid zigzagging. In our experiments we demonstrate that this not only leads to improved matching accuracy in most cases, but also to significantly reduced runtimes (up to two orders of magnitude, depending on the setting). Our GPU implementations are publicly available: https://github.com/paul0noah/product-graph-cycles/.

Generating realistic intermediate shapes between non-rigidly deformed shapes is a challenging task in computer vision, especially with unstructured data (e.g., point clouds) where temporal consistency across frames is lacking, and topologies are changing. Most interpolation methods are designed for structured data (i.e., meshes) and do not apply to real-world point clouds. In contrast, our approach, 4Deform, leverages neural implicit representation (NIR) to enable free topology changing shape deformation. Unlike previous mesh-based methods that learn vertex-based deformation fields, our method learns a continuous velocity field in Euclidean space. Thus, it is suitable for less structured data such as point clouds. Additionally, our method does not require intermediate-shape supervision during training; instead, we incorporate physical and geometrical constraints to regularize the velocity field. We reconstruct intermediate surfaces using a modified level-set equation, directly linking our NIR with the velocity field. Experiments show that our method significantly outperforms previous NIR approaches across various scenarios (e.g., noisy, partial, topology-changing, non-isometric shapes) and, for the first time, enables new applications like 4D Kinect sequence upsampling and real-world high-resolution mesh deformation.

Finding correspondences between 3D shapes is a crucial problem in computer vision and graphics. While most research has focused on finding correspondences in settings where at least one of the shapes is complete, the realm of partial-to-partial shape matching remains under-explored. Yet, it is important since in many applications shapes are only observed partially due to occlusion or scanning. Finding correspondences between partial shapes comes with an additional challenge: We not only want to identify correspondences between points on either shape but also have to determine which points of each shape actually have a partner. To tackle this challenging problem, we present EchoMatch, a novel framework for partial-to-partial shape matching that incorporates the concept of correspondence reflection to enable an overlap prediction within a functional map framework. With this approach, we show that we can outperform current SOTA methods in challenging partial-to-partial shape matching problems. Our code is available at https://echo-match.github.io.

In this work, we introduce the first unsupervised method that simultaneously predicts time-varying neural implicit surfaces and deformations between pairs of point clouds. We propose to model the point movement using an explicit velocity field and directly deform a time-varying implicit field using the modified level-set equation. This equation utilizes an iso-surface evolution with Eikonal constraints in a compact formulation, ensuring the integrity of the signed distance field. By applying a smooth, volume-preserving constraint to the velocity field, our method successfully recovers physically plausible intermediate shapes. Our method is able to handle both rigid and non-rigid deformations without any intermediate shape supervision. Our experimental results demonstrate that our method significantly outperforms existing works, delivering superior results in both quality and efficiency.

Abstract 3D shape matching plays a fundamental role in applications such as texture transfer and 3D animation. A key requirement for many scenarios is that matchings exhibit geometric consistency, which ensures that matchings preserve neighbourhood relations across shapes. Despite the importance of geometric consistency, few existing methods explicitly address it, and those that do are either local optimisation methods requiring accurate initialisation, or are severely limited in terms of shape resolution, handling shapes with only up to 3,000 triangles. In this work, we present a scalable approach for geometrically consistent 3D shape matching that, for the first time, scales to high‐resolution meshes with up to 10,000 triangles. Our method follows a two‐stage procedure: (i) we compute a globally optimal and geometrically consistent mapping of surface patches on the source shape to the target shape via a novel integer linear programming formulation. (ii) we find geometrically consistent matchings of corresponding surface patches which respect correspondences of boundaries of patches obtained from stage (i). With this, we obtain dense, smooth, and guaranteed geometrically consistent correspondences between high‐resolution shapes. Empirical evaluations demonstrate that our method is scalable and produces high‐quality, geometrically consistent correspondences across a wide range of challenging shapes. Our code is publicly available: https://github.com/NafieAmrani/SuPa‐Match .

Abstract Finding correspondences between 3D deformable shapes is an important and long‐standing problem in geometry processing, computer vision, graphics, and beyond. While various shape matching datasets exist, they are mostly static or limited in size, restricting their adaptation to different problem settings, including both full and partial shape matching. In particular the existing partial shape matching datasets are small (fewer than 100 shapes) and thus unsuitable for data‐hungry machine learning approaches. Moreover, the type of partiality present in existing datasets is often artificial and far from realistic. To address these limitations, we introduce a generic and flexible framework for the procedural generation of challenging full and partial shape matching datasets. Our framework allows the propagation of custom annotations across shapes, making it useful for various applications. By utilising our framework and manually creating cross‐dataset correspondences between seven existing (complete geometry) shape matching datasets, we propose a new large benchmark BeCoS with a total of 2543 shapes. Based on this, we offer several challenging benchmark settings, covering both full and partial matching, for which we evaluate respective state‐of‐the‐art methods as baselines. Visualisations and code of our benchmark can be found at: https://nafieamrani.github.io/BeCoS/ .

We propose a novel unsupervised learning approach for non-rigid 3D shape matching. Our approach improves upon recent state-of-the art deep functional map methods and can be applied to a broad range of different challenging scenarios. Previous deep functional map methods mainly focus on feature extraction and aim exclusively at obtaining more expressive features for functional map computation. However, the importance of the functional map computation itself is often neglected and the relationship between the functional map and point-wise map is underexplored. In this paper, we systematically investigate the coupling relationship between the functional map from the functional map solver and the point-wise map based on feature similarity. To this end, we propose a self-adaptive functional map solver to adjust the functional map regularisation for different shape matching scenarios, together with a vertex-wise contrastive loss to obtain more discriminative features. Using different challenging datasets (including non-isometry, topological noise and partiality), we demonstrate that our method substantially outperforms previous state-of-the-art methods.

Finding correspondences between 3D shapes is a crucial problem in computer vision and graphics, which is for example relevant for tasks like shape interpolation, pose transfer, or texture transfer. An often neglected but essential property of matchings is geometric consistency, which means that neighboring triangles in one shape are consistently matched to neighboring triangles in the other shape. Moreover, while in practice one often has only access to partial observations of a 3D shape (e.g. due to occlusion, or scanning artifacts), there do not exist any methods that directly address geometrically consistent partial shape matching. In this work we fill this gap by proposing to integrate state-of-the-art deep shape features into a novel integer linear programming partial shape matching formulation. Our optimization yields a globally optimal solution on low resolution shapes, which we then refine using a coarse-to-fine scheme. We show that our method can find more reliable results on partial shapes in comparison to existing geometrically consistent algorithms (for which one first has to fill missing parts with a dummy geometry). Moreover, our matchings are substantially smoother than learning-based state-of-the-art shape matching methods. The code of this work is publicly available at https://github.com/vikiehm/ geometrically-consistent-partial-shape-matching.

Although 3D shape matching and interpolation are highly interrelated, they are often studied separately and applied sequentially to relate different 3D shapes, thus resulting in sub-optimal performance. In this work we present a unified framework to predict both point-wise correspondences and shape interpolation between 3D shapes. To this end, we combine the deep functional map framework with classical surface deformation models to map shapes in both spectral and spatial domains. On the one hand, by incorporating spatial maps, our method obtains more accurate and smooth point-wise correspondences compared to previous functional map methods for shape matching. On the other hand, by introducing spectral maps, our method gets rid of commonly used but computationally expensive geodesic distance constraints that are only valid for near-isometric shape deformations. Furthermore, we propose a novel test-time adaptation scheme to capture both pose-dominant and shape-dominant deformations. Using different challenging datasets, we demonstrate that our method outperforms previous state-of-the-art methods for both shape matching and interpolation, even compared to supervised approaches.

Finding correspondences between 3D shapes is an important and long-standing problem in computer vision, graphics and beyond. A prominent challenge are partial-to-partial shape matching settings, which occur when the shapes to match are only observed incompletely (e.g. from 3D scanning). Although partial-to-partial matching is a highly relevant setting in practice, it is rarely explored. Our work bridges the gap between existing (rather artificial) 3D full shape matching and partial-to-partial real-world set-tings by exploiting geometric consistency as a strong constraint. We demonstrate that it is indeed possible to solve this challenging problem in a variety of settings. For the first time, we achieve geometric consistency for partial-to-partial matching, which is realized by a novel integer non-linear program formalism building on triangle prod-uct spaces, along with a new pruning algorithm based on linear integer programming. Further, we generate a new inter-class dataset for partial-to-partial shape-matching. We show that our method outperforms current SOTA meth-ods on both an established intra-class dataset and our novel inter-class dataset. The code of this work is publicly avail-able.11https://github.com/vikiehm/gc-ppsm

Finding shortest paths on product spaces is a popular approach to tackle numerous variants of matching problems, including the dynamic time warping method for matching signals, the matching of curves, or the matching of a curve to a 3D shape. While these approaches admit the computation of globally optimal solutions in polynomial time, their natural generalisation to 3D shape matching is widely known to be intractable. In this work we address this issue by proposing a novel path-based formalism for 3D shape matching. More specifically, we consider an alternative shape discretisation in which one of the 3D shapes (the source shape) is represented as a SpiderCurve, i. e. a long self-intersecting curve that traces the 3D shape surface. We then tackle the 3D shape matching problem as finding a shortest path in the product graph of the Spider-Curve and the target 3D shape. Our approach introduces a set of novel constraints that ensure a globally geometrically consistent matching. Overall, our formalism leads to an integer linear programming problem for which we experimentally show that it can efficiently be solved to global optimality. We demonstrate that our approach is competitive with recent state-of-the-art shape matching methods, while in addition guaranteeing geometric consistency.11https://github.com/pau10noah/spider-match

Understanding 3D object structure from image collections of general object categories remains a long-standing challenge in computer vision. Due to the high relevance of image keypoints (e.g. for graph matching, controlling generative models, scene understanding, etc.), in this work we specifically focus on inferring 3D structure in terms of sparse keypoints. Existing 3D keypoint inference approaches rely on strong priors, such as spatio-temporal con-sistency, multi-view images of the same object, 3D shape priors (e.g. templates, skeleton), or supervisory signals e.g. in the form of 2D keypoint annotations. In contrast, we propose the first unsupervised 3D keypoint inference approach that can be trained for general object categories solely from an inhomogeneous image collection (containing different instances of objects from the same category). Our experiments show that our method not only improves upon unsupervised 2D keypoint inference, but more importantly, it also produces reasonable 3D structure for various object categories, both qualitatively and quantitatively.

In this paper, we present a novel data-free method for merging neural networks in weight space. Our method optimizes for the permutations of network neurons while ensuring global coherence across all layers, and it outperforms recent layer-local approaches in a set of challenging scenarios. We then generalize the formulation to the $N$-models scenario to enforce cycle consistency of the permutations with guarantees, allowing circular compositions of permutations to be computed without accumulating error along the path. We qualitatively and quantitatively motivate the need for such a constraint, showing its benefits when merging homogeneous sets of models in scenarios spanning varying architectures and datasets. We finally show that, when coupled with activation renormalization, the approach yields the best results in the task.

Neural 3D implicit representations learn priors that are useful for diverse applications, such as single- or multiple-view 3D reconstruction. A major downside of existing approaches while rendering an image is that they require evaluating the network multiple times per camera ray so that the high computational time forms a bottleneck for downstream applications. We address this problem by introducing a novel neural scene representation that we call the directional distance function (DDF). To this end, we learn a signed distance function (SDF) along with our DDF model to represent a class of shapes. Specifically, our DDF is defined on the unit sphere and predicts the distance to the surface along any given direction. Therefore, our DDF allows rendering images with just a single network evaluation per camera ray. Based on our DDF, we present a novel fast algorithm (FIRe) to reconstruct 3D shapes given a posed depth map. We evaluate our proposed method on 3D reconstruction from single-view depth images, where we empirically show that our algorithm reconstructs 3D shapes more accurately and it is more than 15 times faster (per iteration) than competing methods.

Many challenges from natural world can be formulated as a graph matching problem. Previous deep learning-based methods mainly consider a full two-graph matching setting. In this work, we study the more general partial matching problem with multi-graph cycle consistency guarantees. Building on a recent progress in deep learning on graphs, we propose a novel data-driven method (URL) for partial multi-graph matching, which uses an object-to-universe formulation and learns latent representations of abstract universe points. The proposed approach advances the state of the art in semantic keypoint matching problem, evaluated on Pascal VOC, CUB, and Willow datasets. Moreover, the set of controlled experiments on a synthetic graph matching dataset demonstrates the scalability of our method to graphs with large number of nodes and its robustness to high partiality.

The matching of 3D shapes has been extensively studied for shapes represented as surface meshes, as well as for shapes represented as point clouds. While point clouds are a common representation of raw real-world 3D data (e.g. from laser scanners), meshes encode rich and expressive topological information, but their creation typically requires some form of (often manual) curation. In turn, methods that purely rely on point clouds are unable to meet the matching quality of mesh-based methods that utilise the additional topological structure. In this work we close this gap by introducing a self-supervised multimodal learning strategy that combines mesh-based functional map regularisation with a contrastive loss that couples mesh and point cloud data. Our shape matching approach allows to obtain intramodal correspondences for triangle meshes, complete point clouds, and partially observed point clouds, as well as correspondences across these data modalities. We demonstrate that our method achieves state-of-the-art results on several challenging benchmark datasets even in comparison to recent supervised methods, and that our method reaches previously unseen cross-dataset generalisation ability. Our code is available at https://github.com/dongliangcao/Self-Supervised-Multimodal-Shape-Matching.

We consider the problem of finding a continuous and non-rigid matching between a 2D contour and a 3D mesh. While such problems can be solved to global optimality by finding a shortest path in the product graph between both shapes, existing solutions heavily rely on unrealistic prior assumptions to avoid degenerate solutions (e.g. knowledge to which region of the 3D shape each point of the 2D contour is matched). To address this, we propose a novel 2D-3D shape matching formalism based on the conjugate prod-uct graph between the 2D contour and the 3D shape. Doing so allows us for the first time to consider higher-order costs, i.e. defined for edge chains, as opposed to costs de-fined for single edges. This offers substantially more flexi-bility, which we utilise to incorporate a local rigidity prior. By doing so, we effectively circumvent degenerate solutions and thereby obtain smoother and more realistic matchings, even when using only a one-dimensional feature descrip-tor. Overall, our method finds globally optimal and contin-uous 2D-3D matchings, has the same asymptotic complex-ity as previous solutions, produces state-of-the-art results for shape matching and is even capable of matching partial shapes. Our code is publicly available.11https://github.com/paulOnoah/sm-2D3D

We propose a novel mixed-integer programming (MIP) formulation for generating precise sparse correspondences for highly non-rigid shapes. To this end, we introduce a projected Laplace-Beltrami operator (PLBO) which combines intrinsic and extrinsic geometric information to measure the deformation quality induced by predicted correspondences. We integrate the PLBO, together with an orientation-aware regulariser, into a novel MIP formulation that can be solved to global optimality for many practical problems. In contrast to previous methods, our approach is provably invariant to rigid transformations and global scaling, initialisation-free, has optimality guarantees, and scales to high resolution meshes with (empirically observed) linear time. We show state-of-the-art results for sparse non-rigid matching on several challenging 3D datasets, including data with inconsistent meshing, as well as applications in mesh-to-point-cloud matching.

Neural networks have recently been used to analyze diverse physical systems and to identify the underlying dynamics. While existing methods achieve impressive results, they are limited by their strong demand for training data and their weak generalization abilities to out-of-distribution data. To overcome these limitations, we propose to combine neural implicit representations for appearance modeling with neural ordinary differential equations (ODEs) for modelling planar physical phenomena to obtain a dynamic scene representation that can be identified directly from visual observations. Our proposed model combines several unique advantages: (i) Contrary to existing approaches that require large training datasets, we are able to identify physical parameters from only a single video. (ii) The use of neural implicit representations enables the processing of high-resolution videos and the synthesis of photo-realistic images. (iii) The embedded neural ODE has a known parametric form that allows for the identification of interpretable physical parameters, and (iv) long-term prediction in state space. (v) Furthermore, the photo-realistic rendering of novel scenes with modified physical parameters becomes possible.

We propose a novel learning-based approach for robust 3D shape matching. Our method builds upon deep functional maps and can be trained in a fully unsupervised manner. Previous deep functional map methods mainly focus on predicting optimised functional maps alone, and then rely on off-the-shelf post-processing to obtain accurate point-wise maps during inference. However, this two-stage procedure for obtaining point-wise maps often yields sub-optimal performance. In contrast, building upon recent insights about the relation between functional maps and point-wise maps, we propose a novel unsupervised loss to couple the functional maps and point-wise maps, and thereby directly obtain point-wise maps without any post-processing. Our approach obtains accurate correspondences not only for near-isometric shapes, but also for more challenging non-isometric shapes and partial shapes, as well as shapes with different discretisation or topological noise. Using a total of nine diverse datasets, we extensively evaluate the performance and demonstrate that our method substantially outperforms previous state-of-the-art methods, even compared to recent supervised methods. Our code is available at https://github.com/dongliangcao/Unsupervised-Learning-of-Robust-Spectral-Shape-Matching.

Graph matching aims to establish correspondences between vertices of graphs such that both the node and edge attributes agree. Various learning-based methods were recently proposed for finding correspondences between image key points based on deep graph matching formulations. While these approaches mainly focus on learning node and edge attributes, they completely ignore the 3D geometry of the underlying 3D objects depicted in the 2D images. We fill this gap by proposing a trainable framework that takes advantage of graph neural networks for learning a deformable 3D geometry model from inhomogeneous image collections, i.e. a set of images that depict different instances of objects from the same category. Experimentally we demonstrate that our method outperforms recent learning-based approaches for graph matching considering both accuracy and cycle-consistency error, while we in addition obtain the underlying 3D geometry of the objects depicted in the 2D images.

The Sinkhorn operator has recently experienced a surge of popularity in computer vision and related fields. One major reason is its ease of integration into deep learning frameworks. To allow for an efficient training of respective neural networks, we propose an algorithm that obtains analytical gradients of a Sinkhorn layer via implicit differentiation. In comparison to prior work, our framework is based on the most general formulation of the Sinkhorn operator. It allows for any type of loss function, while both the target capacities and cost matrices are differentiated jointly. We further construct error bounds of the resulting algorithm for approximate inputs. Finally, we demonstrate that for a number of applications, simply replacing automatic differentiation with our algorithm directly improves the stability and accuracy of the obtained gradients. Moreover, we show that it is computationally more efficient, particularly when resources like GPU memory are scarce.11Our implementation is available under the following link: https://github.com/marvin-eisenberger/implicit-sinkhorn

The estimation of the relative pose of two camera views is a fundamental problem in computer vision. Kneip et al. proposed to solve this problem by introducing the normal epipolar constraint (NEC). However, their approach does not take into account uncertainties, so that the accuracy of the estimated relative pose is highly dependent on accurate feature positions in the target frame. In this work, we introduce the probabilistic normal epipolar constraint (PNEC) that overcomes this limitation by accounting for anisotropic and inhomogeneous uncertainties in the feature positions. To this end, we propose a novel objective function, along with an efficient optimization scheme that effectively minimizes our objective while maintaining real-time performance. In experiments on synthetic data, we demonstrate that the novel PNEC yields more accurate rotation estimates than the original NEC and several popular relative rotation estimation algorithms. Furthermore, we integrate the proposed method into a state-of-the-art monocular rotation-only odometry system and achieve consistently improved results for the real-world KITTI dataset.

We present a scalable combinatorial algorithm for globally optimizing over the space of geometrically consistent mappings between 3D shapes. We use the mathematically elegant formalism proposed by Windheuser et al. [66] where 3D shape matching was formulated as an integer linear program over the space of orientation-preserving diffeomorphisms. Until now, the resulting formulation had limited practical applicability due to its complicated constraint structure and its large size. We propose a novel primal heuristic coupled with a Lagrange dual problem that is several orders of magnitudes faster compared to previous solvers. This allows us to handle shapes with substantially more triangles than previously solvable. We demonstrate compelling results on diverse datasets, and, even showcase that we can address the challenging setting of matching two partial shapes without availability of complete shapes. Our code is publicly available at http://github.com/paulOnoah/sm-comb.

We address the problem of minimizing a class of energy functions consisting of data and smoothness terms that commonly occur in machine learning, computer vision, and pattern recognition. While discrete optimization methods are able to give theoretical optimality guarantees, they can only handle a finite number of labels and therefore suffer from label discretization bias. Existing continuous optimization methods can find sublabel-accurate solutions, but they are not efficient for large label spaces. In this work, we propose an efficient sublabel-accurate method that utilizes the best properties of both continuous and discrete models. We separate the problem into two sequential steps: (i) global discrete optimization for selecting the label range, and (ii) efficient continuous sublabel-accurate local refinement of a convex approximation of the energy function in the chosen range. Doing so allows us to achieve a boost in time and memory efficiency while practically keeping the accuracy at the same level as continuous convex relaxation methods, and in addition, providing theoretical optimality guarantees at the level of discrete methods. Finally, we show the flexibility of the proposed approach to general pairwise smoothness terms, so that it is applicable to a wide range of regularizations. Experiments on the illustrating example of the image denoising problem demonstrate the properties of the proposed method. The code reproducing experiments is available on https://github.com/nurlanov-zh/sublabel-accurate-alpha-expansion.

Finding shortest paths in a graph is relevant for numerous problems in computer vision and graphics, including image segmentation, shape matching, or the computation of geodesic distances on discrete surfaces. Traditionally, the concept of a shortest path is considered for graphs with scalar edge weights, which makes it possible to compute the length of a path by adding up the individual edge weights. Yet, graphs with scalar edge weights are severely limited in their expressivity, since oftentimes edges are used to encode significantly more complex interrelations. In this work we compensate for this modelling limitation and introduce the novel graph-theoretic concept of a shortest path in a graph with matrix-valued edges. To this end, we define a meaningful way for quantifying the path length for matrix-valued edges, and we propose a simple yet effective algorithm to compute the respective shortest path. While our formalism is universal and thus applicable to a wide range of settings in vision, graphics and beyond, we focus on demonstrating its merits in the context of 3D multi-shape analysis.

This paper proposes a new algorithm for simultaneous graph matching and clustering. For the first time in the literature, these two problems are solved jointly and synergetically without relying on any training data, which brings advantages for identifying similar arbitrary objects in compound 3D scenes and matching them. For joint reasoning, we first rephrase graph matching as a rigid point set registration problem operating on spectral graph embeddings. Consequently, we utilise efficient convex semidefinite program relaxations for aligning points in Hilbert spaces and add coupling constraints to model the mutual dependency and exploit synergies between both tasks. We outperform state of the art in challenging cases with non-perfectly matching and noisy graphs, and we show successful applications on real compound scenes with multiple 3D elements. Our source code and data are publicly available.

Finding correspondences between shapes is a fundamental problem in computer vision and graphics, which is relevant for many applications, including 3D reconstruction, object tracking, and style transfer. The vast majority of correspondence methods aim to find a solution between pairs of shapes, even if multiple instances of the same class are available. While isometries are often studied in shape correspondence problems, they have not been considered explicitly in the multi-matching setting. This paper closes this gap by proposing a novel optimisation formulation for isometric multi-shape matching. We present a suitable optimisation algorithm for solving our formulation and provide a convergence and complexity analysis. Our algorithm obtains multi-matchings that are by construction provably cycle-consistent. We demonstrate the superior performance of our method on various datasets and set the new state-of-the-art in isometric multi-shape matching.

We present the first deep implicit 3D morphable model (i3DMM) of full heads. Unlike earlier morphable face models it not only captures identity-specific geometry, texture, and expressions of the frontal face, but also models the entire head, including hair. We collect a new dataset consisting of 64 people with different expressions and hairstyles to train i3DMM. Our approach has the following favorable properties: (i) It is the first full head morphable model that includes hair. (ii) In contrast to mesh-based models it can be trained on merely rigidly aligned scans, without requiring difficult non-rigid registration. (iii) We design a novel architecture to decouple the shape model into an implicit reference shape and a deformation of this reference shape. With that, dense correspondences between shapes can be learned implicitly. (iv) This architecture allows us to semantically disentangle the geometry and color components, as color is learned in the reference space. Geometry is further disentangled as identity, expressions, and hairstyle, while color is disentangled as identity and hairstyle components. We show the merits of i3DMM using ablation studies, comparisons to state-of-the-art models, and applications such as semantic head editing and texture transfer. We will make our model publicly available1.

We address the non-convex optimisation problem of finding a sparse matrix on the Stiefel manifold (matrices with mutually orthogonal columns of unit length) that maximises (or minimises) a quadratic objective function. Optimisation problems on the Stiefel manifold occur for example in spectral relaxations of various combinatorial problems, such as graph matching, clustering, or permutation synchronisation. Although sparsity is a desirable property in such settings, it is mostly neglected in spectral formulations since existing solvers, e.g. based on eigenvalue decomposition, are unable to account for sparsity while at the same time maintaining global optimality guarantees. We fill this gap and propose a simple yet effective sparsity-promoting modification of the Orthogonal Iteration algorithm for finding the dominant eigenspace of a matrix. By doing so, we can guarantee that our method finds a Stiefel matrix that is globally optimal with respect to the quadratic objective function, while in addition being sparse. As a motivating application we consider the task of permutation synchronisation, which can be understood as a constrained clustering problem that has particular relevance for matching multiple images or 3D shapes in computer vision, computer graphics, and beyond. We demonstrate that the proposed approach outperforms previous methods in this domain.

Synthesizing realistic videos of humans using neural networks has been a popular alternative to the conventional graphics-based rendering pipeline due to its high efficiency. Existing works typically formulate this as an image-to-image translation problem in 2D screen space, which leads to artifacts such as over-smoothing, missing body parts, and temporal instability of fine-scale detail, such as pose-dependent wrinkles in the clothing. In this article, we propose a novel human video synthesis method that approaches these limiting factors by explicitly disentangling the learning of time-coherent fine-scale details from the embedding of the human in 2D screen space. More specifically, our method relies on the combination of two convolutional neural networks (CNNs). Given the pose information, the first CNN predicts a dynamic texture map that contains time-coherent high-frequency details, and the second CNN conditions the generation of the final video on the temporally coherent output of the first CNN. We demonstrate several applications of our approach, such as human reenactment and novel view synthesis from monocular video, where we show significant improvement over the state of the art both qualitatively and quantitatively.

We present a convex mixed-integer programming formulation for non-rigid shape matching. To this end, we propose a novel shape deformation model based on an efficient low-dimensional discrete model, so that finding a globally optimal solution is tractable in (most) practical cases. Our approach combines several favourable properties, namely it is independent of the initialisation, it is much more efficient to solve to global optimality compared to analogous quadratic assignment problem formulations, and it is highly flexible in terms of the variants of matching problems it can handle. Experimentally we demonstrate that our approach outperforms existing methods for sparse shape matching, that it can be used for initialising dense shape matching methods, and we showcase its flexibility on several examples.

StyleGAN generates photorealistic portrait images of faces with eyes, teeth, hair and context (neck, shoulders, background), but lacks a rig-like control over semantic face parameters that are interpretable in 3D, such as face pose, expressions, and scene illumination. Three-dimensional morphable face models (3DMMs) on the other hand offer control over the semantic parameters, but lack photorealism when rendered and only model the face interior, not other parts of a portrait image (hair, mouth interior, background). We present the first method to provide a face rig-like control over a pretrained and fixed StyleGAN via a 3DMM. A new rigging network, is trained between the 3DMM's semantic parameters and StyleGAN's input. The network is trained in a self-supervised manner, without the need for manual annotations. At test time, our method generates portrait images with the photorealism of StyleGAN and provides explicit control over the 3D semantic parameters of the face.

We propose to use a model-based generative loss for training hand pose estimators on depth images based on a volumetric hand model. This additional loss allows training of a hand pose estimator that accurately infers the entire set of 21 hand keypoints while only using supervision for 6 easy-to-annotate keypoints (fingertips and wrist). We show that our partially-supervised method achieves results that are comparable to those of fully-supervised methods which enforce articulation consistency. Moreover, for the first time we demonstrate that such an approach can be used to train on datasets that have erroneous annotations, i.e. “ground truth” with notable measurement errors, while obtaining predictions that explain the depth images better than the given “ground truth.”

In this work, we propose a novel model-based deep convolutional autoencoder that addresses the highly challenging problem of reconstructing a 3D human face from a single in-the-wild color image. To this end, we combine a convolutional encoder network with an expert-designed generative model that serves as decoder. The core innovation is the differentiable parametric decoder that encapsulates image formation analytically based on a generative model. Our decoder takes as input a code vector with exactly defined semantic meaning that encodes detailed face pose, shape, expression, skin reflectance, and scene illumination. Due to this new way of combining CNN-based with model-based face reconstruction, the CNN-based encoder learns to extract semantically meaningful parameters from a single monocular input image. For the first time, a CNN encoder and an expert-designed generative model can be trained end-to-end in an unsupervised manner, which renders training on very large (unlabeled) real world datasets feasible. The obtained reconstructions compare favorably to current state-of-the-art approaches in terms of quality and richness of representation. This work is an extended version of [1] , where we additionally present a stochastic vertex sampling technique for faster training of our networks, and moreover, we propose and evaluate analysis-by-synthesis and shape-from-shading refinement approaches to achieve a high-fidelity reconstruction.

In this article, we provide a detailed survey of 3D Morphable Face Models over the 20 years since they were first proposed. The challenges in building and applying these models, namely, capture, modeling, image formation, and image analysis, are still active research topics, and we review the state-of-the-art in each of these areas. We also look ahead, identifying unsolved challenges, proposing directions for future research, and highlighting the broad range of current and future applications.

Editing of portrait images is a very popular and important research topic with a large variety of applications. For ease of use, control should be provided via a semantically meaningful parameterization that is akin to computer animation controls. The vast majority of existing techniques do not provide such intuitive and fine-grained control, or only enable coarse editing of a single isolated control parameter. Very recently, high-quality semantically controlled editing has been demonstrated, however only on synthetically created StyleGAN images. We present the first approach for embedding real portrait images in the latent space of StyleGAN, which allows for intuitive editing of the head pose, facial expression, and scene illumination in the image. Semantic editing in parameter space is achieved based on StyleRig, a pretrained neural network that maps the control space of a 3D morphable face model to the latent space of the GAN. We design a novel hierarchical non-linear optimization problem to obtain the embedding. An identity preservation energy term allows spatially coherent edits while maintaining facial integrity. Our approach runs at interactive frame rates and thus allows the user to explore the space of possible edits. We evaluate our approach on a wide set of portrait photos, compare it to the current state of the art, and validate the effectiveness of its components in an ablation study.

Tracking and reconstructing the 3D pose and geometry of two hands in interaction is a challenging problem that has a high relevance for several human-computer interaction applications, including AR/VR, robotics, or sign language recognition. Existing works are either limited to simpler tracking settings ( e.g. , considering only a single hand or two spatially separated hands), or rely on less ubiquitous sensors, such as depth cameras. In contrast, in this work we present the first real-time method for motion capture of skeletal pose and 3D surface geometry of hands from a single RGB camera that explicitly considers close interactions. In order to address the inherent depth ambiguities in RGB data, we propose a novel multi-task CNN that regresses multiple complementary pieces of information, including segmentation, dense matchings to a 3D hand model, and 2D keypoint positions, together with newly proposed intra-hand relative depth and inter-hand distance maps. These predictions are subsequently used in a generative model fitting framework in order to estimate pose and shape parameters of a 3D hand model for both hands. We experimentally verify the individual components of our RGB two-hand tracking and 3D reconstruction pipeline through an extensive ablation study. Moreover, we demonstrate that our approach offers previously unseen two-hand tracking performance from RGB, and quantitatively and qualitatively outperforms existing RGB-based methods that were not explicitly designed for two-hand interactions. Moreover, our method even performs on-par with depth-based real-time methods.

We consider the problem of inverse kinematics (IK), where one wants to find the parameters of a given kinematic skeleton that best explain a set of observed 3D joint locations. The kinematic skeleton has a tree structure, where each node is a joint that has an associated geometric transformation that is propagated to all its child nodes. The IK problem has various applications in vision and graphics, for example for tracking or reconstructing articulated objects, such as human hands or bodies. Most commonly, the IK problem is tackled using local optimisation methods. A major downside of these approaches is that, due to the non-convex nature of the problem, such methods are prone to converge to unwanted local optima and therefore require a good initialisation. In this paper we propose a convex optimisation approach for the IK problem based on semidefinite programming, which admits a polynomial-time algorithm that globally solves (a relaxation of) the IK problem. Experimentally, we demonstrate that the proposed method significantly outperforms local optimisation methods using different real-world skeletons.

We present a convex relaxation for the multi-graph matching problem. Our formulation allows for partial pairwise matchings, guarantees cycle consistency, and our objective incorporates both linear and quadratic costs. Moreover, we also present an extension to higher-order costs. In order to solve the convex relaxation we employ a message passing algorithm that optimizes the dual problem. We experimentally compare our algorithm on established benchmark problems from computer vision, as well as on large problems from biological image analysis, the size of which exceed previously investigated multi-graph matching instances.

Monocular image-based 3D reconstruction of faces is a long-standing problem in computer vision. Since image data is a 2D projection of a 3D face, the resulting depth ambiguity makes the problem ill-posed. Most existing methods rely on data-driven priors that are built from limited 3D face scans. In contrast, we propose multi-frame video-based self-supervised training of a deep network that (i) learns a face identity model both in shape and appearance while (ii) jointly learning to reconstruct 3D faces. Our face model is learned using only corpora of in-the-wild video clips collected from the Internet. This virtually endless source of training data enables learning of a highly general 3D face model. In order to achieve this, we propose a novel multi-frame consistency loss that ensures consistent shape and appearance across multiple frames of a subject's face, thus minimizing depth ambiguity. At test time we can use an arbitrary number of frames, so that we can perform both monocular as well as multi-frame reconstruction.

The matching of multiple objects (e.g. shapes or images) is a fundamental problem in vision and graphics. In order to robustly handle ambiguities, noise and repetitive patterns in challenging real-world settings, it is essential to take geometric consistency between points into account. Computationally, the multi-matching problem is difficult. It can be phrased as simultaneously solving multiple (NP-hard) quadratic assignment problems (QAPs) that are coupled via cycle-consistency constraints. The main limitations of existing multi-matching methods are that they either ignore geometric consistency and thus have limited robustness, or they are restricted to small-scale problems due to their (relatively) high computational cost. We address these shortcomings by introducing a Higher-order Projected Power Iteration method, which is (i) efficient and scales to tens of thousands of points, (ii) straightforward to implement, (iii) able to incorporate geometric consistency, (iv) guarantees cycle-consistent multi-matchings, and (iv) comes with theoretical convergence guarantees. Experimentally we show that our approach is superior to existing methods.

We propose a method for generating video-realistic animations of real humans under user control. In contrast to conventional human character rendering, we do not require the availability of a production-quality photo-realistic three-dimensional (3D) model of the human but instead rely on a video sequence in conjunction with a (medium-quality) controllable 3D template model of the person. With that, our approach significantly reduces production cost compared to conventional rendering approaches based on production-quality 3D models and can also be used to realistically edit existing videos. Technically, this is achieved by training a neural network that translates simple synthetic images of a human character into realistic imagery. For training our networks, we first track the 3D motion of the person in the video using the template model and subsequently generate a synthetically rendered version of the video. These images are then used to train a conditional generative adversarial network that translates synthetic images of the 3D model into realistic imagery of the human. We evaluate our method for the reenactment of another person that is tracked to obtain the motion data, and show video results generated from artist-designed skeleton motion. Our results outperform the state of the art in learning-based human image synthesis.

We present a novel method for real-time pose and shape reconstruction of two strongly interacting hands. Our approach is the first two-hand tracking solution that combines an extensive list of favorable properties, namely it is marker-less, uses a single consumer-level depth camera, runs in real time, handles inter- and intra-hand collisions, and automatically adjusts to the user's hand shape. In order to achieve this, we embed a recent parametric hand pose and shape model and a dense correspondence predictor based on a deep neural network into a suitable energy minimization framework. For training the correspondence prediction network, we synthesize a two-hand dataset based on physical simulations that includes both hand pose and shape annotations while at the same time avoiding inter-hand penetrations. To achieve real-time rates, we phrase the model fitting in terms of a nonlinear least-squares problem so that the energy can be optimized based on a highly efficient GPU-based Gauss-Newton optimizer. We show state-of-the-art results in scenes that exceed the complexity level demonstrated by previous work, including tight two-hand grasps, significant inter-hand occlusions, and gesture interaction. 1

In this work we address the problem of point-cloud denoising where we assume that a given point-cloud comprises (noisy) points that were sampled from an underlying surface that is to be denoised. We phrase the point-cloud denoising problem in terms of a dictionary learning framework. To this end, for a given point-cloud we (robustly) extract planar patches covering the entire point-cloud, where each patch contains a (noisy) description of the local structure of the underlying surface. Based on the general assumption that many of the local patches (in the noise-free point-cloud) contain redundant information (e.g. due to smoothness of the surface, or due to repetitive structures), we find a low-dimensional affine subspace that (approximately) explains the extracted (noisy) patches. Computationally, this is achieved by solving a structured low-rank matrix factorization problem, where we impose smoothness on the patch dictionary and sparsity on the coefficients. We experimentally demonstrate that our method outperforms existing denoising approaches in various noise scenarios.

In this work we study convex relaxations of quadratic optimisation problems over permutation matrices. While existing semidefinite programming approaches can achieve remarkably tight relaxations, they have the strong disadvantage that they lift the original n×n-dimensional variable to an n2×n2-dimensional variable, which limits their practical applicability. In contrast, here we present a lifting-free convex relaxation that is provably at least as tight as existing (lifting-free) convex relaxations. We demonstrate experimentally that our approach is superior to existing convex and non-convex methods for various problems, including image arrangement and multi-graph matching.

We address the highly challenging problem of real-time 3D hand tracking based on a monocular RGB-only sequence. Our tracking method combines a convolutional neural network with a kinematic 3D hand model, such that it generalizes well to unseen data, is robust to occlusions and varying camera viewpoints, and leads to anatomically plausible as well as temporally smooth hand motions. For training our CNN we propose a novel approach for the synthetic generation of training data that is based on a geometrically consistent image-to-image translation network. To be more specific, we use a neural network that translates synthetic images to "real" images, such that the so-generated images follow the same statistical distribution as real-world hand images. For training this translation network we combine an adversarial loss and a cycle-consistency loss with a geometric consistency loss in order to preserve geometric properties (such as hand pose) during translation. We demonstrate that our hand tracking system outperforms the current state-of-the-art on challenging RGB-only footage.

The reconstruction of dense 3D models of face geometry and appearance from a single image is highly challenging and ill-posed. To constrain the problem, many approaches rely on strong priors, such as parametric face models learned from limited 3D scan data. However, prior models restrict generalization of the true diversity in facial geometry, skin reflectance and illumination. To alleviate this problem, we present the first approach that jointly learns 1) a regressor for face shape, expression, reflectance and illumination on the basis of 2) a concurrently learned parametric face model. Our multi-level face model combines the advantage of 3D Morphable Models for regularization with the out-of-space generalization of a learned corrective space. We train end-to-end on in-the-wild images without dense annotations by fusing a convolutional encoder with a differentiable expert-designed renderer and a self-supervised training loss, both defined at multiple detail levels. Our approach compares favorably to the state-of-the-art in terms of reconstruction quality, better generalizes to real world faces, and runs at over 250 Hz.

In this work we address the problem of capturing human body motion under changing lighting conditions in a multiview setup. In order to account for changing lighting conditions we propose to use an intermediate image representation that is invariant to the scene lighting. In our approach this is achieved by solving time-varying segmentation problems that use frame- and view-dependent appearance costs that are able to adjust to the present conditions. Moreover, we use an adaptive combination of our lighting-invariant segmentation with CNN-based joint detectors in order to increase the robustness to segmentation errors. In our experimental validation we demonstrate that our method is able to handle difficult conditions better than existing works.

We propose a combinatorial solution for the problem of non-rigidly matching a 3D shape to 3D image data. To this end, we model the shape as a triangular mesh and allow each triangle of this mesh to be rigidly transformed to achieve a suitable matching to the image. By penalising the distance and the relative rotation between neighbouring triangles our matching compromises between the image and the shape information. In this paper, we resolve two major challenges: Firstly, we address the resulting large and NP-hard combinatorial problem with a suitable graph-theoretic approach. Secondly, we propose an efficient discretisation of the unbounded 6-dimensional Lie group SE(3). To our knowledge this is the first combinatorial formulation for non-rigid 3D shape-to-image matching. In contrast to existing local (gradient descent) optimisation methods, we obtain solutions that do not require a good initialisation and that are within a bound of the optimal solution. We evaluate the proposed combinatorial method on the two problems of non-rigid 3D shape-to-shape and non-rigid 3D shape-to-image registration and demonstrate that it provides promising results.

In this work we propose a novel model-based deep convolutional autoencoder that addresses the highly challenging problem of reconstructing a 3D human face from a single in-the-wild color image. To this end, we combine a convolutional encoder network with an expert-designed generative model that serves as decoder. The core innovation is the differentiable parametric decoder that encapsulates image formation analytically based on a generative model. Our decoder takes as input a code vector with exactly defined semantic meaning that encodes detailed face pose, shape, expression, skin reflectance and scene illumination. Due to this new way of combining CNN-based with model-based face reconstruction, the CNN-based encoder learns to extract semantically meaningful parameters from a single monocular input image. For the first time, a CNN encoder and an expert-designed generative model can be trained end-to-end in an unsupervised manner, which renders training on very large (unlabeled) real world data feasible. The obtained reconstructions compare favorably to current state-of-the-art approaches in terms of quality and richness of representation.

Representing 3D shape deformations by high-dimensional linear models has many applications in computer vision and medical imaging. Commonly, using Principal Components Analysis a low-dimensional subspace of the high-dimensional shape space is determined. However, the resulting factors (the most dominant eigenvectors of the covariance matrix) have global support, i.e. changing the coefficient of a single factor deforms the entire shape. Based on matrix factorisation with sparsity and graph-based regularisation terms, we present a method to obtain deformation factors with local support. The benefits include better flexibility and interpretability as well as the possibility of interactively deforming shapes locally. We demonstrate that for brain shapes our method outperforms the state of the art in local support models with respect to generalisation and sparse reconstruction, whereas for body shapes our method gives more realistic deformations.

The alignment of a set of objects by means of transformations plays an important role in computer vision. Whilst the case for only two objects can be solved globally, when multiple objects are considered usually iterative methods are used. In practice the iterative methods perform well if the relative transformations between any pair of objects are free of noise. However, if only noisy relative transformations are available (e.g. due to missing data or wrong correspondences) the iterative methods may fail. Based on the observation that the underlying noise-free transformations can be retrieved from the null space of a matrix that can directly be obtained from pairwise alignments, this paper presents a novel method for the synchronisation of pairwise transformations such that they are transitively consistent. Simulations demonstrate that for noisy transformations, a large proportion of missing data and even for wrong correspondence assignments the method delivers encouraging results.