== Experimental Results ==

== Experimental Results ==

The experimental results presented next can also be found in [7]. The image shown in Figure 4(a) is used for embedding the watermark depicted in Figure 4(d) using the first stage of the VQ technique. The codebook size is equal to 16 for each stage. In other words, there is a total of 16 codewords included in the codebook (or in K-means terminology, there is a total of 16 centroids, i.e. <math>K = 16</math>). The normalized Hamming similarity (NHS) measure defined as in the following equation is used for comparison of the different techniques:

The experimental results presented next can also be found in <ref name="Charalampidis2005"/>. The image shown in Figure 4(a) is used for embedding the watermark depicted in Figure 4(d) using the first stage of the VQ technique. The codebook size is equal to 16 for each stage. In other words, there is a total of 16 codewords included in the codebook (or in K-means terminology, there is a total of 16 centroids, i.e. <math>K = 16</math>). The normalized Hamming similarity (NHS) measure defined as in the following equation is used for comparison of the different techniques:

<center><math>NHS = 1-HD(\mathbf{W},\mathbf{W}')/(N_wM_w)</math></center>

<center><math>NHS = 1-HD(\mathbf{W},\mathbf{W}')/(N_wM_w)</math></center>

'''First set of experiments'''

'''First set of experiments'''