An Oblivious Watermarking for 3-D Polygonal Meshes Using Distribution of Vertex Norms

Shape watermarking based on minimizing the quadric error metric

“…As shown in [15], the statistical variableρ ij is close to a uniform distribution. Thus the expected mean value of the statistical variable is 1/2.…”

“…We propose two methods for message bit embedding. The first one corresponds to changing the mean value of each bin and the second method embeds the bit by changing the bin variance, as proposed in [15]. The minimum and maximum distance for each bin are:…”

“…The aim of this watermarking algorithm is to change the location of the vertex V i toV i such that we have the condition OV i =ρ i satisfied, where O represents the object center andρ i is obtained from either equation (11) or (15). In [15] this change was performed along the direction from the object centre to the given vertex V i as − − → OV i . Although the movement along the direction − − → OV i guarantees the minimum Euclidean distance, i.e.…”

“…Watermarking methods can also be categorized as deterministic [14] or statistical [15], [16]. The methods from the first category employ a set of constraints for embedding messages while the second category extract the message by using a statistical test.…”

“…Zafeiriou et al [16] proposed a robust watermarking method using distributions of distances from surface vertices to the local symmetry axis. Cho et al [15] proposed a similar approach as in [16] by considering vector norms. Sets of vertices are grouped into bins according to their distance to the object center.…”