Scale-Rotation-Equivariant Lie Group Convolution Neural Networks (Lie Group-CNNs)

Wei-Dong Qiao; Yang Xu; Hui Li

Home/Archive/arXiv

arXiv · 2306.06934

Scale-Rotation-Equivariant Lie Group Convolution Neural Networks (Lie Group-CNNs)

Wei-Dong Qiao·Yang Xu·Hui Li

View original source ↗Read source document ↗Export metadata ↓

Abstract

The weight-sharing mechanism of convolutional kernels ensures translation-equivariance of convolution neural networks (CNNs). Recently, rotation-equivariance has been investigated. However, research on scale-equivariance or simultaneous scale-rotation-equivariance is insufficient. This study proposes a Lie group-CNN, which can keep scale-rotation-equivariance for image classification tasks. The Lie group-CNN includes a lifting module, a series of group convolution modules, a global pooling layer, and a classification layer. The lifting module transfers the input image from Euclidean space to Lie group space, and the group convolution is parameterized through a fully connected network using Lie-algebra of Lie-group elements as inputs to achieve scale-rotation-equivariance. The Lie group SIM(2) is utilized to establish the Lie group-CNN with scale-rotation-equivariance. Scale-rotation-equivariance of Lie group-CNN is verified and achieves the best recognition accuracy on the blood cell dataset (97.50%) and the HAM10000 dataset (77.90%) superior to Lie algebra convolution network, dilation convolution, spatial transformer network, and scale-equivariant steerable network. In addition, the generalization ability of the Lie group-CNN on SIM(2) on rotation-equivariance is verified on rotated-MNIST and rotated-CIFAR10, and the robustness of the network is verified on SO(2) and SE(2). Therefore, the Lie group-CNN can successfully extract geometric features and performs equivariant recognition on images with rotation and scale transformations.

Explore related subjects

cs.CV

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Wei-Dong Qiao, Yang Xu, Hui Li. 2023-06-12. Scale-Rotation-Equivariant Lie Group Convolution Neural Networks (Lie Group-CNNs). https://arxiv.org/abs/2306.06934

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Privacy Leakage on DNNs: A Survey of Model Inversion Attacks and Defenses

Deep Neural Networks (DNNs) have revolutionized various domains with their exceptional performance across numerous applications. However, Model Inversion (MI) attacks, which disclose private information about the training dataset by abusing access to the trained models, have emerged as a formidable privacy threat. Given a trained network, these attacks enable adversaries to reconstruct high-fidelity data that closely aligns with the private training samples, posing significant privacy concerns. Despite the rapid advances in the field, we lack a comprehensive and systematic overview of existing MI attacks and defenses. To fill this gap, this paper thoroughly investigates this realm and presents a holistic survey. Firstly, our work briefly reviews early MI studies on traditional machine learning scenarios. We then elaborately analyze and compare numerous recent attacks and defenses on Deep Neural Networks (DNNs) across multiple modalities and learning tasks. By meticulously analyzing their distinctive features, we summarize and classify these methods into different categories and provide a novel taxonomy. Finally, this paper discusses promising research directions and presents potential solutions to open issues. To facilitate further study on MI attacks and defenses, we have implemented an open-source model inversion toolbox on GitHub (https://github.com/ffhibnese/Model-Inversion-Attack-ToolBox).

cs.CV↗

arXiv2026

ALINA: Advanced Line Identification and Notation Algorithm

Labels are the cornerstone of supervised machine learning algorithms. Most visual recognition methods are fully supervised, using bounding boxes or pixel-wise segmentations for object localization. Traditional labeling methods, such as crowd-sourcing, are prohibitive due to cost, data privacy, amount of time, and potential errors on large datasets. To address these issues, we propose a novel annotation framework, Advanced Line Identification and Notation Algorithm (ALINA), which can be used for labeling taxiway datasets that consist of different camera perspectives and variable weather attributes (sunny and cloudy). Additionally, the CIRCular threshoLd pixEl Discovery And Traversal (CIRCLEDAT) algorithm has been proposed, which is an integral step in determining the pixels corresponding to taxiway line markings. Once the pixels are identified, ALINA generates corresponding pixel coordinate annotations on the frame. Using this approach, 60,249 frames from the taxiway dataset, AssistTaxi have been labeled. To evaluate the performance, a context-based edge map (CBEM) set was generated manually based on edge features and connectivity. The detection rate after testing the annotated labels with the CBEM set was recorded as 98.45%, attesting its dependability and effectiveness.

cs.CV↗

arXiv2026

DisasterInsight: A Building-Centric Benchmark for Evaluating Vision--Language Models in Disaster Response

Vision--language models (VLMs) show promise for disaster-response remote sensing, but existing benchmarks mainly emphasize scene-level or damage-centric assessment. To study this building-centric gap, we introduce \method{}, a diagnostic benchmark built on xBD, a pre/post-disaster satellite dataset with building-level damage labels. \method{} enriches building instances with OpenStreetMap-derived functional labels and contains 134{,}108 task-specific instruction records across 15 task types, spanning instance-level assessment, scene-level counting, multi-instance reasoning, and structured report generation. The benchmark supports RGB pre/post-disaster imagery, single- and multi-view instance formulations, and scene-level RGB/SAR diagnostic inputs. Experiments with general-domain and remote-sensing VLMs show that models perform better on visible damage cues than on building-function understanding, multi-instance reasoning, counting, and grounded reporting. Instruction tuning improves performance on several tasks but does not close this building-centric gap.

cs.CV↗