adopt $h^3$ instead of $h$ (here, $h$ corresponds to the L-channel). $R$ is expressed in $mm$.

\[tb:GRA\_res\]

Robustness over different surface tessellations {#ss:robustness_part}
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The strength of the edgeLBP is its ring definition, which is robust to different surface tessellations: in this Section we experimentally discuss this robustness. To this aim we re-sample the triangles meshes with a decreasing number of vertices. The triangle mesh re-sampling with $x$ vertices is done with the MeshLAB tool [@meshlab] that approximates the original mesh preserving its geometry as much as possible with the given number of vertices (for instance, $x=40K$ vertices). This process generally modifies the mesh connectivity and the area of the triangles, discards the smallest details and keeps the overall shape, unless the number of vertices drastically diminishes and the new vertices are too few to preserve it.

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                                                                                                                              $40K$                                                                                                                                                                                                                                                         $24K$                                                                                                                                                                                                                                                       $8K$
   ![The degradation of one of the model used to test the robustness of the descriptor of both edgeLBP and meshLBP. The number on each image is the respective vertex resolution.[]{data-label="fig:comparison_model"}](pic/deg_ori.png "fig:"){width="2.45cm"}   ![The degradation of one of the model used to test the robustness of the descriptor of both edgeLBP and meshLBP. The number on each image is 