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Facial expression retargeting from humans to virtual characters is a useful technique in computer graphics and animation. Traditional methods use markers or blendshapes to construct a mapping between the human and avatar faces. However, these approaches require a tedious 3D modeling process, and the performance relies on the modelers' experience. In this paper, we propose a brand-new solution to this cross-domain expression transfer problem via nonlinear expression embedding and expression domain translation. We first build low-dimensional latent spaces for the human and avatar facial expressions with variational autoencoder. Then we construct correspondences between the two latent spaces guided by geometric and perceptual constraints. Specifically, we design geometric correspondences to reflect geometric matching and utilize a triplet data structure to express users' perceptual preference of avatar expressions. A user-friendly method is proposed to automatically generate triplets for a system allowing users to easily and efficiently annotate the correspondences. Using both geometric and perceptual correspondences, we trained a network for expression domain translation from human to avatar. Extensive experimental results and user studies demonstrate that even nonprofessional users can apply our method to generate high-quality facial expression retargeting results with less time and effort.