Image-to-Image Translation Framework Embedded with Rotation Symmetry Priors

2026-04-14

AI Summary

This work addresses the challenge of preserving domain-invariant geometric structures—such as rotational symmetry—in unpaired and unsupervised image-to-image translation, where existing methods often fail. To this end, the authors propose a rotation-equivariant generative framework that, for the first time, incorporates group-equivariant convolutions with respect to rotation groups into unsupervised image translation. They introduce a novel TL-Conv module capable of learning transformation groups in a data-driven manner, thereby adaptively modeling symmetry priors specific to different datasets. Theoretical analysis provides an equivariance error bound for the proposed module. Extensive experiments demonstrate that the method significantly improves generation quality across diverse translation tasks, outperforming current approaches in terms of structural consistency and generalization capability.

Technology Category

• Computer Vision: Generative Adversarial Networks (GANs) for Vision
• Machine Learning: Transfer, Domain Adaptation, Multi-Task Learning
• Natural Language Processing: Generation

Application Category

• Security and Privacy: Data transparency and provenance
• Responsible Web: Algorithmic accountability and transparency on the web
• Search and Retrieval-Augmented AI: Multilingual and cross-lingual Web search

Abstract

Image-to-image translation (I2I) is a fundamental task in computer vision, focused on mapping an input image from a source domain to a corresponding image in a target domain while preserving domain-invariant features and adapting domain-specific attributes. Despite the remarkable success of deep learning-based I2I approaches, the lack of paired data and unsupervised learning framework still hinder their effectiveness. In this work, we address the challenge by incorporating transformation symmetry priors into image-to-image translation networks. Specifically, we introduce rotation group equivariant convolutions to achieve rotation equivariant I2I framework, a novel contribution, to the best of our knowledge, along this research direction. This design ensures the preservation of rotation symmetry, one of the most intrinsic and domain-invariant properties of natural and scientific images, throughout the network. Furthermore, we conduct a systematic study on image symmetry priors on real dataset and propose a novel transformation learnable equivariant convolutions (TL-Conv) that adaptively learns transformation groups, enhancing symmetry preservation across diverse datasets. We also provide a theoretical analysis of the equivariance error of TL-Conv, proving that it maintains exact equivariance in continuous domains and provide a bound for the error in discrete cases. Through extensive experiments across a range of I2I tasks, we validate the effectiveness and superior performance of our approach, highlighting the potential of equivariant networks in enhancing generation quality and its broad applicability. Our code is available at https://github.com/tanfy929/Equivariant-I2I

Problem

• image-to-image translation
• rotation symmetry
• equivariance
• unsupervised learning
• domain-invariant features

Innovation

• rotation equivariance
• image-to-image translation
• symmetry priors
• equivariant convolution
• unsupervised learning