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Despite acceleration in the use of 3D meshes, it is difficult to find effective mesh quality assessment algorithms that can produce predictions highly correlated with human subjective opinions. Defining mesh quality features is challenging due to the irregular topology of meshes, which are defined on vertices and triangles. To address this, we propose a novel 3D projective structural similarity index ( 3D- PSSIM) for meshes that is robust to differences in mesh topology. We address topological differences between meshes by introducing multi-view and multi-layer projections that can densely represent the mesh textures and geometrical shapes irrespective of mesh topology. It also addresses occlusion problems that occur during projection. We propose visual sensitivity weights that capture the perceptual sensitivity to the degree of mesh surface curvature. 3D- PSSIM computes perceptual quality predictions by aggregating quality-aware features that are computed in multiple projective spaces onto the mesh domain, rather than on 2D spaces. This allows 3D- PSSIM to determine which parts of a mesh surface are distorted by geometric or color impairments. Experimental results show that 3D- PSSIM can predict mesh quality with high correlation against human subjective judgments, across the presence of noise, even when there are large topological differences, outperforming existing mesh quality assessment models.