  We design an interpretable clustering algorithm aware of the nonlinear
structure of image manifolds. Our approach leverages the interpretability of
$K$-means applied in the image space while addressing its clustering
performance issues. Specifically, we develop a measure of similarity between
images and centroids that encompasses a general class of deformations:
diffeomorphisms, rendering the clustering invariant to them. Our work leverages
the Thin-Plate Spline interpolation technique to efficiently learn
diffeomorphisms best characterizing the image manifolds. Extensive numerical
simulations show that our approach competes with state-of-the-art methods on
various datasets.
