Abstract

Symmetry and asymmetry play an important role in image processing and computer vision, particularly when visual structures are corrupted by irregular and spatially heterogeneous degradation. In cultural heritage restoration, ancient murals often contain locally symmetric patterns, repeated decorative motifs, balanced compositions, and style-sensitive contours, while long-term aging introduces asymmetric damage such as cracks, pigment fading, flaking, and partial content loss. Restoring such images therefore requires models that can recover structural regularity from asymmetric degradation while preserving culturally meaningful visual details. In this paper, we propose a symmetry-aware progressive generative framework for non-invasive digital restoration of Dunhuang murals. The proposed model is implemented as a Cauchy–Schwarz-regularized cascading variational autoencoder, which decomposes restoration into three coarse-to-fine stages: global structural recovery, semantic and chromatic refinement, and fine-detail enhancement. To support this progressive process, the latent dimensionality is gradually expanded across stages, enabling the model to move from compact structural abstraction to detail-aware representation learning. Moreover, a Cauchy–Schwarz-divergence-based regularization strategy is introduced to align the aggregated posterior with a mixture-of-Gaussians prior, providing a tractable mechanism for modeling the multi-modal latent structure of mural images. Experiments on the MuralDH benchmark under irregular-mask, crack-like, and mixed degradation settings show that the proposed method achieves competitive restoration quality compared with representative inpainting and diffusion-based baselines, while requiring substantially lower inference cost. Qualitative results further demonstrate improved contour continuity, chromatic coherence, and texture preservation. These results suggest that symmetry-aware progressive generative modeling is a promising tool for sustainable, non-invasive cultural heritage restoration.

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