arXiv subjects

Pavlo Melnyk

Publications and source records attributed to Pavlo Melnyk.

11 recordsLinked to original sources

arXiv2026

CQF-HMR: Continuous Quaternion Flows for Probabilistic 3D Human Mesh Recovery from a Single Image

Recovering 3D digital humans from a single 2D image is an ill-posed computer vision problem due to the loss of depth information. Probabilistic 3D human pose estimation compensates for this by estimating a set of 3D hypotheses from a prior distribution via generative models. However, most prior work focuses only on 3D keypoints, which often leads to implausible poses that are difficult to apply to downstream tasks, e.g. animation or digital humans. SMPL-based methods are more scalable thanks to the explicit body priors, but it requires more complex modeling of the generation process due to the non-additive nature of the joint rotations. In this work, we propose a novel approach for probabilistic 3D humans using quaternion-constrained continuous normalizing flows conditioned on 2D pose estimations. Our proposed quaternion flows show significant advantages over approaches using other rotation representations. Experiments demonstrate state-of-the-art results of our method on Human3.6M, particularly in ambiguous settings, and comparable pose estimation accuracy on challenging 3DPW and EMDB benchmarks.

cs.CV↗

arXiv2026

Benchmark Dataset for Catalysis on 2D MXenes

Merging first-principles calculations with machine learning (ML), we aim to accelerate the exploration of catalytic behaviour in novel materials. We focus on two-dimensional (2D) Ti$_2$CT$_y$ MXenes, whose versatile surface chemistry makes them particularly compelling candidates for catalysis. Resolving their composition and structure under realistic conditions exceeds the reach of standard density functional theory (DFT) due to computational cost. To address this challenge, we generate a comprehensive dataset of 50,000 DFT calculations for training and 10,000 for testing, encompassing both Ti$_2$CT$_y$ MXene configurations and molecular systems, along with an additional test dataset with 1000 genuinely new, larger systems to investigate how well models generalise. We train and validate widely used and competitive machine learning interatomic potential (MLIP) models, including EquiformerV2, MACE, MatRIS, and UPET, that accurately predict atomic forces and formation energies -- quantities that DFT must repeatedly compute for structural and catalytic investigations -- for these 2D materials. This combined DFT-ML framework achieves computational acceleration on the order of approximately $1-4 \cdot 10^3$ (on a CPU) while maintaining desired-level accuracy (approximately +/- $10$ meV/A for forces and approximately +/- $1$ meV for per-atom energies), paving the way for more efficient investigations of MXene catalytic behaviour. Moreover, we perform an extensive qualitative evaluation of the trained models, showcasing the importance of comprehensive simulation-based comparison beyond benchmark metrics. The dataset and the trained models with the code are available at https://huggingface.co/datasets/CatalystAnonymous/catalyst_mxenes.

cond-mat.mtrl-sci↗

arXiv2026

QuaMo: Quaternion Motions for Vision-based 3D Human Kinematics Capture

Vision-based 3D human motion capture from videos remains a challenge in computer vision. Traditional 3D pose estimation approaches often ignore the temporal consistency between frames, causing implausible and jittery motion. The emerging field of kinematics-based 3D motion capture addresses these issues by estimating the temporal transitioning between poses instead. A major drawback in current kinematics approaches is their reliance on Euler angles. Despite their simplicity, Euler angles suffer from discontinuity that leads to unstable motion reconstructions, especially in online settings where trajectory refinement is unavailable. Contrarily, quaternions have no discontinuity and can produce continuous transitions between poses. In this paper, we propose QuaMo, a novel Quaternion Motions method using quaternion differential equations (QDE) for human kinematics capture. We utilize the state-space model, an effective system for describing real-time kinematics estimations, with quaternion state and the QDE describing quaternion velocity. The corresponding angular acceleration is computed from a meta-PD controller with a novel acceleration enhancement that adaptively regulates the control signals as the human quickly changes to a new pose. Unlike previous work, our QDE is solved under the quaternion unit-sphere constraint that results in more accurate estimations. Experimental results show that our novel formulation of the QDE with acceleration enhancement accurately estimates 3D human kinematics with no discontinuity and minimal implausibilities. QuaMo outperforms comparable state-of-the-art methods on multiple datasets, namely Human3.6M, Fit3D, SportsPose and AIST. The code is available at https://github.com/cuongle1206/QuaMo

cs.CV↗

arXiv2026

Flow Matching for Probabilistic Monocular 3D Human Pose Estimation

Recovering 3D human poses from a monocular camera view is a highly ill-posed problem due to the depth ambiguity. Earlier studies on 3D human pose lifting from 2D often contain incorrect-yet-overconfident 3D estimations. To mitigate the problem, emerging probabilistic approaches treat the 3D estimations as a distribution, taking into account the uncertainty measurement of the poses. Falling in a similar category, we proposed FMPose, a probabilistic 3D human pose estimation method based on the flow matching generative approach. Conditioned on the 2D cues, the flow matching scheme learns the optimal transport from a simple source distribution to the plausible 3D human pose distribution via continuous normalizing flows. The 2D lifting condition is modeled via graph convolutional networks, leveraging the learnable connections between human body joints as the graph structure for feature aggregation. While trade-offs between processing time and precision exist, already in the equal-accuracy comparison, FMPose exhibits significantly faster processing time than the diffusion model, and also offers another faster and more accurate configuration. Experimental results show major improvements of our FMPose over current state-of-the-art methods on two common benchmarks for 3D human pose estimation, namely Human3.6M, MPI-INF-3DHP. Additionally, FMPose shows competitive performance on the more challenging 3DPW dataset. The code implementation is available at https://github.com/cuongle1206/FMPose

cs.CV↗

arXiv2026

On the Role of Rotation Equivariance in Monocular 2D-to-3D Human Pose Lifting

We consider monocular 3D human pose estimation (HPE), where the goal is to predict 3D human skeletal joints from a single 2D image, typically via 2D keypoint detection followed by 2D-to-3D lifting. Despite their success, we find that current lifting models exhibit strong performance degradation under rotations. We systematically study rotation equivariance across lifting architectures with increasing degrees of equivariant inductive bias, and investigate whether equivariance should be enforced by architectural design or learned from data, given the inherent ambiguity of monocular 2D-to-3D lifting. Utilising common HPE benchmarks, we demonstrate that rotation equivariance can be effectively learned via rotation-based data augmentation applied jointly to input and output poses. Compared with non-augmented models, this reduces error on rotated poses by over 30% across the benchmarks, with reductions of up to 72%. Moreover, augmentation-based models achieve up to 15% lower error than methods that are fully equivariant by design, while providing up to 37$\times$ faster inference. We further show that these findings generalise to real-world human pose sequences involving full-body rotations and to a state-of-the-art HPE model.

cs.CV↗

arXiv2024

O$n$ Learning Deep O($n$)-Equivariant Hyperspheres

In this paper, we utilize hyperspheres and regular $n$-simplexes and propose an approach to learning deep features equivariant under the transformations of $n$D reflections and rotations, encompassed by the powerful group of O$(n)$. Namely, we propose O$(n)$-equivariant neurons with spherical decision surfaces that generalize to any dimension $n$, which we call Deep Equivariant Hyperspheres. We demonstrate how to combine them in a network that directly operates on the basis of the input points and propose an invariant operator based on the relation between two points and a sphere, which as we show, turns out to be a Gram matrix. Using synthetic and real-world data in $n$D, we experimentally verify our theoretical contributions and find that our approach is superior to the competing methods for O$(n)$-equivariant benchmark datasets (classification and regression), demonstrating a favorable speed/performance trade-off. The code is available at https://github.com/pavlo-melnyk/equivariant-hyperspheres.

cs.LG↗

arXiv2024

TetraSphere: A Neural Descriptor for O(3)-Invariant Point Cloud Analysis

In many practical applications, 3D point cloud analysis requires rotation invariance. In this paper, we present a learnable descriptor invariant under 3D rotations and reflections, i.e., the O(3) actions, utilizing the recently introduced steerable 3D spherical neurons and vector neurons. Specifically, we propose an embedding of the 3D spherical neurons into 4D vector neurons, which leverages end-to-end training of the model. In our approach, we perform TetraTransform--an equivariant embedding of the 3D input into 4D, constructed from the steerable neurons--and extract deeper O(3)-equivariant features using vector neurons. This integration of the TetraTransform into the VN-DGCNN framework, termed TetraSphere, negligibly increases the number of parameters by less than 0.0002%. TetraSphere sets a new state-of-the-art performance classifying randomly rotated real-world object scans of the challenging subsets of ScanObjectNN. Additionally, TetraSphere outperforms all equivariant methods on randomly rotated synthetic data: classifying objects from ModelNet40 and segmenting parts of the ShapeNet shapes. Thus, our results reveal the practical value of steerable 3D spherical neurons for learning in 3D Euclidean space. The code is available at https://github.com/pavlo-melnyk/tetrasphere.

cs.CV↗

arXiv2023

Learning to Augment: Hallucinating Data for Domain Generalized Segmentation

Domain generalized semantic segmentation (DGSS) is an essential but highly challenging task, in which the model is trained only on source data and any target data is not available. Existing DGSS methods primarily standardize the feature distribution or utilize extra domain data for augmentation. However, the former sacrifices valuable information and the latter introduces domain biases. Therefore, generating diverse-style source data without auxiliary data emerges as an attractive strategy. In light of this, we propose GAN-based feature augmentation (GBFA) that hallucinates stylized feature maps while preserving their semantic contents with a feature generator. The impressive generative capability of GANs enables GBFA to perform inter-channel and trainable feature synthesis in an end-to-end framework. To enable learning GBFA, we introduce random image color augmentation (RICA), which adds a diverse range of variations to source images during training. These augmented images are then passed through a feature extractor to obtain features tailored for GBFA training. Both GBFA and RICA operate exclusively within the source domain, eliminating the need for auxiliary datasets. We conduct extensive experiments, and the generalization results from the synthetic GTAV and SYNTHIA to the real Cityscapes, BDDS, and Mapillary datasets show that our method achieves state-of-the-art performance in DGSS.

cs.CV↗

arXiv2022

Steerable 3D Spherical Neurons

Emerging from low-level vision theory, steerable filters found their counterpart in prior work on steerable convolutional neural networks equivariant to rigid transformations. In our work, we propose a steerable feed-forward learning-based approach that consists of neurons with spherical decision surfaces and operates on point clouds. Such spherical neurons are obtained by conformal embedding of Euclidean space and have recently been revisited in the context of learning representations of point sets. Focusing on 3D geometry, we exploit the isometry property of spherical neurons and derive a 3D steerability constraint. After training spherical neurons to classify point clouds in a canonical orientation, we use a tetrahedron basis to quadruplicate the neurons and construct rotation-equivariant spherical filter banks. We then apply the derived constraint to interpolate the filter bank outputs and, thus, obtain a rotation-invariant network. Finally, we use a synthetic point set and real-world 3D skeleton data to verify our theoretical findings. The code is available at https://github.com/pavlo-melnyk/steerable-3d-neurons.

cs.CV↗

arXiv2021

Embed Me If You Can: A Geometric Perceptron

Solving geometric tasks involving point clouds by using machine learning is a challenging problem. Standard feed-forward neural networks combine linear or, if the bias parameter is included, affine layers and activation functions. Their geometric modeling is limited, which motivated the prior work introducing the multilayer hypersphere perceptron (MLHP). Its constituent part, i.e., the hypersphere neuron, is obtained by applying a conformal embedding of Euclidean space. By virtue of Clifford algebra, it can be implemented as the Cartesian dot product of inputs and weights. If the embedding is applied in a manner consistent with the dimensionality of the input space geometry, the decision surfaces of the model units become combinations of hyperspheres and make the decision-making process geometrically interpretable for humans. Our extension of the MLHP model, the multilayer geometric perceptron (MLGP), and its respective layer units, i.e., geometric neurons, are consistent with the 3D geometry and provide a geometric handle of the learned coefficients. In particular, the geometric neuron activations are isometric in 3D, which is necessary for rotation and translation equivariance. When classifying the 3D Tetris shapes, we quantitatively show that our model requires no activation function in the hidden layers other than the embedding to outperform the vanilla multilayer perceptron. In the presence of noise in the data, our model is also superior to the MLHP.

cs.LG↗

arXiv2019

A High-Performance CNN Method for Offline Handwritten Chinese Character Recognition and Visualization

Recent researches introduced fast, compact and efficient convolutional neural networks (CNNs) for offline handwritten Chinese character recognition (HCCR). However, many of them did not address the problem of network interpretability. We propose a new architecture of a deep CNN with high recognition performance which is capable of learning deep features for visualization. A special characteristic of our model is the bottleneck layers which enable us to retain its expressiveness while reducing the number of multiply-accumulate operations and the required storage. We introduce a modification of global weighted average pooling (GWAP) - global weighted output average pooling (GWOAP). This paper demonstrates how they allow us to calculate class activation maps (CAMs) in order to indicate the most relevant input character image regions used by our CNN to identify a certain class. Evaluating on the ICDAR-2013 offline HCCR competition dataset, we show that our model enables a relative 0.83% error reduction while having 49% fewer parameters and the same computational cost compared to the current state-of-the-art single-network method trained only on handwritten data. Our solution outperforms even recent residual learning approaches.

cs.CV↗