Abstract: We present a dense correspondence method for isometric shapes, which is accurate yet computationally efficient. We minimize the isometric distortion directly in the 3D Euclidean space, i.e., in the domain where isometry is originally defined, by using a coarse-to-fine sampling and combinatorial matching algorithm. Our method does not require any initialization and aims to find an accurate solution in the minimum-distortion sense for perfectly isometric shapes. We demonstrate the performance of our method on various isometric (or nearly isometric) pairs of shapes.