# A Fragile Watermarking Scheme for Authenticity Verification of 3D Models in GLB Format
## 4 Results and Discussion
### Effect of Embedding a Watermark in Position Bits on Interference Levels  
The analysis of the developed method began by examining the effects of embedding the watermark in the vertex position bits, since this is an attribute that is always present. The algorithm allows the use of 1 to 32 bits, but an excessive number of modified bits leads to noticeable distortions (Figure 6). Therefore, the authors, first of all, focused on analysing the use of a maximum of eight LSBs in the coordinates of the vertex position. The modification of eight LSBs does not cause noticeable changes, as can be observed in Figure 6. The top row in Figure 6 shows the marked models where eight LSBs from the position coordinates were used. The bottom row shows the marked models, where 23 LSBs from the position coordinates were used. The positions of the resulting artefacts were highlighted by adding a red outline to them. As can be seen, swapping the entire mantissa of a floating-point number leads to clear deformations of the model, while changing 8 LSBs remains below the threshold of noticeable distortion. The authors also tested whether the number of bits allocated to embed the HMAC code affects the algorithm's efficiency. Table 2 shows the average duration in milliseconds of both the marking and verification processes. As the results show, regardless of the number of modified bits in each vertex used, the execution time of the algorithm can be considered identical. In the current context, the differences belong to the measurement error range. To modify the data of a single vertex, it is first necessary to locate its place in the buffer. Hence, making changes to 512 vertices requires 512 jumps to different locations in the data buffer. In contrast, modifying 512/8 = 64 vertices involves only 64 jumps (eight LSBs used per vertex). The motivation for the execution time study was to see if the number of jumps could affect performance. In addition, the results shown in Table 2 show that the marking process takes longer than the verification process. A popular metric for measuring interference in 3D models and 2D images is PSNR. For each test model, this measure was calculated according to the Formula (2), and the results are shown in Table 3. A higher PSNR value should be interpreted as a lower level of introduced distortion. This metric also depends on the number of vertices in the model, which is natural--the more detailed the mesh or the more complex the geometry, the lower the significance of the introduced changes in the context of the whole model. The gate.glb model achieves the highest PSNR value because it contains the largest number of vertices (362,771) (Table 3). In contrast, duck.glb contains about 12,000 vertices (Table 3), so the PSNR value is the lowest for this model. The data in Table 3 also indicate that increasing  
Figure 6: Comparison of the effect of using 8 LSBs **(top row)** and 23 LSBs **(bottom row)** of each position coordinate on HMAC code placement. The graphical artefacts that occurred are highlighted with a red outline. the number of bits used leads to a decrease in the PSNR value. This means that it is more advantageous to modify more vertices with minimal changes than to modify fewer vertices with more disruption. It is worth noting that the decrease in PSNR between the first and last column of Table 3 is almost identical for each model and is about 34-35 dB. To ensure a comprehensive evaluation of the presented method, the SNR metric was also calculated, serving as a valuable complement to the PSNR metric (Table 4). Given that a wide range of metrics is employed in the field of watermarking, it is beneficial to assess the proposed methods using multiple evaluation criteria. This facilitates meaningful comparisons with other studies. Table 4 presents the SNR values computed for the test models with respect to the LSBs of the vertex position attribute used during the watermarking process.