  Let $\mathcal{D}$ be a dataset of smooth 3D-surfaces, partitioned into
disjoint classes $\mathit{CL}_j$, $j= 1, \ldots, k$. We show how optimized
diffeomorphic registration applied to large numbers of pairs $S,S' \in
\mathcal{D}$ can provide descriptive feature vectors to implement automatic
classification on $\mathcal{D}$, and generate classifiers invariant by rigid
motions in $\mathbb{R}^3$. To enhance accuracy of automatic classification, we
enrich the smallest classes $\mathit{CL}_j$ by diffeomorphic interpolation of
smooth surfaces between pairs $S,S' \in \mathit{CL}_j$. We also implement small
random perturbations of surfaces $S\in \mathit{CL}_j$ by random flows of smooth
diffeomorphisms $F_t:\mathbb{R}^3 \to \mathbb{R}^3$. Finally, we test our
automatic classification methods on a cardiology data base of discretized
mitral valve surfaces.
