of more than 10,000 distinct identity scans with 28K vertices which cover a wide range of gender ethnicity and age. For the subsequent experiments, the MeIn3D dataset was randomly split within demographic constraints to ensure gender, ethnic and age diversity, into 9K train and 1K test meshes.

![image](coma_errors.png){width="0.33\linewidth"} ![image](dfaust_errors.png){width="0.33\linewidth"} ![image](mein3d_errors.png){width="0.33\linewidth"}

For the quantitative experiments of sections \[ablation\] and \[3dmm\_comparison\] the evaluation metric used is **generalisation**, which measures the ability of a model to represent novel shapes from the same distribution as it was trained on. More specifically we evaluate the average per sample and per vertex euclidean distance in the 3D space (in millimetres) between corresponding vertices in the input and its reconstruction.

Implementation Details {#implementation}
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We denote as $SC(h,w)$ a spiral convolution of $h$ hops and $w$ filters, $DS(p)$ and $US(p)$ a downsampling and an upsampling by a factor of $p$, respectively, $FC(d)$ a fully connected layer, $l$ the number of vertices after the last downsampling layer. The simple Neural3DMM for COMA and DFAUST datasets is the following:

$\mathit{Enc:} \, SC(1,16)\rightarrow DS(4)\rightarrow SC(1,16)\rightarrow DS(4)\rightarrow SC(1,16)\rightarrow DS(4)\rightarrow SC(1,32)\rightarrow DS(4)\rightarrow FC(d)$

$\mathit{Dec:} \,FC(l*32)\rightarrow US(4)\rightarrow SC(1,32)\rightarrow US(4)\rightarrow SC(1,16)\rightarrow US(4)\rightarrow SC(1,16)\rightarrow US(4)\rightarrow SC(1,3)$ For Mein3D, due to the high vertex count, we 