  3D shape reconstruction typically requires identifying object features or
textures in multiple images of a subject. This approach is not viable when the
subject is semi-transparent and moving in and out of focus. Here we overcome
these challenges by rendering a candidate shape with adaptive blurring and
transparency for comparison with the images. We use the microscopic nematode
Caenorhabditis elegans as a case study as it freely explores a 3D complex fluid
with constantly changing optical properties. We model the slender worm as a 3D
curve using an intrinsic parametrisation that naturally admits
biologically-informed constraints and regularisation. To account for the
changing optics we develop a novel differentiable renderer to construct images
from 2D projections and compare against raw images to generate a pixel-wise
error to jointly update the curve, camera and renderer parameters using
gradient descent. The method is robust to interference such as bubbles and dirt
trapped in the fluid, stays consistent through complex sequences of postures,
recovers reliable estimates from blurry images and provides a significant
improvement on previous attempts to track C. elegans in 3D. Our results
demonstrate the potential of direct approaches to shape estimation in complex
physical environments in the absence of ground-truth data.
