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.

Complex dendritic trees are a distinctive feature of neurons. Alterations to dendritic morphology are associated with developmental, behavioral and neurodegenerative changes. The highly-arborized PVD neuron of C. elegans serves as a model to study dendritic patterning; however, quantitative, objective and automated analyses of PVD morphology are missing. Here, we present a method for neuronal feature extraction, based on deep-learning and fitting algorithms. The extracted neuronal architecture is represented by a database of structural elements for abstracted analysis. We obtain excellent automatic tracing of PVD trees and uncover that dendritic junctions are unevenly distributed. Surprisingly, these junctions are three-way-symmetrical on average, while dendritic processes are arranged orthogonally. We quantify the effect of mutation in git-1, a regulator of dendritic spine formation, on PVD morphology and discover a localized reduction in junctions. Our findings shed new light on PVD architecture, demonstrating the effectiveness of our objective analyses of dendritic morphology and suggest molecular control mechanisms.