arXiv subjects

Florian Bernard

Publications and source records attributed to Florian Bernard.

At least 55 records · Page 3Linked to original sources

arXiv2023

Non-Separable Multi-Dimensional Network Flows for Visual Computing

Flows in networks (or graphs) play a significant role in numerous computer vision tasks. The scalar-valued edges in these graphs often lead to a loss of information and thereby to limitations in terms of expressiveness. For example, oftentimes high-dimensional data (e.g. feature descriptors) are mapped to a single scalar value (e.g. the similarity between two feature descriptors). To overcome this limitation, we propose a novel formalism for non-separable multi-dimensional network flows. By doing so, we enable an automatic and adaptive feature selection strategy - since the flow is defined on a per-dimension basis, the maximizing flow automatically chooses the best matching feature dimensions. As a proof of concept, we apply our formalism to the multi-object tracking problem and demonstrate that our approach outperforms scalar formulations on the MOT16 benchmark in terms of robustness to noise.

cs.CV↗

arXiv2023

Conjugate Product Graphs for Globally Optimal 2D-3D 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 product 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 defined for single edges. This offers substantially more flexibility, 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 descriptor. Overall, our method finds globally optimal and continuous 2D-3D matchings, has the same asymptotic complexity 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 (https://github.com/paul0noah/sm-2D3D).

cs.CV↗

arXiv2022

Universe Points Representation Learning for Partial Multi-Graph Matching

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.

cs.CV↗

arXiv2022

HandFlow: Quantifying View-Dependent 3D Ambiguity in Two-Hand Reconstruction with Normalizing Flow

Reconstructing two-hand interactions from a single image is a challenging problem due to ambiguities that stem from projective geometry and heavy occlusions. Existing methods are designed to estimate only a single pose, despite the fact that there exist other valid reconstructions that fit the image evidence equally well. In this paper we propose to address this issue by explicitly modeling the distribution of plausible reconstructions in a conditional normalizing flow framework. This allows us to directly supervise the posterior distribution through a novel determinant magnitude regularization, which is key to varied 3D hand pose samples that project well into the input image. We also demonstrate that metrics commonly used to assess reconstruction quality are insufficient to evaluate pose predictions under such severe ambiguity. To address this, we release the first dataset with multiple plausible annotations per image called MultiHands. The additional annotations enable us to evaluate the estimated distribution using the maximum mean discrepancy metric. Through this, we demonstrate the quality of our probabilistic reconstruction and show that explicit ambiguity modeling is better-suited for this challenging problem.

cs.CV↗

arXiv2022

A Comparative Study of Graph Matching Algorithms in Computer Vision

The graph matching optimization problem is an essential component for many tasks in computer vision, such as bringing two deformable objects in correspondence. Naturally, a wide range of applicable algorithms have been proposed in the last decades. Since a common standard benchmark has not been developed, their performance claims are often hard to verify as evaluation on differing problem instances and criteria make the results incomparable. To address these shortcomings, we present a comparative study of graph matching algorithms. We create a uniform benchmark where we collect and categorize a large set of existing and publicly available computer vision graph matching problems in a common format. At the same time we collect and categorize the most popular open-source implementations of graph matching algorithms. Their performance is evaluated in a way that is in line with the best practices for comparing optimization algorithms. The study is designed to be reproducible and extensible to serve as a valuable resource in the future. Our study provides three notable insights: 1.) popular problem instances are exactly solvable in substantially less than 1 second and, therefore, are insufficient for future empirical evaluations; 2.) the most popular baseline methods are highly inferior to the best available methods; 3.) despite the NP-hardness of the problem, instances coming from vision applications are often solvable in a few seconds even for graphs with more than 500 vertices.

cs.CV↗

arXiv2022

Unsupervised Deep Multi-Shape Matching

3D shape matching is a long-standing problem in computer vision and computer graphics. While deep neural networks were shown to lead to state-of-the-art results in shape matching, existing learning-based approaches are limited in the context of multi-shape matching: (i) either they focus on matching pairs of shapes only and thus suffer from cycle-inconsistent multi-matchings, or (ii) they require an explicit template shape to address the matching of a collection of shapes. In this paper, we present a novel approach for deep multi-shape matching that ensures cycle-consistent multi-matchings while not depending on an explicit template shape. To this end, we utilise a shape-to-universe multi-matching representation that we combine with powerful functional map regularisation, so that our multi-shape matching neural network can be trained in a fully unsupervised manner. While the functional map regularisation is only considered during training time, functional maps are not computed for predicting correspondences, thereby allowing for fast inference. We demonstrate that our method achieves state-of-the-art results on several challenging benchmark datasets, and, most remarkably, that our unsupervised method even outperforms recent supervised methods.

cs.CV↗

arXiv2022

Efficient and Flexible Sublabel-Accurate Energy Minimization

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 at \url{https://github.com/nurlanov-zh/sublabel-accurate-alpha-expansion}.

cs.CV↗

arXiv2022

A Unified Framework for Implicit Sinkhorn Differentiation

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.

cs.CV↗

arXiv2022

Joint Deep Multi-Graph Matching and 3D Geometry Learning from Inhomogeneous 2D Image Collections

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.

cs.CV↗

arXiv2022

A Scalable Combinatorial Solver for Elastic Geometrically Consistent 3D Shape Matching

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. (ICCV 2011) 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/paul0noah/sm-comb .

cs.CV↗

arXiv2022

The Probabilistic Normal Epipolar Constraint for Frame-To-Frame Rotation Optimization under Uncertain Feature Positions

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.

cs.CV↗

arXiv2021

Shortest Paths in Graphs with Matrix-Valued Edges: Concepts, Algorithm and Application to 3D Multi-Shape Analysis

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.

cs.CV↗

arXiv2021

Convex Joint Graph Matching and Clustering via Semidefinite Relaxations

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.

cs.CV↗

arXiv2021

Sparse Quadratic Optimisation over the Stiefel Manifold with Application to Permutation Synchronisation

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.

math.OC↗

arXiv2021

Neural Human Video Rendering by Learning Dynamic Textures and Rendering-to-Video Translation

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 paper, 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.

cs.GR↗

arXiv2021

RGB2Hands: Real-Time Tracking of 3D Hand Interactions from Monocular RGB Video

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.

cs.CV↗

arXiv2021

Real-time Pose and Shape Reconstruction of Two Interacting Hands With a Single Depth Camera

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.

cs.CV↗

arXiv2021

Generative Model-Based Loss to the Rescue: A Method to Overcome Annotation Errors for Depth-Based Hand Pose Estimation

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".

cs.CV↗