R2Det: Exploring Relaxed Rotation Equivariance in 2D object detection (2408.11760v3)

Abstract: Group Equivariant Convolution (GConv) empowers models to explore underlying symmetry in data, improving performance. However, real-world scenarios often deviate from ideal symmetric systems caused by physical permutation, characterized by non-trivial actions of a symmetry group, resulting in asymmetries that affect the outputs, a phenomenon known as Symmetry Breaking. Traditional GConv-based methods are constrained by rigid operational rules within group space, assuming data remains strictly symmetry after limited group transformations. This limitation makes it difficult to adapt to Symmetry-Breaking and non-rigid transformations. Motivated by this, we mainly focus on a common scenario: Rotational Symmetry-Breaking. By relaxing strict group transformations within Strict Rotation-Equivariant group $\mathbf{C}_n$, we redefine a Relaxed Rotation-Equivariant group $\mathbf{R}_n$ and introduce a novel Relaxed Rotation-Equivariant GConv (R2GConv) with only a minimal increase of $4n$ parameters compared to GConv. Based on R2GConv, we propose a Relaxed Rotation-Equivariant Network (R2Net) as the backbone and develop a Relaxed Rotation-Equivariant Object Detector (R2Det) for 2D object detection. Experimental results demonstrate the effectiveness of the proposed R2GConv in natural image classification, and R2Det achieves excellent performance in 2D object detection with improved generalization capabilities and robustness. The code is available in \texttt{https://github.com/wuer5/r2det}.

• The paper introduces a novel approach with relaxed rotation-equivariant convolutions, enhancing object detection by addressing symmetry-breaking transformations.
• It leverages a learnable parameter to relax strict rotation symmetry, allowing the network to adapt to real-world perturbations.
• Experimental results on benchmarks like PASCAL VOC and MS COCO show significant gains in average precision, highlighting its practical potential.

SBDet: A Symmetry-Breaking Object Detector via Relaxed Rotation-Equivariance

The paper under consideration presents a novel approach to the design of object detection networks, focused on accommodating real-world complexities inherent in visual data, specifically addressing challenges posed by Symmetry-Breaking and non-rigid transformations. The proposed method introduces the Symmetry-Breaking Object Detector (SBDet), which leverages a novel Relaxed Rotation-Equivariant Group Convolution (R2GConv). This development stands on the foundation of prior research in Equivariant Neural Networks (ENNs), extending these principles to create a more flexible and adaptive detection tool.

Key Contributions

The cornerstone of this research is the Relaxed Rotation-Equivariant Group Convolution, spearheaded by the definition of a Relaxed Rotation-Equivariant group $\mathbf{R}_4$. This paradigm permits a controlled departure from strict rotation symmetry, allowing the detection network to adapt more gracefully to variations and perturbations typical in real-world data. The approach modifies traditional group convolutions, introducing a learnable parameter $\Delta$ that adjusts the input-output transformations beyond the confines of predefined symmetrical transformations.

1. Relaxed Rotation-Equivariance Implementation: The implementation centers on perturbing the group operations associated with the traditional $\mathbf{C}_4$ rotation group. By adopting a Relaxed Rotation-Equivariant Network (R2Net) as a primary structure, this method encourages networks to manage symmetry-breaking through adaptive parameter adjustments, thus becoming more resilient against unanticipated rotational disruptions.
2. Symmetry-Breaking Object Detector (SBDet): SBDet builds upon the R2Net backbone to achieve superior object detection accuracy. Its design integrates the flexibility offered by relaxed group convolutions, which are adept at recognizing and processing symmetry deviations across 2D visual datasets. The resulting model demonstrated excellence in natural image classification and object detection tasks, as reported in the experimental outcomes.

Experimental Validation and Implications

The experiments detailed in the paper underscore the enhanced performance of SBDet in object detection, specifically within scenarios exhibiting rotational and scale variances—where traditional ENNs often struggle. In benchmark tests on datasets like PASCAL VOC and MS COCO, SBDet showcases significant improvements in average precision (AP), underscoring its capability to generalize better beyond standard symmetric operations. These empirical results highlight the potential of SBDet to become consequential across sectors relying on computer vision, such as autonomous systems and environmental monitoring.

Future Directions

The research opens several avenues for future exploration. Firstly, the integration of CUDA acceleration could ameliorate training speed limitations highlighted during experimentation. Furthermore, the principles of Relaxed Rotation-Equivariance could be extrapolated beyond the present confines to enhance models dealing with three-dimensional data or more intricate transformational symmetries. Lastly, the extension of this method to other problem domains, such as video processing or medical imaging, offers promising prospects.

This paper represents a noteworthy advancement in object detection methodologies, proposing an innovative framework that reconciles the need for symmetry in modeling with the flexibility required to handle real-world deviations. As research in this direction progresses, the applications of Relaxed Rotation-Equivariant Convolutional Networks could reshape current understanding and implementation standards within computer vision tasks.