  Data-driven cell tracking and segmentation methods in biomedical imaging
require diverse and information-rich training data. In cases where the number
of training samples is limited, synthetic computer-generated data sets can be
used to improve these methods. This requires the synthesis of cell shapes as
well as corresponding microscopy images using generative models. To synthesize
realistic living cell shapes, the shape representation used by the generative
model should be able to accurately represent fine details and changes in
topology, which are common in cells. These requirements are not met by 3D voxel
masks, which are restricted in resolution, and polygon meshes, which do not
easily model processes like cell growth and mitosis. In this work, we propose
to represent living cell shapes as level sets of signed distance functions
(SDFs) which are estimated by neural networks. We optimize a fully-connected
neural network to provide an implicit representation of the SDF value at any
point in a 3D+time domain, conditioned on a learned latent code that is
disentangled from the rotation of the cell shape. We demonstrate the
effectiveness of this approach on cells that exhibit rapid deformations
(Platynereis dumerilii), cells that grow and divide (C. elegans), and cells
that have growing and branching filopodial protrusions (A549 human lung
carcinoma cells). A quantitative evaluation using shape features and Dice
similarity coefficients of real and synthetic cell shapes shows that our model
can generate topologically plausible complex cell shapes in 3D+time with high
similarity to real living cell shapes. Finally, we show how microscopy images
of living cells that correspond to our generated cell shapes can be synthesized
using an image-to-image model.
