Static meshes with texture maps have attracted considerable attention in both industrial manufacturing and academic research, leading to an urgent requirement for effective and robust objective quality evaluation. However, current model-based static mesh quality metrics have obvious limitations: most of them only consider geometry information, while color information is ignored, and they have strict constraints for the meshes' geometrical topology. Other metrics, such as image-based and point-based metrics, are easily influenced by the prepossessing algorithms, e.g., projection and sampling, hampering their ability to perform at their best. In this paper, we propose Geodesic Patch Similarity (GeodesicPSIM), a novel model-based metric to accurately predict human perception quality for static meshes. After selecting a group keypoints, 1-hop geodesic patches are constructed based on both the reference and distorted meshes cleaned by an effective mesh cleaning algorithm. A two-step patch cropping algorithm and a patch texture mapping module refine the size of 1-hop geodesic patches and build the relationship between the mesh geometry and color information, resulting in the generation of 1-hop textured geodesic patches. Three types of features are extracted to quantify the distortion: patch color smoothness, patch discrete mean curvature, and patch pixel color average and variance. To the best of our knowledge, GeodesicPSIM is the first model-based metric especially designed for static meshes with texture maps. GeodesicPSIM provides state-of-the-art performance in comparison with image-based, point-based, and video-based metrics on a newly created and challenging database. We also prove the robustness of GeodesicPSIM by introducing different settings of hyperparameters. Ablation studies also exhibit the effectiveness of three proposed features and the patch cropping algorithm.
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