  The Gaussian reconstruction kernels have been proposed by Westover (1990) and
studied by the computer graphics community back in the 90s, which gives an
alternative representation of object 3D geometry from meshes and point clouds.
On the other hand, current state-of-the-art (SoTA) differentiable renderers,
Liu et al. (2019), use rasterization to collect triangles or points on each
image pixel and blend them based on the viewing distance. In this paper, we
propose VoGE, which utilizes the volumetric Gaussian reconstruction kernels as
geometric primitives. The VoGE rendering pipeline uses ray tracing to capture
the nearest primitives and blends them as mixtures based on their volume
density distributions along the rays. To efficiently render via VoGE, we
propose an approximate closeform solution for the volume density aggregation
and a coarse-to-fine rendering strategy. Finally, we provide a CUDA
implementation of VoGE, which enables real-time level rendering with a
competitive rendering speed in comparison to PyTorch3D. Quantitative and
qualitative experiment results show VoGE outperforms SoTA counterparts when
applied to various vision tasks, e.g., object pose estimation, shape/texture
fitting, and occlusion reasoning. The VoGE library and demos are available at:
https://github.com/Angtian/VoGE.
