  We propose a principled approach for non-isometric landmark-preserving
non-rigid shape matching. Our method is based on the functional maps framework,
but rather than promoting isometries we focus instead on near-conformal maps
that preserve landmarks exactly. We achieve this, first, by introducing a novel
landmark-adapted basis using an intrinsic Dirichlet-Steklov eigenproblem.
Second, we establish the functional decomposition of conformal maps expressed
in this basis. Finally, we formulate a conformally-invariant energy that
promotes high-quality landmark-preserving maps, and show how it can be solved
via a variant of the recently proposed ZoomOut method that we extend to our
setting. Our method is descriptor-free, efficient and robust to significant
mesh variability. We evaluate our approach on a range of benchmark datasets and
demonstrate state-of-the-art performance on non-isometric benchmarks and near
state-of-the-art performance on isometric ones.
