Compositional Retrieval-Based Image Synthesis, CR-IS

Current text-to-image generation (AIGC) technologies based on diffusion models and Transformer architectures typically rely on black-box, unstructured pixel rendering. This often leads to stochastic geometric distortions in spatial compositions, and makes digital copyright tracking extremely difficult due to the lack of rigid features in derivative images. To address these bottlenecks, this study proposes a structured image generation and geometric invariant source-tracing framework based on transform-domain geometric constraints, termed the CR-IS architecture. The proposed method first extracts the closed geometric boundaries of target objects using the Suzuki-Abe topological border-following algorithm, and translates spatial coordinates into frequency-domain complex Fourier Descriptors (FDs) via a forward Discrete Fourier Transform (DFT). To mitigate the ripples caused by the Gibbs phenomenon at polygonal boundary discontinuities, a general term for the Fourier coefficients of a regular N-sided polygon is derived and injected as a residual compensation factor, achieving a smooth and fluid contour reconstruction. During the geometric manipulation stage, cross-modal text prompts are forced onto the magnitude spectrum semantic space via a linear projection layer, and automatically translated into geometric operators: scale factor (S), spatial translation (Δz), and rotation angle (θ). Matrix algebraic operations are subsequently performed in the frequency domain, completely eliminating random structural deformations. For provenance verification, a scalar feature vector with high mathematical rigidity—serving as a "digital DNA"—is distilled by taking the amplitude ratios of Fourier descriptors to eliminate geometric transformation interferences. Empirical verification was conducted using the "Silver Fern" logo (represented by 1024 Fourier coefficients), which features highly non-linear serrated edges. Experimental results demonstrate that under semantic guidance involving extreme scaling to one-quarter size and multi-angle spatial rotations, the generated images strictly adhere to the designated geometric boundaries. Furthermore, quantitative evaluations of the Euclidean geometric distance (D) between the transformed derivative feature vectors and the original feature vector consistently yield D