Ramón Casero Cañas, MRC Harwell (Oxford) and Oxford Institute of Biomedical Engineering

Title - Transformation diffusion reconstruction of three-dimensional histology volumes from two-dimensional image stacks

Abstract - Reconstructing the original 3D shape of an organ from a stack of 2D histology slices is a challenging problem. In this talk, we present a theoretical framework based on the heat diffusion equation that provides insights into the problem, such as when an external reference is needed or the amount of smoothing that should be applied to the stack. Within this framework, stack misalignment is described by spatial transformations, and reconstruction follows from a "diffusion" process until the slices reach "thermal equilibrium". Moreover, the theoretical framework leads to an algorithm with interesting properties: 1) it is independent of the particular registration method, 2) it is simple to understand and implement, and coincides with previous ad hoc methods, 3) it allows to replace some registration operations by operations on transformations, several orders of magnitude faster, 4) the amount of smoothing can be controlled with a single robust parameter that has a simple interpretation in terms of a spatial frequency filter. We have applied the method to the reconstruction of a mouse heart.