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.

Copyright Protection of 3D Digitized Artistic Sculptures by Adding Unique Local Inconspicuous Errors by Sculptors

“…Authors pointed out that the methods presented earlier for watermarking 3D models based on geospatial domain (changing topology, length, area, or value of the vertices or geometric features) or frequency domain (such as discrete Fourier transform, discrete wavelet transform [62], or discrete cosine transform) are useful for copyrights protection of the digital 3D models but not for physical and printed 3D models. The same authors created an algorithm for copyright protection of 3D printed models based on Menger facet curvature and K-mean clustering [20]. Another algorithm based on slices of 3D mesh, which are embedded into watermark data, was also presented [21].…”

“…To analyze the protection of 3D models, we have researched on the Internet a number of techniques for sharing 3D models in a safe and secure way. One of the ways that are often mentioned is watermark [14,[20][21][22][23][24][25][26][27][28][29][30]. In this research, we will use an example of a sculpture to describe and present our conceptual solution for the protection of 3D models created by 3D digitization of cultural heritage (i.e., 3D models in general) from misuse and copying.…”

Analysis of Driving Behavior Based on Dynamic Changes of Personality States

“…Based on the principle of distance similarity, the K-means clustering algorithm divides two groups of samples with small distance into the same cluster, and finally forms different clusters from all the sample data with similar distances to obtain compact and independent categories [34]. First, k groups of initial clustering centers are randomly selected from the input data set, and then, according to the principle of distance proximity, the appropriate distance formula is used to calculate the distance between each data object and the k cluster centers, after which the data are divided into the cluster domains where the nearest cluster centers are located.…”

“…The driving indicators used included the reaction ability and two indicators derived from speed. The K-means clustering method was chosen as the clustering learning algorithm, as it allows scalability and efficiency to be maintained when dealing with large datasets [34,35].…”

Accelerating Density Peak Clustering Algorithm

“…Clustering is the process of categorizing objects into groups (called clusters) of similar objects and is a widely-used data mining technique both in academic and applied research [1,2]. Many clustering methods appear in the literature, but they differ in the notion of similarity.…”