Inferring Grammar-based Structure Models from 3D Microscopy Data

We present a new method to fit grammar-based stochastic models for biological structure to stacks of microscopic images captured at incremental focal lengths. Providing the ability to quantitatively represent structure and automatically fit it to image data enables important biological research. We consider the case where individuals can be represented as an instance of a stochastic grammar, similar to L-systems used in graphics to produce realistic plant models. In particular, we construct a stochastic grammar of Alternaria, a genus of fungus, and fit instances of it to microscopic image stacks. We express the image data as the result of a generative process composed of the underlying probabilistic structure model together with the parameters of the imaging system. Fitting the model then becomes probabilistic inference. For this we create a reversible-jump MCMC sampler to traverse the parameter space. We observe that incorporating spatial structure helps fit the model parts, and that simultaneously fitting the imaging system is also very helpful.