  Finding correspondences between shapes is a fundamental problem in computer
vision and graphics, which is relevant for many applications, including 3D
reconstruction, object tracking, and style transfer. The vast majority of
correspondence methods aim to find a solution between pairs of shapes, even if
multiple instances of the same class are available. While isometries are often
studied in shape correspondence problems, they have not been considered
explicitly in the multi-matching setting. This paper closes this gap by
proposing a novel optimisation formulation for isometric multi-shape matching.
We present a suitable optimisation algorithm for solving our formulation and
provide a convergence and complexity analysis. Our algorithm obtains
multi-matchings that are by construction provably cycle-consistent. We
demonstrate the superior performance of our method on various datasets and set
the new state-of-the-art in isometric multi-shape matching.
