  4D style transfer aims at transferring arbitrary visual style to the
synthesized novel views of a dynamic 4D scene with varying viewpoints and
times. Existing efforts on 3D style transfer can effectively combine the visual
features of style images and neural radiance fields (NeRF) but fail to handle
the 4D dynamic scenes limited by the static scene assumption. Consequently, we
aim to handle the novel challenging problem of 4D style transfer for the first
time, which further requires the consistency of stylized results on dynamic
objects. In this paper, we introduce StyleDyRF, a method that represents the 4D
feature space by deforming a canonical feature volume and learns a linear style
transformation matrix on the feature volume in a data-driven fashion. To obtain
the canonical feature volume, the rays at each time step are deformed with the
geometric prior of a pre-trained dynamic NeRF to render the feature map under
the supervision of pre-trained visual encoders. With the content and style cues
in the canonical feature volume and the style image, we can learn the style
transformation matrix from their covariance matrices with lightweight neural
networks. The learned style transformation matrix can reflect a direct matching
of feature covariance from the content volume to the given style pattern, in
analogy with the optimization of the Gram matrix in traditional 2D neural style
transfer. The experimental results show that our method not only renders 4D
photorealistic style transfer results in a zero-shot manner but also
outperforms existing methods in terms of visual quality and consistency.
