  We propose a parametric model that maps free-view images into a vector space
of coded facial shape, expression and appearance with a neural radiance field,
namely Morphable Facial NeRF. Specifically, MoFaNeRF takes the coded facial
shape, expression and appearance along with space coordinate and view direction
as input to an MLP, and outputs the radiance of the space point for
photo-realistic image synthesis. Compared with conventional 3D morphable models
(3DMM), MoFaNeRF shows superiority in directly synthesizing photo-realistic
facial details even for eyes, mouths, and beards. Also, continuous face
morphing can be easily achieved by interpolating the input shape, expression
and appearance codes. By introducing identity-specific modulation and texture
encoder, our model synthesizes accurate photometric details and shows strong
representation ability. Our model shows strong ability on multiple applications
including image-based fitting, random generation, face rigging, face editing,
and novel view synthesis. Experiments show that our method achieves higher
representation ability than previous parametric models, and achieves
competitive performance in several applications. To the best of our knowledge,
our work is the first facial parametric model built upon a neural radiance
field that can be used in fitting, generation and manipulation. The code and
data is available at https://github.com/zhuhao-nju/mofanerf.
