A new mesh visual quality metric using saliency weighting-based pooling strategy

Several metrics have been proposed to assess the visual quality of 3D triangular meshes during the last decade. In this paper, we propose a mesh visual quality metric by integrating mesh saliency into mesh visual quality assessment. We use the Tensor-based Perceptual Distance Measure metric to estimate the local distortions for the mesh, and pool local distortions into a quality score using a saliency weighting-based pooling strategy. Three well-known mesh saliency detection methods are used to demonstrate the superiority and effectiveness of our metric. Experimental results show that our metric with any of three saliency maps performs better than state-of-the-art metrics on the LIRIS/EPFL general-purpose database. We generate a synthetic saliency map by assembling salient regions from individual saliency maps. Experimental results reveal that the synthetic saliency map achieves better performance than individual saliency maps, and the performance gain is closely correlated with the similarity between the individual saliency maps.

in the community. Many computational saliency methods 24 [8][9][10][11][12] have been proposed to detect perceptually important 25 regions where human visual attention is focused on the mesh. 26 Since the receptor of both mesh visual quality and mesh 27 saliency is the human visual system, we believe that it is 28 possible to improve the performance of MVQ metrics by 29 incorporating mesh saliency. Actually, in the community 30 of image quality assessment, there are already some works 31 [13][14][15][16][17] that investigated incorporating either visual attention 32 or computational visual saliency into image quality metrics 33 (IQMs). Zhang et al. [18] presented a statistical evaluation 34 to investigate the added value of integrating computational 35 saliency into IQMs. They concluded that the computational 36 saliency models can yield a performance gain statistically 37 when integrating computational saliency into IQMs though 38 the specific amount of performance gain depends on the com-39 bination of saliency model and IQM [18]. Compared with the 40 works in image quality assessment, there are relatively fewer 41 works that investigated the relationship between mesh salien-42 cy and mesh visual quality, not to mention the incorporation 43 of mesh saliency in MVQ metrics. In [13][14][15][16][17][18], either visual 44 attention or computational visual saliency was incorporated 45 in image quality metrics to improve the performance based 46 on the assumption that distortions occurring in more salient 47 areas of an image are more visible and thus more annoying, 48 which was finally verified by the experimental results. Since 49 the ultimate assessors of both mesh quality and image quality 50 3D computational saliency models which were previously 23 proposed in [9,22,23]. But there is a lack of comprehensive 24 quantitative analysis to reveal the accuracy and reliability of 25 state-of-the-art mesh saliency detection methods. In [8][9][10][11][12], 26 the effectiveness of the mesh saliency detection methods was 27 justified mostly through either application-guided evaluation 28 [8][9][10] or subjective visual analysis [11,12]. Since the 29 three mesh saliency detection methods proposed in [8][9][10] 30 were demonstrated to be capable of enhancing the results 31 of graphics applications, such as mesh simplification and 32 viewpoint selection, we use them [8][9][10] to evaluate the 33 benefits of incorporating mesh saliency into MVQ metric in 34 this paper. We firstly generate a distortion map with the 35 TPDM metric [5], which is one of the best-performing MVQ 36 metrics until now, then generate a saliency map with each 37 of three mesh saliency detection methods [8][9][10], and finally 38 derive the overall quality score for the mesh via saliency 39 weighting-based pooling of local distortions. 40 The remainder of this paper is organized as follows: We 41 review related work on MVQ metrics, mesh saliency detection 42 methods and the incorporation of visual saliency in IQMs 43 in Section 2. We introduce our proposed MVQ metric in 44 Section 3. We give a brief description of three mesh saliency 45 detection methods used in this paper and present an analysis 46 of the saliency maps generated by three methods in Section 4.
We present the experimental results and analysis in Section 5 48 and conclude the paper in Section 6. In the last decade, some MVQ metrics have been de-51 signed to predict human judgement on the quality of 3D 52 triangular mesh. Detailed reviews of MVQ metrics can be 53 found in [24,25]. The classical geometric distances, such 54 as Hausdorff Distance and Root Mean Squared Error, are 55 demonstrated to have weak correlation with human visual 56 perception [25]. There is still no clear consensus on the 57 suitability of image-based metrics in MVQ assessment. The 58 literature [26] argues that image-based metrics [27,28] are 59 not suitable for evaluating the quality of meshes while the 60 literature [29] suggests that image-based metrics can be used 61 for evaluating the quality of distorted meshes of the same 62 object under a single type of distortion. Some model-based 63 perceptual metrics have been proposed for MVQ assessment 64 by exploiting geometric features. Karni and Gotsman [30] 65 measured the distance between the distorted mesh and the 66 reference mesh by comparing both vertex coordinates and 67 geometric Laplacian values of two meshes. Sorkine et al. 68 [31] improved the method [30] by assigning a greater weight 69 to geometric Laplacian values. Corsini et al. [32] developed 70 two perceptual metrics, 3DWPM 1 and 3DWPM 2 , based on 71 the roughness difference between two meshes. Bian et al. 72 [33] proposed a physically-inspired metric based on strain 73 energy that induces the deformation to the reference mesh. 74 Lavoué et al. proposed the MSDM metric [1] by extending 75 structural similarity index [34] in image quality assessment to 76 MVQ assessment. Later, a multiscale version MSDM2 [2] 77 was proposed to address the issue of changed connectivity 78 of distorted meshes based on the work [1]. Wang et al. 79 [3] introduced the FMPD metric to compute the perceptual 80 distortion between two meshes based on global roughness 81 derived from the Laplacian of Gaussian curvature. Váša 82 and Rus [4] developed the DAME metric by computing the 83 differences of oriented dihedral angles between two meshes. 84 Torkhani et al. [5] proposed the TPDM metric based on the 85 measurement of the distance between curvature tensors of 86 two meshes. Dong et al. [6] proposed a MVQ metric by 87 integrating roughness distortion and structure similarity. 88 Liu et al.
[7] provided a survey on mesh saliency de-89 tection methods and their applications in computer graphics. 90 The mesh saliency detection methods are classified into two 91 categories, namely local contrast-based methods and global 92 contrast-based methods [7]. Interested reader can find a 93 detailed description of advantages and drawbacks of state-of-94 the-art mesh saliency detection methods in [7]. Lee et al. [8] 95 developed a mesh saliency detection method using a center-96 surround operator on Gaussian-weighted mean curvatures. 97 Song et al. [9] proposed a method for detecting mesh saliency 98 by analyzing the properties of the log-Laplacian spectrum 99 of the mesh. Limper et al. [10] proposed a mesh saliency 100 detection method, named Local Curvature Entropy, by apply-101 ing Shannon entropy to the mean curvature of vertices of 3D 102 meshes. Nouri et al. [11] proposed a local surface descriptor 103 based on adapative patches to characterize the perceptual 104 saliency of each vertex of the mesh. Tao et al. [12] proposed 105 to detect mesh saliency via manifold ranking in a descriptor 106 space that is composed of patch descriptors based on Zernike 107 coefficients. In this paper, we use three well-known mesh 108 saliency detection methods [8][9][10]  for the LIRIS/EPFL general-purpose database [1]. Thirdly, 52 we assemble salient regions from individual saliency maps 53 to generate a synthetic saliency map for saliency weighting. 54 Experimental results show that the synthetic saliency map 55 achieves better performance than individual saliency maps 56 when used in our metric, and the performance gain is closely 57 correlated with the similarity between the individual saliency 58 maps. In this section, we propose a mesh visual quality metric 61 by integrating mesh saliency into mesh visual quality assess-62 ment. As we mentioned in Section 1, we are inspired by the 63 works [13][14][15][16][17][18] in image quality assessment and assume that 64 distortions appearing in more salient regions of a mesh are 65 more annoying. We use a saliency weighting-based pooling 66 strategy at the pooling step to emphasize the distortions on 67 the salient regions.

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Among state-of-the-art MVQ metrics [1][2][3][4][5][6], the TPDM 69 metric [5] correlates well with the human perception of mesh 70 quality and is one of the best-performing MVQ metrics so 71 far. The TPDM metric consists of a two-step computation 72 process: firstly constructing a distortion map for the mesh, 73 and then pooling local distortions via Minkowski summation. 74 In our metric, given a reference mesh and a distorted mesh, we 75 firstly use the TPDM metric [5] to generate a distortion map 76 for the reference mesh, then generate a saliency map for the 77 reference mesh with a mesh saliency detection method, and 78 finally compute an overall quality score for the distorted mesh 79 via the saliency weighting-based pooling of local distortions. 80 The flowchart of our proposed mesh visual quality metric is 81 illustrated in Fig. 1.

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We follow the first-step computation process of the TPDM 83 metric [5] to compute the local distortion for each vertex 84 of the reference mesh. The TPDM metric computes the 85 perceptual difference between the reference mesh and the 86 distorted mesh based on the distance between curvature ten-87 sors of two meshes. It establishes a correspondence between 88 the reference mesh and the distorted mesh to allow changed 89 connectivity of distorted meshes. It performs the vertex 90 projection from the reference mesh M r to the distorted mesh 91 M d using the AABB tree data structure. Each vertex v i in the 92 reference mesh corresponds to a point v i in the distorted mesh. 93 There are three vertices v i,1 , v i,2 and v i,3 on the triangular facet 94 T i that contains the point v i . (1 ≤ k ≤ 3) denote the 100 curvature tensors of the vertices v i and v i,k respectively. The 101 correspondence relationship between the principal curvature 102 directions / amplitudes of T v i and T v i,k is established based 103 on the minimum angular distance criterion. For the minimum 104 principal curvature direction γ min of T v i , the principal curva-105 ture direction γ 1 of T v i,k that has the smallest angular distance 106 to γ min is found as the corresponding direction. Accordingly, 107 the minimum curvature amplitude κ min of T v i corresponds to 108 the curvature amplitude κ 1 of T v i,k that is associated to γ 1 . 109  T v i , the corresponding principal curvature direction γ 2 and 3 curvature amplitude κ 2 of T v i,k can be found in a similar way.

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Then the local distance LPD v i ,v i,k between the vertex v i in the 5 reference mesh and the vertex v i,k of triangular facet T i in the 6 distorted mesh is computed as: where θ min is the angle between the principal curvature 8 directions γ min and γ 1 , θ max is the angle between the principal 9 curvature directions γ max and γ 2 , δ κ min is the Michelson-like   respectively: We compute the overall quality score of the distorted mesh 32 M d via saliency weighting-based pooling of local distortions. 33 We firstly use the Minkowski exponent p to highlight the 34 contributions of severe distortions to the quality judgement, 35 then weight the local distortion by the saliency value for 36 each vertex to emphasize the distortions on salient regions, 37 and finally pool the weighted local distortions into an overall 38 quality score. Our proposed MVQ metric TPDMVS is shown 39 in Eq.
(3): . We 47 investigated the influence of the value of p on the performance 48 in a preliminary experiment and found that the overall best 49 performance is achieved when p is set to 4. N is the number 50 of vertices of the reference mesh. We generate a saliency map 51 s, either individual saliency map or synthetic saliency map, 52 for the reference mesh using the saliency methods [8][9][10] as 53 we describe in Section 4 and Section 5. The saliency map is 54 normalized so that the saliency value s i of each vertex v i of 55 the mesh lies in the range [0, 1].

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Note that we do not include the surface area in our metric 57 while the TPDM metric [5] uses surface area to weight local 58 distortion for each vertex. We provide an analysis of the 59 influence of surface area on the performance of the metric in 60 Section 5.3.

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Many computational methods have been proposed to detect 63 mesh saliency [7][8][9][10][11][12]. In this paper, we employ three well-64 known mesh saliency detection methods [8][9][10] to investigate 65 the benefit of integrating mesh saliency into MVQ metric 1 since they were demonstrated to be effective in graphics 2 applications. We generate a saliency map for the reference 3 mesh with each method. We denote the method in [8] as MS, 4 the method in [9] as MSSP and the method in [10] as MSLCE.

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A detailed description of each method can be found in [8][9][10].  vertex v at scale level t is defined as where σ t is the standard deviation of the Gaussian filter at 21 scale t. 22 After each saliency map S t at each scale level is normal-   Limper et al. proposed a method MSLCE [10] to detect 70 mesh saliency via computing local curvature entropy for each 71 vertex of the mesh within the geodesic neighborhood. The 72 mean curvature C (v i ) for each vertex v i of the mesh is firstly 73 computed in the same way as in [8]. By considering the 74 are partitioned into n 1 bins using a uniform sampling, which 77 results in a set of discrete symbols {ρ 0 , ρ 1 , · · · , ρ n 1 }. Let A k 78 denote the surface area of each vertex v k within N (v i , r). 79 The probability of symbol ρ j (0 ≤ j ≤ n 1 ) within local 80 neighbourhood of vertex v i is computed by the surface area 81 and the affiliation of each neighbourhood vertex.

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By applying Shannon entropy to the set of symbols ρ j , the 83 saliency value of vertex v i is computed as its local curvature 84 entropy. In order to detect salient regions at multiple scales, 85 the radius parameter r is varied up to a maximum value 86 r max . The saliency maps are computed at multiple levels 87 l 0 , · · · , l t 0 −1 , where the radius parameter for each level l t is 88 defined as r t = 2 −t r max . A final saliency map s is generated for 89 the mesh by combining the saliency maps at all levels using 90 an average weighting scheme. In this section, we perform an analysis of three mesh 93 saliency detection methods [8][9][10] with the Dinosaur mod-94 el and the RockerArm model in the LIRIS/EPFL general-95 purpose database [1]. We generate a normalized saliency 96 map for the reference mesh of each model with each mesh 97 saliency detection method, and provide a visual illustration 98 of each saliency map in Fig. 2. The colormap is used to 99 map the saliency value to RGB color for each vertex of the 100 mesh. As indicated by Fig. 2(e), for each vertex in the 101 mesh, the red color represents a high saliency value, the green 102 color represents a median saliency value, and the blue color 103 represents a low saliency value. When the saliency value of 104 warmer than the saliency map of MS. We also observe 6 that three saliency methods detect some common vertices as 7 salient at some regions though the salient vertices that each 8 saliency method [8][9][10] detects are not exactly the same. 9 Particularly, there is a relatively higher similarity between at the remaining part of these regions. 25 In order to observe the statistical distribution characteristics 26 of each saliency map, we plot a histogram of each saliency 27 map generated by three saliency methods on two models 28 in Fig. 3. We list the statistical characteristics of three 29 individual saliency maps on the Dinosaur model and the 30 RockerArm model respectively in Table 1 and    In this paper, we use the LIRIS/EPFL general-purpose 20 database [1] as a test bed to validate the superiority and 21 effectiveness of our MVQ metric. The LIRIS/EPFL general-22 purpose database consists of four models, and for each model 23 there are one reference mesh and 21 distorted meshes. The 24 distorted meshes are generated by applying either noise ad-25 dition or smoothing distortion with different strengths either 26 locally or globally to the reference mesh. The observer was 27 asked to remember the mesh that was considered to have 28 the worst quality among the distorted meshes. Then the 29 observer provided an opinion score that reflects the degree of 30 perceived distortion for each mesh of each model, including 31 the reference mesh and distorted meshes. The opinion score 32 ranges from 0 (best quality) to 10 (worst quality). Twelve 33 observers participated in the subjective evaluation. Finally, 34 a normalized Mean Opinion Score (MOS) was computed 35 for each mesh by averaging the opinion scores of all the 36 observers. 37 We use our metric TPDMVS to compute objective quality 38 scores for the meshes in the LIRIS/EPFL general-purpose 39 database. We evaluate the performance of our metric by mea-40 suring the correlation between the quality scores and MOSs 41 with two coefficients: Pearson linear correlation coefficient 42 (PLCC) that measures the prediction accuracy of quality met-43 ric and Spearman rank-order correlation coefficient (SROCC) 44 that measures the prediction monotonicity of quality metric 45 [27,41]. Both values of PLCC and SROCC range from -1 46 to 1, where -1 indicates fully negative correlation, 1 indicates 47 fully positive correlation, and 0 indicates no correlation. Since 48 the nonlinear quality rating compression may exist at the 49 extremes of the test range during the subjective testing, there 50 is typically a nonlinearity between the subjective ratings and 51 objective predictions [42]. Thus, in many works on both mesh 52 quality metrics and image quality metrics [1, 3, 5, 6, 43], 1 a psychometric fitting was performed between the objective 2 quality scores and MOS values to remove the nonlinearity. In 3 this paper, we also conduct a psychometric fitting to remove 4 the nonlinearity between the set of objective quality scores 5 and the set of MOS values before computing the correlation 6 coefficients. We apply the cumulative Gaussian function 7 [5, 44] for psychometric fitting: where Q is the objective quality score. Each mesh in the psychometric fitting and will be the predicted MOS value 22 after the values of a and b are determined. 23 We provide the correlation coefficients of our metric in 24 three cases. In each case, we use one of the three saliency 25 methods described in Section 4 to generate a saliency map s 26 for each reference mesh in the LIRIS/EPFL general-purpose 27 database and then generate quality scores for the distorted 28 meshes using the saliency map s in our metric through Eq.

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(3). Note that the MS saliency method [8]  indicates the performance of our metric with the MSSP 52 saliency method [9], and TPDMVS(MSLCE) indicates the 53 performance of our metric with the MSLCE saliency method 54 [10]. From Table 4, we observe that our metric with each 55 saliency method achieves significant performance gain over 56 the TPDM metric [5] and achieves the best performance 57 among all the metrics in Table 4. This indicates that incor-58 porating mesh saliency in mesh quality metric can improve 59 the performance of quality prediction, and thus supports the 60 assumption that we made in Section 1.

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From Table 4, we also observe that our metric shows 62 similar performances for three saliency methods despite the 63 significant differences in the generated saliency maps as 64 illustrated in Fig. 2 and Fig. 3. The reason may be that the 65 performance of the TPDM metric [5] is already relatively high 66 as shown in Table 4 and there is a performance bottleneck for 67 the LIRIS/EPFL general-purpose database [1] that consists 68 of a small number of meshes. Note that any of the existing 69 subjective image quality databases [34, 47-50] consists of 70 hundreds or even thousands of image samples while the 71 LIRIS/EPFL general-purpose database which is the largest 72 available subjective mesh quality database consists of only 73 88 mesh samples. Even though it is hard to achieve further 74 performance gain over the TPDM metric, our proposed metric 75 by incorporating mesh saliency still achieves a performance 76 improvement and the performances for three saliency maps 77 are similar. As pointed out in [18], how human attention 78 affects the perception of visual quality is still unknown and 79 there is a lack of solid theoretical basis for the investigation on 80 the relationship between human attention and visual quality. 81 Thus, it is still difficult to explain in a theoretical way how 82 much the performance improvement would be when incorpo-83 rating human attention or visual saliency in a visual quality 84 metric. In this paper, we have demonstrated the added value 85 of mesh saliency empirically by incorporating three well-86 known saliency methods [8][9][10] in the mesh quality metric 87 in a similar way as previous scholars did in the community of 88 image quality assessment [13][14][15][16][17][18].

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For each saliency method, we use our metric to compute 90 quality scores for all the meshes in the LIRIS/EPFL general-91 purpose database [1] and then perform psychometric fitting 92 between the quality scores and MOSs using the cumulative 93 Gaussian psychometric function in Eq. (5). We plot the psy-94 chometric function curves with scatter plots of QualityScore-95 MOS pairs for three saliency methods in Fig. 4, where we 96 observe that the QualityScore-MOS pairs are fitted well by 97 the psychometric function curve for each saliency method.

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In order to demonstrate the generalization capability of 99 our metric on a variety of models, we use our metric T-100 PDMVS(MS) to compute the quality scores of some rep-101 resentative distorted models in the LIRIS/EPFL general-102 purpose database [1]. For each of the four 3D objects in 103 the LIRIS/EPFL general-purpose database, we select four 104 distorted models with various distortion levels which are gen-105 erated by applying the smoothing filter or adding noise with 106 different strengths either locally or globally on the reference 107 model. As stated in [1], these distortions reflect the distortions 108 Note that though we use the MS saliency method [8] to 20 demonstrate the generalization capability of our metric, we 21 can find a similar consistency between the MOS values and 22 QS values of the distorted models when using the other two 23 saliency methods [9,10] in our metric.  However, we do not include surface area in our metric in Eq.   distortion by the surface area will lead to overemphasis on 39 the local distortions on the smooth regions and then result in 40 overestimation of quality degradation of the mesh. Finally, 41 the correlation between the quality scores and MOSs of the 42 meshes in the entire database may decline to some extent. If 43 the surface area is used as a weighting coefficient for the local 44 distortion, the metric incorporating the surface area will be where w i = a i /∑ N i=1 a i is the surface area weighting coefficient 46 of vertex v i with a i one-third of the total areas of all the 47 incident facets of vertex v i in the reference mesh. 48 We use the TPDMVS-W metric with three saliency meth-49 ods to generate quality scores for the meshes and provide 50 a performance comparison among the TPDM metric  the TPDMVS-W metric and the TPDMVS metric on the 1 LIRIS/EPFL general-purpose database in Table 6. From 2 Table 6, we observe that, for each saliency method, the 3 TPDMVS metric always achieves better performance than the  As we analyzed in Section 4.4, there is a significant differ-2 ence among the saliency maps generated by the three saliency 3 methods [8][9][10]. When some vertices are detected as salient 4 by one saliency method, they may be detected as non-salient 5 by the other two saliency methods. In spite of the difference 6 among three saliency maps, each saliency method leads to 7 performance gain when used in our metric, as we described in 8 Section 5.2. Therefore, we come up with a question naturally: 9 is it possible to further improve the performance using the 10 synthetic saliency map generated by assembling the salient 11 regions from different saliency maps? We firstly assume that 12 better performance can be obtained if the salient regions from 13 individual saliency maps are assembled together. In order to 14 validate the assumption, we firstly merge the saliency maps by where s i is the saliency value for vertex v i before standard-23 ization, s i is the saliency value after standardization, s mean 24 and s std are the mean and standard deviation of the saliency 25 map s respectively. We use the max function to assign the 26 higher saliency value from the standardized saliency maps as 27 the saliency value for each vertex. Let s a and s b denote two 28 standardized saliency maps obtained via Eq. (7), the synthetic 29 saliency map is generated by applying the max function to 30 each element value of saliency maps s a and s b 31 where s a i and s b i are the saliency values for vertex v i in the 32 saliency maps s a and s b respectively, and s m i is the saliency 33 value for vertex v i in the synthetic saliency map. The saliency 34 values in the synthetic saliency map are normalized into the 35 range [0, 1] before the synthetic saliency map is used in our 36 metric.     Table 7 and 10  Table 8. From Fig. 6, we observe that the synthetic saliency 11 map MSSP-MSLCE is overall warmer than the other three 12 other three synthetic saliency maps on both models. regions (in the red rectangles) as shown in Fig. 2(b). 21 MSSP detects high saliency at the #1, #2 and #3 regions, 22 and low saliency at the #4 region as shown in Fig. 2(c).

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-On the RockerArm model, MS detects high saliency at 27 the #4 region (in the black rectangle) and low saliency 28 at some parts of the #1, #2, and #3 regions (in the 29 blue rectangles) as shown in Fig. 2(g). MSSP detects 30 generally high saliency at the #1, #2, and #3 regions and 31 median saliency at the #4 region as shown in Fig. 2(h).

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Finally, the synthetic saliency map MS-MSSP shows 33 high saliency at the #1, #2, #3, and #4 regions as shown 34 in Fig. 6(e). 35 We provide a performance comparison between the indi-36 vidual saliency maps and the synthetic saliency maps on the 37 LIRIS/EPFL general-purpose database [1] in Table 9. From 38 is the least. As we analyzed in Section 4.4, the similarity 48 between the saliency maps of MS and MSLCE is the lowest 49 while the similarity between the saliency maps of MSSP 50 and MSLCE is the highest. So we conclude that there 51 is a close correlation between the performance gain of the 52 synthetic saliency map over individual saliency maps and the 53 similarity between the individual saliency maps. Specifically, 54 our analysis based on three saliency methods indicates that the 55 lower the similarity between two individual saliency maps is, 56 the greater the performance gain of the synthetic saliency map 57 over the individual saliency maps will be. From Table 9, we 58 also observe that MS-MSSP-MSLCE does not achieve better 59 performance than MS-MSLCE. The reason is that there is 60 already a high similarity between the saliency maps of MSSP 61 and MSLCE, and thus it is hard to achieve performance gain 62 over MS-MSLCE by further merging the synthetic saliency 63 map MS-MSLCE with the saliency map of MSSP. Due to a 64 lack of sufficient knowledge of human visual system [13][14][15][16][17][18], 65 a perfect theoretic interpretation for the performance gain of 66 the synthetic saliency map over individual saliency maps is 67 not yet available. However, we believe that our work in this 68 paper will facilitate the investigation on how human attention 69 or visual saliency affects the perception of mesh quality and 70 on the correlation analysis among different mesh saliency 71 methods.

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Based on the aforementioned analysis, we draw the fol-73 lowing conclusions: (1) After standardizing two individual 74 saliency maps and applying the max function to the stan-75 dardized saliency maps, the salient regions of each individual 76 saliency map will be preserved in the synthetic saliency map. 77 (2) The synthetic saliency map achieves better performance 78 than each individual saliency map when used in our metric. 79 (3) There is a close correlation between the performance gain 80 of the synthetic saliency map over the individual saliency 81 maps and the similarity between individual saliency maps. If 82 the similarity between two individual saliency maps is lower, 83 the performance gain of the synthetic saliency map over the 84 individual saliency maps will be greater. 85

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In this paper, we have proposed a mesh visual quality 87 metric using a saliency weighting-based pooling strategy. We 88 have demonstrated the superiority and effectiveness of our 89 metric with three well-known mesh saliency detection meth-90 ods. The performance comparison shows that our metric with 91 any of the three saliency maps achieves better performance 92 than state-of-the-art MVQ metrics. The experimental result 93 reveals that it is inappropriate to include the surface area 94 in the metric for the LIRIS/EPFL general-purpose database. 95 Our analysis shows that there is a significant difference in on the incorporation of mesh saliency into MVQ assessment 11 in this paper will benefit the design of better perceptual 12 mesh quality metrics. The proposed metric can be used 13 to guide the algorithm design in other mesh processing op- 14 erations, such as mesh smoothing, mesh simplification and 15 mesh watermarking, in order to achieve the optimal algorithm 16 performance with least visual degradations. One typical 17 practical application of our metric is to evaluate the visual 18 quality of the transmitted 3D models over the network at 19 the receiver ends or client terminals efficiently. The visual 20 quality data can be used as a feedback for the content and 21 service providers to optimize the quality of user experience. 22 One of our future projects involves the following works: to 23 build a large database that consists of more geometric models, 24 to investigate a more advanced feature representation that 25 reflects the local distortions of a mesh better, and to explore 26 the relationship between mesh saliency and mesh quality 27 assessment in a theoretical way. It will also be interesting to 28 integrate visual attention instead of mesh saliency into MVQ 29 assessment when the eye-tracking data of mesh becomes 30 available in the future.