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Let $$\mathcal{D}$$ be a dataset of smooth {3D}-surfaces, partitioned into disjoint classes $$\mli{CL}_j$$, $$j= 1, \ldots, k$$. We show how \emph{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 $$\mli{CL}_j$$ by diffeomorphic interpolation of smooth surfaces between pairs $$S,S' \in \mli{CL}_j$$. We also implement small random perturbations of surfaces $$S\in \mli{CL}_j$$ 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.
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