We present a simple and efficient method for refining maps or correspondences
by iterative upsampling in the spectral domain that can be implemented in a few
lines of code. Our main observation is that high quality maps can be obtained
even if the input correspondences are noisy or are encoded by a small number of
coefficients in a spectral basis. We show how this approach can be used in
conjunction with existing initialization techniques across a range of
application scenarios, including symmetry detection, map refinement across
complete shapes, non-rigid partial shape matching and function transfer. In
each application we demonstrate an improvement with respect to both the quality
of the results and the computational speed compared to the best competing
methods, with up to two orders of magnitude speed-up in some applications. We
also demonstrate that our method is both robust to noisy input and is scalable
with respect to shape complexity. Finally, we present a theoretical
justification for our approach, shedding light on structural properties of
functional maps.

论文介绍了一种基于频谱域迭代上采样的简单有效的地图或对应关系细化方法，并说明了如何将该方法应用于对称性检测、完整形状的地图细化、非刚性部分形状匹配和函数转换等一系列应用场景中，证明了该方法相比最佳竞争方法具有更高的结果质量和计算速度，并且对于噪声输入具有鲁棒性和扩展形状复杂性。最后，文章提出了一个理论上的方法，揭示了功能地图的结构属性。