10,191 research outputs found
Indirect Image Registration with Large Diffeomorphic Deformations
The paper adapts the large deformation diffeomorphic metric mapping framework
for image registration to the indirect setting where a template is registered
against a target that is given through indirect noisy observations. The
registration uses diffeomorphisms that transform the template through a (group)
action. These diffeomorphisms are generated by solving a flow equation that is
defined by a velocity field with certain regularity. The theoretical analysis
includes a proof that indirect image registration has solutions (existence)
that are stable and that converge as the data error tends so zero, so it
becomes a well-defined regularization method. The paper concludes with examples
of indirect image registration in 2D tomography with very sparse and/or highly
noisy data.Comment: 43 pages, 4 figures, 1 table; revise
3D mesh processing using GAMer 2 to enable reaction-diffusion simulations in realistic cellular geometries
Recent advances in electron microscopy have enabled the imaging of single
cells in 3D at nanometer length scale resolutions. An uncharted frontier for in
silico biology is the ability to simulate cellular processes using these
observed geometries. Enabling such simulations requires watertight meshing of
electron micrograph images into 3D volume meshes, which can then form the basis
of computer simulations of such processes using numerical techniques such as
the Finite Element Method. In this paper, we describe the use of our recently
rewritten mesh processing software, GAMer 2, to bridge the gap between poorly
conditioned meshes generated from segmented micrographs and boundary marked
tetrahedral meshes which are compatible with simulation. We demonstrate the
application of a workflow using GAMer 2 to a series of electron micrographs of
neuronal dendrite morphology explored at three different length scales and show
that the resulting meshes are suitable for finite element simulations. This
work is an important step towards making physical simulations of biological
processes in realistic geometries routine. Innovations in algorithms to
reconstruct and simulate cellular length scale phenomena based on emerging
structural data will enable realistic physical models and advance discovery at
the interface of geometry and cellular processes. We posit that a new frontier
at the intersection of computational technologies and single cell biology is
now open.Comment: 39 pages, 14 figures. High resolution figures and supplemental movies
available upon reques
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