Controlled Accuracy Degradation of Photogrammetric 3D City Models

Photogrammetric 3D city models contain detailed planimetric and elevation information that supports urban visualization and low-altitude applications. However, the direct dissemination of high-accuracy models may expose sensitive geometric measurements. Existing protection methods mainly focus on conventional encryption, coordinate scrambling, or two-dimensional data perturbation and do not adequately balance geometric accuracy degradation with the visual usability of textured 3D meshes. This study proposes a controlled geometric deformation method that processes the planimetric and elevation components independently. In the horizontal domain, a normalized Sigmoid function generates smooth, bounded, and spatially varying coordinate displacements. In the vertical domain, a normalized deformation function combines global elevation stretching with amplitude-constrained sine-wave superposition. The sine-wave parameters are generated using a seed-sensitive hybrid cascaded chaotic system, producing reproducible but model-dependent nonlinear deformation patterns. During processing, the mesh connectivity, face indices, texture coordinates, texture images, and material relationships remain unchanged. The method was evaluated using low-rise and high-rise photogrammetric 3D scenes with different horizontal extents and elevation characteristics. Under the selected 10 m planimetric and 5% elevation settings, the mean planimetric displacements were 10.474 and 10.045 m, while the relative elevation deformations were 5.01% and 5.30%, respectively. Both datasets maintained monotonic elevation relationships and achieved 100% direction consistency. Their spatial-shape coefficients deviated from the corresponding reference values by only 0.02% and 1.33%. The results demonstrate that the proposed method provides controllable and spatially continuous geometric deformation while maintaining mesh connectivity, overall morphology, and visual interpretability. It can therefore serve as a practical pre-processing approach for the risk-reduced dissemination and non-measurement-oriented visualization of photogrammetric 3D city models.