Evaluating the topological quality of watermarked vector maps

The pervasive use and exchange of digital content led to increased efforts in the research community for efficient approaches to protect intellectual property rights. While watermarking techniques have been used extensively for raster image format, watermarking approaches for the vector map format have been largely inspired from existing image watermarking techniques, without due consideration to the suitability of these techniques for this different data format. A key requirement of any watermarking approach of vector data is the preservation of the topological quality of the watermarked data. This is sometimes referred to as the invisibility of the watermark. For vector map data, the topological quality and invisibility are fundamentally different, but currently submerged into one and measured with error metrics borrowed from image watermarking, such as Root Mean Squared Error (RMSE) and Peak Signal to Noise Ratio (PSNR). Over the last 10 year, the research community on watermarking vector map data has repeatedly posed that error metrics alone are not appropriate for the evaluation of watermarked vector map topological quality. In this paper, a metric for measuring topological quality by measuring topological distortions is proposed based on topological properties of polygon-based vector maps. To evaluate the proposed metric, experiments with controlled watermarking capacity (i.e. how much is embedded) were run on maps of various sizes, using two popular embedding approaches, i.e. coordinate-based and distance-based embedding. The results indicate that the metrics allow comparisons between watermarked maps of different sizes and of different watermark sizes, and, thus, can be used to assess the quality of watermarked vector maps. The advantages and limitations of the proposed metric are discussed and further research directions are highlighted toward an agreed metric by the research community.