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Fig. 8. Minimal spanning trees of the 3D cow sub-meshes and their corresponding hash values: (a) and (b) back feet, (c) and (e) front feet, (d) back-tail, (f) neck, (g) and (h head-horn.

Figure 8 Minimal spanning trees of the 3D cow sub-meshes and their corresponding hash values: (a) and (b) back feet, (c) and (e) front feet, (d) back-tail, (f) neck, (g) and (h head-horn.

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Fig. 2. Illustration of Laplace—Beltrami angles a; and fj. Fig. 1. Vertex neighborhood v¥.
Fig. 2. Illustration of Laplace—Beltrami angles a; and fj. Fig. 1. Vertex neighborhood v¥.
Fig. 3. (a) 3D tank model and its (b) Laplace—-Beltrami matrix.
Fig. 3. (a) 3D tank model and its (b) Laplace—-Beltrami matrix.
Fig. 4. 3D models and their minimal, (b) spanning trees.
Fig. 4. 3D models and their minimal, (b) spanning trees.
Fig. 6. 3D models used for experimentation: (a) camel, (b) cow, (c) shark, (d) triceratops, (e) baby, and (f) arm. Fig. 5. 3D mesh partitioning: each sub-mesh is colored randomly. (a) 3D arm model, (b) 3D cow model, and (c) 3D camel model.
Fig. 6. 3D models used for experimentation: (a) camel, (b) cow, (c) shark, (d) triceratops, (e) baby, and (f) arm. Fig. 5. 3D mesh partitioning: each sub-mesh is colored randomly. (a) 3D arm model, (b) 3D cow model, and (c) 3D camel model.
Fig. 7. Minimal spanning trees of the 3D camel sub-meshes and their corresponding hash values: (a) head, (b) neck, (c)-(d) front feet, (e) hump, (f) shoulders, and (g)-(h) back.
Fig. 7. Minimal spanning trees of the 3D camel sub-meshes and their corresponding hash values: (a) head, (b) neck, (c)-(d) front feet, (e) hump, (f) shoulders, and (g)-(h) back.
Fig. 9. 3D camel model under different attacks: (a) x-axis scaling, (b) y-axis scaling, (c) z-axis scaling, (d) Laplacian mesh smoothing using 10 iterations, (e) rotation around x axis by 45°, (f) rotation around y-axis by 45°, (g) rotation around z-axis by 45°, (h) mesh simplification 70%, and (i) additive Gaussian noise with o = 0.25.
Fig. 9. 3D camel model under different attacks: (a) x-axis scaling, (b) y-axis scaling, (c) z-axis scaling, (d) Laplacian mesh smoothing using 10 iterations, (e) rotation around x axis by 45°, (f) rotation around y-axis by 45°, (g) rotation around z-axis by 45°, (h) mesh simplification 70%, and (i) additive Gaussian noise with o = 0.25.
Fig. 10. 3D cow model under different attacks: (a) x-axis scaling, (b) y-axis scaling, (c) z-axis scaling, (d) Laplacian mesh smoothing using 10 iterations, (e) rotation around x- axis by 45°, (f) rotation around y-axis by 45°, (g) rotation around z-axis by 45°, (h) mesh simplification 70%, and (i) additive Gaussian noise with o = 0.25.
Fig. 10. 3D cow model under different attacks: (a) x-axis scaling, (b) y-axis scaling, (c) z-axis scaling, (d) Laplacian mesh smoothing using 10 iterations, (e) rotation around x- axis by 45°, (f) rotation around y-axis by 45°, (g) rotation around z-axis by 45°, (h) mesh simplification 70%, and (i) additive Gaussian noise with o = 0.25.
Normalized hash correlation results for different 3D models. Table 1 Table 2 sub-meshes, followed by applying eigen-decomposition to the La- place-Beltrami matrix of each sub-mesh in order to obtain the hash values of all the sub-meshes. The performance of the pro- posed method was evaluated through extensive experiments which clearly showed satisfactory resiliency against a variety of attacks.
Normalized hash correlation results for different 3D models. Table 1 Table 2 sub-meshes, followed by applying eigen-decomposition to the La- place-Beltrami matrix of each sub-mesh in order to obtain the hash values of all the sub-meshes. The performance of the pro- posed method was evaluated through extensive experiments which clearly showed satisfactory resiliency against a variety of attacks.
Normalized correlation coefficients results between different 3D hashed models.
Normalized correlation coefficients results between different 3D hashed models.
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Multimedia SecuritySpectral Graph Theory
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