  We present a differentiable rendering framework to learn structured 3D
abstractions in the form of primitive assemblies from sparse RGB images
capturing a 3D object. By leveraging differentiable volume rendering, our
method does not require 3D supervision. Architecturally, our network follows
the general pipeline of an image-conditioned neural radiance field (NeRF)
exemplified by pixelNeRF for color prediction. As our core contribution, we
introduce differential primitive assembly (DPA) into NeRF to output a 3D
occupancy field in place of density prediction, where the predicted occupancies
serve as opacity values for volume rendering. Our network, coined DPA-Net,
produces a union of convexes, each as an intersection of convex quadric
primitives, to approximate the target 3D object, subject to an abstraction loss
and a masking loss, both defined in the image space upon volume rendering. With
test-time adaptation and additional sampling and loss designs aimed at
improving the accuracy and compactness of the obtained assemblies, our method
demonstrates superior performance over state-of-the-art alternatives for 3D
primitive abstraction from sparse views.
