Detection of deformable objects in 3D images using Markov-Chain Monte Carlo and spherical harmonics.

We address the problem of segmenting 3D microscopic volumetric intensity images of a collection of spatially correlated objects (such as fluorescently labeled nuclei in a tissue). This problem arises in the study of tissue morphogenesis where cells and cellular components are organized in accord with biological role and fate. We formulate the image model as stochastically generated based on biological priors and physics of image formation. We express the segmentation problem in terms of Bayesian inference and use data-driven Markov Chain Monte Carlo to fit the image model to data. We perform an initial step in which the intensity volume is approximated as an expansion in 4D spherical harmonics, the coefficients of which capture the general organization of objects. Since cell nuclei are membrane-bound their shapes are subject to membrane lipid bilayer bending energy, which we use to constrain individual contours. Moreover, we parameterize the nuclear contours using spherical harmonic functions, which provide a shape description with no restriction to particular symmetries. We demonstrate the utility of our approach using synthetic and real fluorescence microscopy data.