  Recently, differentiable volume rendering in neural radiance fields (NeRF)
has gained a lot of popularity, and its variants have attained many impressive
results. However, existing methods usually assume the scene is a homogeneous
volume so that a ray is cast along the straight path. In this work, the scene
is instead a heterogeneous volume with a piecewise-constant refractive index,
where the path will be curved if it intersects the different refractive
indices. For novel view synthesis of refractive objects, our NeRF-based
framework aims to optimize the radiance fields of bounded volume and boundary
from multi-view posed images with refractive object silhouettes. To tackle this
challenging problem, the refractive index of a scene is reconstructed from
silhouettes. Given the refractive index, we extend the stratified and
hierarchical sampling techniques in NeRF to allow drawing samples along a
curved path tracked by the Eikonal equation. The results indicate that our
framework outperforms the state-of-the-art method both quantitatively and
qualitatively, demonstrating better performance on the perceptual similarity
metric and an apparent improvement in the rendering quality on several
synthetic and real scenes.
