Abstract
In the era of rapid advancements in smart cities and digital technology, the application of oblique photography 3D models has become increasingly widespread, and data security issues have garnered significant attention. However, most existing watermarking algorithms lack strong robustness against scaling, cropping, and composite attacks. To address this problem, this paper proposes an oblique photography 3D model watermarking algorithm based on multi-level curvature and weighted distance grouping. First, the curvature values of vertices in different neighborhood levels are calculated using principal component analysis (PCA), and vertices with curvature values exceeding a predefined threshold are selected as feature points. Next, vertices are grouped according to the principle of minimizing the weighted comprehensive distance between feature points and vertices. Finally, the height difference between each vertex and its corresponding feature point within a group is normalized to serve as the carrier for embedding watermark information, and the Quantization Index Modulation (QIM) method is employed for watermark embedding. Experimental results show that the algorithm achieves high imperceptibility and demonstrates strong robustness against common attacks such as geometric transformations, vertex reordering, and composite attacks. Even under cropping attacks of up to 80%, the complete watermark information can still be successfully retrieved.
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Funding
This work was funded by National Natural Science Foundation of China [Grant numbers 42271430, 42371463 and 41761080]; the Guidance Project of Universities in Gansu Province [grant numbers 2019C-04].
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Ruigang Nan: conceptualization, investigation, methodology, writing original draft. Liming Zhang: funding acquisition, supervision, validation, writing original draft, writing review & editing, conceptualization. Yan Jin: writing original draft. Jianing Xie: validation, methodology. Shuaikang Liu: validation, investigation, methodology. Haoran Wang: formal analysis, methodology.
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Communicated by: Hassan Babaie
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Nan, R., Zhang, L., Jin, Y. et al. Robust watermarking algorithm for oblique photography 3D models based on multi-level curvature and weighted distance. Earth Sci Inform 18, 321 (2025). https://doi.org/10.1007/s12145-025-01836-7
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DOI: https://doi.org/10.1007/s12145-025-01836-7
