Correspondence-Steered Volumetric Descriptor Learning Using Deep Functional Maps

In this paper, we consider the dense correspondence of volumetric images and propose a convolutional network-based descriptor learning framework using the functional map representation. Our main observation is that the correspondence-steered descriptor learning improves dense volumetric mapping compared with the hand-crafted descriptors. We present an unsupervised way to find the optimal network parameters by aligning volumetric probe functions and the enforcement of invertible coupled maps. The proposed framework takes the one-channel volume as input and outputs the multi-channel volumetric descriptors using the cascaded convolutional operators, which are faster than the conventional descriptor computations. We follow the deep functional map framework and represent the dense correspondence by the low-dimensional spectral mapping for the functional transfer and dense correspondence using the linear algebra. We demonstrate that by using the correspondence-steered deep descriptor learning, the quality of both the dense correspondence and attribute transfer are improved in the extensive experiments.