Traditional Chinese Painting Completion via Hierarchical Optimal Transport

Traditional Chinese painting completion presents unique challenges where sparse ink distributions and intentional blank spaces serve aesthetic rather than functional purposes, contradicting assumptions in conventional inpainting methods. We propose Hierarchical Optimal Transport for Painting (HOT-Paint) that formulates completion as controlled texture redistribution in Wasserstein space. By interpreting texture synthesis through transport flow dynamics, we model brush stroke propagation using the static Kantorovich formulation while preserving characteristic sparsity through regularized transport plans.Our approach constructs multi-scale probability measures capturing artistic elements from fine strokes to global composition. The framework introduces adaptive cost functions integrating geometric distances, texture similarities via Gabor filters, and semantic relationships from pre-trained features. A modified Sinkhorn algorithm with soft-thresholding enforces sparsity constraints, while inter-scale consistency mechanisms ensure coherent information flow across resolutions. Experiments on CPDD and CelebA-HQ datasets demonstrate over 25.1% improvements in FID scores over state-of-the-art methods. Real-world restoration of authentic museum paintings validates practical utility. The proposed framework advances optimal transport theory for artistic image synthesis while addressing fundamental challenges in cultural heritage preservation.