Robust watermarking of point-sampled geometry
We present a new scheme for digital watermarking of point-sampled geometry based on spectral analysis. By extending existing algorithms designed for polygonal data to unstructured point clouds, our method is particularly suited for scanned models, where the watermark can be directly embedded in the raw data obtained from the 3D acquisition device. To handle large data sets efficiently, we apply a fast hierarchical clustering algorithm that partitions the model into a set of patches. Each patch is mapped into the space of eigenfunctions of an approximate Laplacian operator to obtain a decomposition of the patch surface into discrete frequency bands. The watermark is then embedded into the low frequency components to minimize visual artifacts in the model geometry. During extraction, the target model is resampled at optimal resolution using an MLS projection. After extracting a watermark from this model, the corresponding bit stream is analyzed using statistical methods based on correlation. We have applied our method to a number of point-sampled models of different geometric and topological complexity. These experiments show that our watermarking scheme is robust against numerous attacks, including low-pass filtering, resampling, affine transformations, cropping, additive random noise, and combinations of the above.