A Watermarking Method for 3D Printing Based on Menger Curvature and K-Mean Clustering

Abstract

Nowadays, 3D printing is widely used in many areas of life. This leads to 3D printing models often being used illegally without any payment to the original providers. Therefore, providers need a solution to identify and protect the copyright of 3D printing. This paper presents a novel watermarking method for the copyright protection of 3D printing based on the Menger facet curvature and K-mean clustering. The facets of the 3D printing model are classified into groups based on the value of Menger curvature and the K-mean clustering, and the mean Menger curvature of each group will then be computed for embedding the watermark data. The watermark data are embedded into the groups of facets by changing the mean Menger curvature of each group according to the bit of watermark data. In each group, we select a facet that has the Menger curvature closest to the changed mean Menger curvature, and we then transform the vertices of the selected facet according to the changed Menger curvature for the watermarked 3D printing model generation. Watermark data are extracted from 3D-printed objects, which are printed from the watermarked 3D printing models by the 3D printer. Experimental results after embedding the watermark verified that the proposed method is invisible and robust to geometric attacks such as rotation, scaling and translation. In experiments with an XYZ Printing Pro 3D printer and 3D scanner, the accuracy and performance of the proposed method was higher than the two previous methods in the 3D printing watermarking domain. The proposed method provides a better solution for the copyright protection of 3D printing.