# Evaluation method

The evaluation will be based on the normalized geodesic error $g_{err}$ of the given matching from the ground-truth sub-vertex correspondence. Different indices will be computed for the two datasets in order to analyze the performance of each method under different kinds of partiality.

The following performance indices will be considered separately for each dataset:

• total percentage of matched points within a variable amount of normalized geodesic error.
• mean geodesic error with respect to the percentage of missing area of the shape (i.e. shapes will be considered in subsets containing only shapes whose missing area is at most a given percentage).

The evaluation code will be released for reference.

## Error measure

For the evaluation of the correspondence quality, we refer to the Princeton benchmark protocol [KLF11] for point-wise maps. Let $\mathcal{M}$ be the full model shape in a canonical pose and $\mathcal{N}$ one of its corresponding partial version. Assume that a correspondence algorithm produces a pair of points $(x,y) \in \mathcal{N} \times \mathcal{M}$, whereas the ground-truth correspondence is $(x,y^*)$. Then, the inaccuracy of the correspondence is measured as

$\epsilon(x) = \frac{d_\mathcal{M}(y,y^*)}{ \mathrm{area}(\mathcal{M})^{1/2} }$

and has units of normalized length on $\mathcal{M}$ (ideally, zero). Here $d_{\mathcal{M}}$ is the geodesic distance on $\mathcal{M}$.