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Researcher profile

Tolga Birdal

Tolga Birdal contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Computer VisionMachine LearningRoboticsGraphicsArtificial Intelligenceeess.IVComputational Geometrymath.OC

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Published work

16 published item(s)

preprint2026arXiv

COMPOSE: Hypergraph Cover Optimization for Multi-view 3D Human Pose Estimation

3D pose estimation from sparse multi-views is a critical task for numerous applications, including action recognition, sports analysis, and human-robot interaction. Optimization-based methods typically follow a two-stage pipeline, first detecting 2D keypoints in each view and then associating these detections across views to triangulate the 3D pose. Existing methods rely on mere pairwise associations to model this correspondence problem, treating global consistency between views (i.e., cycle consistency) as a soft constraint. Yet, reconciling these constraints for multiple views becomes brittle when spurious associations propagate errors. We thus propose COMPOSE, a novel framework that formulates multi-view pose correspondence matching as a hypergraph partitioning problem rather than through pairwise association. While the complexity of the resulting integer linear program grows exponentially in theory, we introduce an efficient geometric pruning strategy to substantially reduce the search space. COMPOSE achieves improvements of up to 23% in average precision over previous optimization-based methods and up to 11% over self-supervised end-to-end learned methods, offering a promising solution to a widely studied problem.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Variational Inference for Lévy Process-Driven SDEs via Neural Tilting

Modelling extreme events and heavy-tailed phenomena is central to building reliable predictive systems in domains such as finance, climate science, and safety-critical AI. While Lévy processes provide a natural mathematical framework for capturing jumps and heavy tails, Bayesian inference for Lévy-driven stochastic differential equations (SDEs) remains intractable with existing methods: Monte Carlo approaches are rigorous but lack scalability, whereas neural variational inference methods are efficient but rely on Gaussian assumptions that fail to capture discontinuities. We address this tension by introducing a neural exponential tilting framework for variational inference in Lévy-driven SDEs. Our approach constructs a flexible variational family by exponentially reweighting the Lévy measure using neural networks. This parametrization preserves the jump structure of the underlying process while remaining computationally tractable. To enable efficient inference, we develop a quadratic neural parametrization that yields closed-form normalization of the tilted measure, a conditional Gaussian representation for stable processes that facilitates simulation, and symmetry-aware Monte Carlo estimators for scalable optimization. Empirically, we demonstrate that the method accurately captures jump dynamics and yields reliable posterior inference in regimes where Gaussian-based variational approaches fail, on both synthetic and real-world datasets.

0 citations0 reviewsNo code linkedOpen access
preprint2023arXiv

Riemannian Functional Map Synchronization for Probabilistic Partial Correspondence in Shape Networks

We consider the problem of graph-matching on a network of 3D shapes with uncertainty quantification. We assume that the pairwise shape correspondences are efficiently represented as \emph{functional maps}, that match real-valued functions defined over pairs of shapes. By modeling functional maps between nearly isometric shapes as elements of the Lie group $SO(n)$, we employ \emph{synchronization} to enforce cycle consistency of the collection of functional maps over the graph, hereby enhancing the accuracy of the individual maps. We further introduce a tempered Bayesian probabilistic inference framework on $SO(n)$. Our framework enables: (i) synchronization of functional maps as maximum-a-posteriori estimation on the Riemannian manifold of functional maps, (ii) sampling the solution space in our energy based model so as to quantify uncertainty in the synchronization problem. We dub the latter \emph{Riemannian Langevin Functional Map (RLFM) Sampler}. Our experiments demonstrate that constraining the synchronization on the Riemannian manifold $SO(n)$ improves the estimation of the functional maps, while our RLFM sampler provides for the first time an uncertainty quantification of the results.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

6D Camera Relocalization in Visually Ambiguous Extreme Environments

We propose a novel method to reliably estimate the pose of a camera given a sequence of images acquired in extreme environments such as deep seas or extraterrestrial terrains. Data acquired under these challenging conditions are corrupted by textureless surfaces, image degradation, and presence of repetitive and highly ambiguous structures. When naively deployed, the state-of-the-art methods can fail in those scenarios as confirmed by our empirical analysis. In this paper, we attempt to make camera relocalization work in these extreme situations. To this end, we propose: (i) a hierarchical localization system, where we leverage temporal information and (ii) a novel environment-aware image enhancement method to boost the robustness and accuracy. Our extensive experimental results demonstrate superior performance in favor of our method under two extreme settings: localizing an autonomous underwater vehicle and localizing a planetary rover in a Mars-like desert. In addition, our method achieves comparable performance with state-of-the-art methods on the indoor benchmark (7-Scenes dataset) using only 20% training data.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Multiway Non-rigid Point Cloud Registration via Learned Functional Map Synchronization

We present SyNoRiM, a novel way to jointly register multiple non-rigid shapes by synchronizing the maps relating learned functions defined on the point clouds. Even though the ability to process non-rigid shapes is critical in various applications ranging from computer animation to 3D digitization, the literature still lacks a robust and flexible framework to match and align a collection of real, noisy scans observed under occlusions. Given a set of such point clouds, our method first computes the pairwise correspondences parameterized via functional maps. We simultaneously learn potentially non-orthogonal basis functions to effectively regularize the deformations, while handling the occlusions in an elegant way. To maximally benefit from the multi-way information provided by the inferred pairwise deformation fields, we synchronize the pairwise functional maps into a cycle-consistent whole thanks to our novel and principled optimization formulation. We demonstrate via extensive experiments that our method achieves a state-of-the-art performance in registration accuracy, while being flexible and efficient as we handle both non-rigid and multi-body cases in a unified framework and avoid the costly optimization over point-wise permutations by the use of basis function maps.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Point2Cyl: Reverse Engineering 3D Objects from Point Clouds to Extrusion Cylinders

We propose Point2Cyl, a supervised network transforming a raw 3D point cloud to a set of extrusion cylinders. Reverse engineering from a raw geometry to a CAD model is an essential task to enable manipulation of the 3D data in shape editing software and thus expand their usages in many downstream applications. Particularly, the form of CAD models having a sequence of extrusion cylinders -- a 2D sketch plus an extrusion axis and range -- and their boolean combinations is not only widely used in the CAD community/software but also has great expressivity of shapes, compared to having limited types of primitives (e.g., planes, spheres, and cylinders). In this work, we introduce a neural network that solves the extrusion cylinder decomposition problem in a geometry-grounded way by first learning underlying geometric proxies. Precisely, our approach first predicts per-point segmentation, base/barrel labels and normals, then estimates for the underlying extrusion parameters in differentiable and closed-form formulations. Our experiments show that our approach demonstrates the best performance on two recent CAD datasets, Fusion Gallery and DeepCAD, and we further showcase our approach on reverse engineering and editing.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Projective Manifold Gradient Layer for Deep Rotation Regression

Regressing rotations on SO(3) manifold using deep neural networks is an important yet unsolved problem. The gap between the Euclidean network output space and the non-Euclidean SO(3) manifold imposes a severe challenge for neural network learning in both forward and backward passes. While several works have proposed different regression-friendly rotation representations, very few works have been devoted to improving the gradient backpropagating in the backward pass. In this paper, we propose a manifold-aware gradient that directly backpropagates into deep network weights. Leveraging Riemannian optimization to construct a novel projective gradient, our proposed regularized projective manifold gradient (RPMG) method helps networks achieve new state-of-the-art performance in a variety of rotation estimation tasks. Our proposed gradient layer can also be applied to other smooth manifolds such as the unit sphere. Our project page is at https://jychen18.github.io/RPMG.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Q-FW: A Hybrid Classical-Quantum Frank-Wolfe for Quadratic Binary Optimization

We present a hybrid classical-quantum framework based on the Frank-Wolfe algorithm, Q-FW, for solving quadratic, linearly-constrained, binary optimization problems on quantum annealers (QA). The computational premise of quantum computers has cultivated the re-design of various existing vision problems into quantum-friendly forms. Experimental QA realizations can solve a particular non-convex problem known as the quadratic unconstrained binary optimization (QUBO). Yet a naive-QUBO cannot take into account the restrictions on the parameters. To introduce additional structure in the parameter space, researchers have crafted ad-hoc solutions incorporating (linear) constraints in the form of regularizers. However, this comes at the expense of a hyper-parameter, balancing the impact of regularization. To date, a true constrained solver of quadratic binary optimization (QBO) problems has lacked. Q-FW first reformulates constrained-QBO as a copositive program (CP), then employs Frank-Wolfe iterations to solve CP while satisfying linear (in)equality constraints. This procedure unrolls the original constrained-QBO into a set of unconstrained QUBOs all of which are solved, in a sequel, on a QA. We use D-Wave Advantage QA to conduct synthetic and real experiments on two important computer vision problems, graph matching and permutation synchronization, which demonstrate that our approach is effective in alleviating the need for an explicit regularization coefficient.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Weakly Supervised Learning of Rigid 3D Scene Flow

We propose a data-driven scene flow estimation algorithm exploiting the observation that many 3D scenes can be explained by a collection of agents moving as rigid bodies. At the core of our method lies a deep architecture able to reason at the \textbf{object-level} by considering 3D scene flow in conjunction with other 3D tasks. This object level abstraction, enables us to relax the requirement for dense scene flow supervision with simpler binary background segmentation mask and ego-motion annotations. Our mild supervision requirements make our method well suited for recently released massive data collections for autonomous driving, which do not contain dense scene flow annotations. As output, our model provides low-level cues like pointwise flow and higher-level cues such as holistic scene understanding at the level of rigid objects. We further propose a test-time optimization refining the predicted rigid scene flow. We showcase the effectiveness and generalization capacity of our method on four different autonomous driving datasets. We release our source code and pre-trained models under \url{github.com/zgojcic/Rigid3DSceneFlow}.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

6D Camera Relocalization in Ambiguous Scenes via Continuous Multimodal Inference

We present a multimodal camera relocalization framework that captures ambiguities and uncertainties with continuous mixture models defined on the manifold of camera poses. In highly ambiguous environments, which can easily arise due to symmetries and repetitive structures in the scene, computing one plausible solution (what most state-of-the-art methods currently regress) may not be sufficient. Instead we predict multiple camera pose hypotheses as well as the respective uncertainty for each prediction. Towards this aim, we use Bingham distributions, to model the orientation of the camera pose, and a multivariate Gaussian to model the position, with an end-to-end deep neural network. By incorporating a Winner-Takes-All training scheme, we finally obtain a mixture model that is well suited for explaining ambiguities in the scene, yet does not suffer from mode collapse, a common problem with mixture density networks. We introduce a new dataset specifically designed to foster camera localization research in ambiguous environments and exhaustively evaluate our method on synthetic as well as real data on both ambiguous scenes and on non-ambiguous benchmark datasets. We plan to release our code and dataset under $\href{https://multimodal3dvision.github.io}{multimodal3dvision.github.io}$.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Continuous Geodesic Convolutions for Learning on 3D Shapes

The majority of descriptor-based methods for geometric processing of non-rigid shape rely on hand-crafted descriptors. Recently, learning-based techniques have been shown effective, achieving state-of-the-art results in a variety of tasks. Yet, even though these methods can in principle work directly on raw data, most methods still rely on hand-crafted descriptors at the input layer. In this work, we wish to challenge this practice and use a neural network to learn descriptors directly from the raw mesh. To this end, we introduce two modules into our neural architecture. The first is a local reference frame (LRF) used to explicitly make the features invariant to rigid transformations. The second is continuous convolution kernels that provide robustness to sampling. We show the efficacy of our proposed network in learning on raw meshes using two cornerstone tasks: shape matching, and human body parts segmentation. Our results show superior results over baseline methods that use hand-crafted descriptors.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Deformation-Aware 3D Model Embedding and Retrieval

We introduce a new problem of retrieving 3D models that are deformable to a given query shape and present a novel deep deformation-aware embedding to solve this retrieval task. 3D model retrieval is a fundamental operation for recovering a clean and complete 3D model from a noisy and partial 3D scan. However, given a finite collection of 3D shapes, even the closest model to a query may not be satisfactory. This motivates us to apply 3D model deformation techniques to adapt the retrieved model so as to better fit the query. Yet, certain restrictions are enforced in most 3D deformation techniques to preserve important features of the original model that prevent a perfect fitting of the deformed model to the query. This gap between the deformed model and the query induces asymmetric relationships among the models, which cannot be handled by typical metric learning techniques. Thus, to retrieve the best models for fitting, we propose a novel deep embedding approach that learns the asymmetric relationships by leveraging location-dependent egocentric distance fields. We also propose two strategies for training the embedding network. We demonstrate that both of these approaches outperform other baselines in our experiments with both synthetic and real data. Our project page can be found at https://deformscan2cad.github.io/.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

From Planes to Corners: Multi-Purpose Primitive Detection in Unorganized 3D Point Clouds

We propose a new method for segmentation-free joint estimation of orthogonal planes, their intersection lines, relationship graph and corners lying at the intersection of three orthogonal planes. Such unified scene exploration under orthogonality allows for multitudes of applications such as semantic plane detection or local and global scan alignment, which in turn can aid robot localization or grasping tasks. Our two-stage pipeline involves a rough yet joint estimation of orthogonal planes followed by a subsequent joint refinement of plane parameters respecting their orthogonality relations. We form a graph of these primitives, paving the way to the extraction of further reliable features: lines and corners. Our experiments demonstrate the validity of our approach in numerous scenarios from wall detection to 6D tracking, both on synthetic and real data.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Learning multiview 3D point cloud registration

We present a novel, end-to-end learnable, multiview 3D point cloud registration algorithm. Registration of multiple scans typically follows a two-stage pipeline: the initial pairwise alignment and the globally consistent refinement. The former is often ambiguous due to the low overlap of neighboring point clouds, symmetries and repetitive scene parts. Therefore, the latter global refinement aims at establishing the cyclic consistency across multiple scans and helps in resolving the ambiguous cases. In this paper we propose, to the best of our knowledge, the first end-to-end algorithm for joint learning of both parts of this two-stage problem. Experimental evaluation on well accepted benchmark datasets shows that our approach outperforms the state-of-the-art by a significant margin, while being end-to-end trainable and computationally less costly. Moreover, we present detailed analysis and an ablation study that validate the novel components of our approach. The source code and pretrained models are publicly available under https://github.com/zgojcic/3D_multiview_reg.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Quaternion Equivariant Capsule Networks for 3D Point Clouds

We present a 3D capsule module for processing point clouds that is equivariant to 3D rotations and translations, as well as invariant to permutations of the input points. The operator receives a sparse set of local reference frames, computed from an input point cloud and establishes end-to-end transformation equivariance through a novel dynamic routing procedure on quaternions. Further, we theoretically connect dynamic routing between capsules to the well-known Weiszfeld algorithm, a scheme for solving \emph{iterative re-weighted least squares} (IRLS) problems with provable convergence properties. It is shown that such group dynamic routing can be interpreted as robust IRLS rotation averaging on capsule votes, where information is routed based on the final inlier scores. Based on our operator, we build a capsule network that disentangles geometry from pose, paving the way for more informative descriptors and a structured latent space. Our architecture allows joint object classification and orientation estimation without explicit supervision of rotations. We validate our algorithm empirically on common benchmark datasets.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Synchronizing Probability Measures on Rotations via Optimal Transport

We introduce a new paradigm, $\textit{measure synchronization}$, for synchronizing graphs with measure-valued edges. We formulate this problem as maximization of the cycle-consistency in the space of probability measures over relative rotations. In particular, we aim at estimating marginal distributions of absolute orientations by synchronizing the $\textit{conditional}$ ones, which are defined on the Riemannian manifold of quaternions. Such graph optimization on distributions-on-manifolds enables a natural treatment of multimodal hypotheses, ambiguities and uncertainties arising in many computer vision applications such as SLAM, SfM, and object pose estimation. We first formally define the problem as a generalization of the classical rotation graph synchronization, where in our case the vertices denote probability measures over rotations. We then measure the quality of the synchronization by using Sinkhorn divergences, which reduces to other popular metrics such as Wasserstein distance or the maximum mean discrepancy as limit cases. We propose a nonparametric Riemannian particle optimization approach to solve the problem. Even though the problem is non-convex, by drawing a connection to the recently proposed sparse optimization methods, we show that the proposed algorithm converges to the global optimum in a special case of the problem under certain conditions. Our qualitative and quantitative experiments show the validity of our approach and we bring in new perspectives to the study of synchronization.

0 citations0 reviewsNo code linkedOpen access