Watermarking curves using 2D mesh spectral transform

This paper presents a robust watermarking method for curves that uses informed-detection. To embed watermarks, the presented algorithm parameterizes a curve using the B-spline model and acquires the control points of the B-spline model. For these control points, 2D mesh are created by applying Delaunay triangulation and then the mesh spectral analysis is performed to calculate the mesh spectral coefficients where watermark messages are embedded in a spread spectrum way. The watermarked coefficients are inversely transformed to the coordinates of the control points and the watermarked curve is reconstructed by calculating B-spline model with the control points. To detect the embedded watermark, we calculate the difference between the original and watermarked mesh spectral coefficients with the same process for embedding. By calculating correlation coefficients between the detected and candidate watermark, we decide which watermark was embedded.