Although 3D shape matching and interpolation are highly interrelated, they
are often studied separately and applied sequentially to relate different 3D
shapes, thus resulting in sub-optimal performance. In this work we present a
unified framework to predict both point-wise correspondences and shape
interpolation between 3D shapes. To this end, we combine the deep functional
map framework with classical surface deformation models to map shapes in both
spectral and spatial domains. On the one hand, by incorporating spatial maps,
our method obtains more accurate and smooth point-wise correspondences compared
to previous functional map methods for shape matching. On the other hand, by
introducing spectral maps, our method gets rid of commonly used but
computationally expensive geodesic distance constraints that are only valid for
near-isometric shape deformations. Furthermore, we propose a novel test-time
adaptation scheme to capture both pose-dominant and shape-dominant
deformations. Using different challenging datasets, we demonstrate that our
method outperforms previous state-of-the-art methods for both shape matching
and interpolation, even compared to supervised approaches.

本研究提出了一个统一的框架，用于预测 3D 形状之间的点对应和形状插值，结合了深度函数映射和经典表面变形模型，在谱域和空间域中进行形状映射。实验结果表明，该方法在形状匹配和插值方面优于以往最先进的方法，甚至超过了有监督学习方法。