Search Results (82)

Robust visual perception and geometric alignment are crucial for intelligent automation in various domains, such as industrial processes and infrastructure monitoring. Accurately aligning structured visual elements, such as floor markings or road-marking templates, is essential for tasks like automated guidance, verification, and condition assessment. However, traditional feature-based methods struggle with templates that feature simple geometries and lack rich textures, making reliable feature matching and alignment difficult, even under controlled conditions. To address this, we propose GeoTemplateKPNet, a novel self-supervised deep-learning framework, built upon Convolutional Neural Networks (CNNs), designed to learn robust, geometrically consistent keypoints specifically in synthetic template images. The model is trained exclusively in a synthetic template dataset by enforcing equivariance to geometric transformations and utilizing self-supervised losses, including inside mask loss, peakiness loss, repulsion loss, and keypoint-driven image reprojection loss, thereby eliminating the need for manual keypoint annotations. We evaluate the method in a synthetic template test set, using metrics such as a keypoint-matching comparison, the Inside Mask Rate (IMR), and the Alignment Reconstruction Error (ARE). The results demonstrate that GeoTemplateKPNet successfully learns to predict meaningful keypoints on template structures, enabling accurate alignment between templates and their transformed counterparts. Ablation studies reveal that the number of keypoints (K) impacts the performance, with K = 3 providing the most suitable balance for the overall alignment accuracy, although the performance varies across different template geometries. GeoTemplateKPNet offers a foundational self-supervised solution for the robust geometric analysis of templates, which is crucial for downstream alignment tasks and applications. Full article

Image-level weakly supervised semantic segmentation is a challenging problem in computer vision and has gained a lot of attention in recent years. Most existing models utilize class activation mapping (CAM) to generate initial pseudo-labels for each image pixel. However, CAM usually focuses only on the most discriminating regions of target objects and treats each channel feature map independently, which may overlook some important regions due to the lack of accurate pixel-level labels, leading to the underactivation of the target objects. In this paper, we propose a dual attention equivariant network (DAEN) model to address this problem by considering both channel and spatial information of different feature maps. Specifically, we first design a channel–spatial attention module (CSM) for DAEN to extract accurately features of target objects by considering the correlation among feature maps in different channels, and then integrate the CSM with equivariant regularization and pixel-correlation modules to achieve more accurate and effective pixel-level semantic segmentation. Extensive experimental results show that the DAEN model achieved 2.1% and 1.3% higher mIoU scores than the existing weakly supervised semantic segmentation models on the PASCAL VOC 2012 and LUAD-HistoSeg datasets, respectively, validating the effectiveness and efficiency of the DAEN model. Full article

Ground texture-based localization leverages environment-invariant, planar-constrained features to enhance pose estimation robustness, thus offering inherent advantages for seamless localization. However, traditional feature extraction methods struggle with reliable performance under large-scale rotations and texture sparsity in the case of ground texture-based localization. This study addresses these challenges through a learning-based feature extraction framework—Ground Texture Rotation-Equivariant Keypoints and Descriptors (GT-REKD). The GT-REKD framework employs group-equivariant convolutions over the cyclic rotation group, augmented with directional attention and orientation-encoding heads, to produce dense keypoints and descriptors that are exactly invariant to 0–360° in-plane rotations. The experimental results for ground texture localization show that GT-REKD achieves 96.14% matching in pure rotation tests, 94.08% in incremental localization, and relocalization errors of 5.55° and 4.41 px (≈0.1 cm), consistently outperforming baseline methods under extreme rotations and sparse textures, highlighting its applicability to visual localization and simultaneous localization and mapping (SLAM) tasks. Full article

This study introduces a novel contrastive learning-based X-ray diffraction (XRD) analysis framework, an SE(3)-equivariant graph neural network (E3NN) based Atomic Cluster Expansion Neural Network (EACNN), which reduces the strong dependency on databases and initial models in traditional methods. By integrating E3NN with atomic cluster expansion (ACE) techniques, a dual-tower contrastive learning model has been developed, mapping crystal structures and XRD patterns to a continuous embedding space. The EACNN model retains hierarchical features of crystal systems through symmetry-sensitive encoding mechanisms and utilizes relationship mining via contrastive learning to replace rigid classification boundaries. This approach reveals gradual symmetry-breaking patterns between monoclinic and orthorhombic crystal systems in the latent space, effectively addressing the recognition challenges associated with low-symmetry systems and small sample space groups. Our investigation further explores the potential for model transfer to experimental data and multimodal extensions, laying the theoretical foundation for establishing a universal structure–property mapping relationship. Full article

Currently, deep learning has become a mainstream approach for automatic modulation classification (AMC) with its powerful feature extraction capability. Complex-valued neural networks (CVNNs) show unique advantages in the field of communication signal processing because of their ability to directly process complex data and obtain signal amplitude and phase information. However, existing models face deployment challenges due to excessive parameters and computational complexity. To address these limitations, a lightweight dual-branch complex-valued neural network (LDCVNN) is proposed. The framework uses dual pathways to separately capture features with phase information and complex-scaling-equivariant representations, adaptively fused via trainable weighted fusion. Spatial and channel reconstruction convolution (SCConv) is extended to complex domain and combined with complex-valued depthwise separable convolution block (CBlock) and complex-valued average pooling to eliminate feature redundancy and extract higher order features. Finally, efficient classification is realized through complex-valued fully connected layers and a complex-valued Softmax. The evaluations demonstrate that LDCVNN achieves the highest average accuracy on RML2016.10a with only 9.0 K parameters and without data augmentation, which reducing the number of parameters by 99.33% compared to CDSN and by 97.25% compared to CSDNN. Additionally, LDCVNN achieves a better balance between efficiency and performance across other datasets. Full article

It is a famous hypothesis that orbifold D-brane charges in string theory can be classified in twisted equivariant K-theory. Recently, it is believed that the hypothesis has a non-trivial lift to M-branes classified in twisted real equivariant 4-Cohomotopy. Quasi-elliptic cohomology, which is defined as an equivariant cohomology of a cyclification of orbifolds, potentially interpolates the two statements, by approximating equivariant 4-Cohomotopy classified by 4-sphere orbifolds. In this paper we compute Real and complex quasi-elliptic cohomology theories of 4-spheres under the action by some finite subgroups that are the most interesting isotropy groups where the M5-branes may sit. The computation connects the M-brane charges in the presence of discrete symmetries to Real quasi-elliptic cohomology theories, and those with the symmetry omitted to complex quasi-elliptic cohomology theories. Full article

This paper introduces a model that automates the diagnosis of a patient’s condition, reducing reliance on highly trained professionals, particularly in resource-constrained settings. To ensure data consistency, the dataset was preprocessed for uniformity in size, format, and color channels. Image quality was further enhanced using histogram equalization to improve the dynamic range. Lung regions were isolated using segmentation techniques, which also eliminated extraneous areas from the images. A modified segmentation-based cropping technique was employed to define an optimal cropping rectangle. Feature extraction was performed using persistent homology, deep learning, and hybrid methodologies. Persistent homology captured topological features across multiple scales, while the deep learning model leveraged convolutional transition equivariance, input-adaptive weighting, and the global receptive field provided by Vision Transformers. By integrating features from both methods, the classification model effectively predicted severity levels (mild, moderate, severe). The segmentation-based cropping method showed a modest improvement, achieving 80% accuracy, while stand-alone persistent homology features reached 66% accuracy. Notably, the hybrid model outperformed existing approaches, including SVM, ResNet50, and VGG16, achieving an accuracy of 82%. Full article

We develop a new unsupervised symmetry learning method that starts with raw data and provides the minimal generator of an underlying Lie group of symmetries, together with a symmetry-equivariant representation of the data, which turns the hidden symmetry into an explicit one. The method is able to learn the pixel translation operator from a dataset with only an approximate translation symmetry and can learn quite different types of symmetries that are not apparent to the naked eye. The method is based on the formulation of an information-theoretic loss function that measures both the degree of symmetry of a dataset under a candidate symmetry generator and a proposed notion of locality of the samples, which is coupled to symmetry. We demonstrate that this coupling between symmetry and locality, together with an optimization technique developed for entropy estimation, results in a stable system that provides reproducible results. Full article

For networks that process 3D data, estimating the orientation and position of 3D objects is a challenging task. This is because the traditional networks are not robust to the rotation of the data, and their internal workings are largely opaque and uninterpretable. To solve this problem, a novel equivariant self-supervised vector network for point clouds is proposed. The network can learn the rotation direction information of the 3D target and estimate the rotational pose change of the target, and the interpretability of the equivariant network is studied using information theory. The utilization of vector neurons within the network lifts the scalar data to vector representations, enabling the network to learn the pose information inherent in the 3D target. The network can perform complex rotation-equivariant tasks after pre-training, and it shows impressive performance in complex tasks like category-level pose change estimation and rotation-equivariant reconstruction. We demonstrate through experiments that our network can accurately detect the orientation and pose change of point clouds and visualize the latent features. Moreover, it performs well in invariant tasks such as classification and category-level segmentation. Full article

For the high-dimensional covariance estimation problem, when ${lim}_{n\to \infty }p/n=c\in (0,1)$, the orthogonally equivariant estimator of the population covariance matrix proposed by Tsai and Tsai exhibits certain optimal properties. Under some regularity conditions, the authors showed that their novel estimators of eigenvalues are consistent with the eigenvalues of the population covariance matrix. In this paper, under the multinormal setup, we show that they are consistent estimators of the population covariance matrix under a high-dimensional asymptotic setup. We also show that the novel estimator is the MLE of the population covariance matrix when $c\in (0,1)$. The novel estimator is used to establish that the optimal decomposite $T_T^2$-test has been retained. A high-dimensional statistical hypothesis testing problem is used to carry out statistical inference for high-dimensional principal component analysis-related problems without the sparsity assumption. In the final section, we discuss the situation in which $p>n$, especially for high-dimensional low-sample size categorical data models in which $p>>n$. Full article

Reconfigurable Intelligent Surface (RIS) panels have garnered significant attention with the emergence of next-generation network technologies. This paper proposes a novel data-driven approach that leverages Light Detecting and Ranging (LiDAR) sensors to enhance user localization and beamforming in RIS-assisted networks. Integrating LiDAR sensors into the network will be instrumental, offering high-speed and precise 3D mapping capabilities, even in low light or adverse weather conditions. LiDAR data facilitate user localization, enabling the determination of optimal RIS coefficients. Our approach extends a Graph Neural Network (GNN) by integrating LiDAR-captured user locations as inputs. This extension enables the GNN to effectively learn the mapping from received pilots to optimal beamformers and reflection coefficients to maximize the RIS-assisted sumrate among multiple users. The permutation-equivariant and -invariant properties of the GNN proved advantageous in efficiently handling the LiDAR data. Our simulation results demonstrated significant improvements in sum rates compared with conventional methods. Specifically, including locations improved on excluding locations by up to 25% and outperformed the Linear Minimum Mean Squared Error (LMMSE) channel estimation by up to 85% with varying downlink power and 98% with varying pilot lengths, and showed a remarkable 190% increase with varying downlink power compared with scenarios excluding the RIS. Full article

The aim here is to describe all isomorphism classes of $\mathrm{SU}(n+1)$-equivariant Hermitian holomorphic vector bundles on the complex projective space $\mathbb{C}{\mathbb{P}}^n$. If $G\subset \mathrm{SU}(n+1)$ is the isotropy subgroup of a chosen point $x_0\in \mathbb{C}{\mathbb{P}}^n$, and $\rho :G⟶\mathrm{GL}\left(V\right)$ is a unitary representation, we obtain $\mathrm{SU}(n+1)$-equivariant holomorphic Hermitian vector bundles on $\mathbb{C}{\mathbb{P}}^n$. Next, given any $v\in \mathrm{End}\left(V_{\rho }\right)\otimes {\left(T_{z_0}^{0,1}\mathbb{C}{\mathbb{P}}^n\right)}^{\ast }$ satisfying certain conditions, a new structure of an $\mathrm{SU}(n+1)$-equivariant holomorphic Hermitian vector bundle on this underlying $C^{\infty }$ holomorphic Hermitian bundle is obtained. It is shown that all $\mathrm{SU}(n+1)$-equivariant holomorphic Hermitian vector bundles on $\mathbb{C}{\mathbb{P}}^n$ arise this way. Full article

Based on finite-dimensional time-frequency analysis, we study the properties of time-frequency shift equivariant maps that are generally nonlinear. We first establish a one-to-one correspondence between $\mathsf{\Lambda }$-equivariant maps and certain phase-homogeneous functions and also provide a reconstruction formula that expresses $\mathsf{\Lambda }$-equivariant maps in terms of these phase-homogeneous functions, leading to a deeper understanding of the class of $\mathsf{\Lambda }$-equivariant maps. Next, we consider the approximation of $\mathsf{\Lambda }$-equivariant maps by neural networks. In the case where $\mathsf{\Lambda }$ is a cyclic subgroup of order N in ${\mathbb{Z}}_N\times {\mathbb{Z}}_N$, we prove that every $\mathsf{\Lambda }$-equivariant map can be approximated by a shallow neural network whose affine linear maps are simply linear combinations of time-frequency shifts by $\mathsf{\Lambda }$. This aligns well with the proven suitability of convolutional neural networks (CNNs) in tasks requiring translation equivariance, particularly in image and signal processing applications. Full article

Let G be a compact connected Lie group, $(X,\omega ,\mu )$ a Hamiltonian G-manifold with moment map $\mu$, and Z a codimension-2 Hamiltonian G-submanifold of X. We study the boundedness of the differential of symplectic vortices $(A,u)$ near Z, where A is a connection 1-form of a principal G-bundle P over a punctured Riemann surface $\mathring{\Sigma }$, and u is a G-equivariant map from P to an open cylinder model near Z. We show that if the total energy of a family of symplectic vortices on $\mathring{\Sigma }\cong [0,+\infty )\times S^1$ is finite, then the A-twisted differential $d_{A}u(r,\theta )$ is uniformly bounded for all $(r,\theta )\in [0,+\infty )\times S^1$. Full article

Object detection in aerial images has had a broader range of applications in the past few years. Unlike the targets in the images of horizontal shooting, targets in aerial photos generally have arbitrary orientation, multi-scale, and a high aspect ratio. Existing methods often employ a classification backbone network to extract translation-equivariant features (TEFs) and utilize many predefined anchors to handle objects with diverse appearance variations. However, they encounter misalignment at three levels, spatial, feature, and task, during different detection stages. In this study, we propose a model called the Staged Adaptive Alignment Detector (SAADet) to solve these challenges. This method utilizes a Spatial Selection Adaptive Network (SSANet) to achieve spatial alignment of the convolution receptive field to the scale of the object by using a convolution sequence with an increasing dilation rate to capture the spatial context information of different ranges and evaluating this information through model dynamic weighting. After correcting the preset horizontal anchor to an oriented anchor, feature alignment is achieved through the alignment convolution guided by oriented anchor to align the backbone features with the object’s orientation. The decoupling of features using the Active Rotating Filter is performed to mitigate inconsistencies due to the sharing of backbone features in regression and classification tasks to accomplish task alignment. The experimental results show that SAADet achieves equilibrium in speed and accuracy on two aerial image datasets, HRSC2016 and UCAS-AOD. Full article