  Compared to facial expression recognition, expression synthesis requires a
very high-dimensional mapping. This problem exacerbates with increasing image
sizes and limits existing expression synthesis approaches to relatively small
images. We observe that facial expressions often constitute sparsely
distributed and locally correlated changes from one expression to another. By
exploiting this observation, the number of parameters in an expression
synthesis model can be significantly reduced. Therefore, we propose a
constrained version of ridge regression that exploits the local and sparse
structure of facial expressions. We consider this model as masked regression
for learning local receptive fields. In contrast to the existing approaches,
our proposed model can be efficiently trained on larger image sizes.
Experiments using three publicly available datasets demonstrate that our model
is significantly better than $\ell_0, \ell_1$ and $\ell_2$-regression, SVD
based approaches, and kernelized regression in terms of mean-squared-error,
visual quality as well as computational and spatial complexities. The reduction
in the number of parameters allows our method to generalize better even after
training on smaller datasets. The proposed algorithm is also compared with
state-of-the-art GANs including Pix2Pix, CycleGAN, StarGAN and GANimation.
These GANs produce photo-realistic results as long as the testing and the
training distributions are similar. In contrast, our results demonstrate
significant generalization of the proposed algorithm over out-of-dataset human
photographs, pencil sketches and even animal faces.
