Zacharopoulos, Athanasios Dimitriou;
(2005)
Three-dimensional shape-based reconstructions in medical imaging.
Doctoral thesis , UCL (University College London).
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Abstract
This thesis describes methods for reconstruction in non-linear tomography applications. The specific example application in this thesis is Optical Tomography (OT), which seeks the recovery of optical properties such as absorption, scattering and refractive index, given measurements of transmitted light through biological tissue of several centimetres in thickness. Previous methods pose such a problem as the optimisation of a model fitting procedure over a space of piecewise local basis functions such as pixels (or voxels in 3D). We employ a parametrisation of closed surfaces using spherical harmonics based on constrained minimisation of the distortions occurring by the mapping of the surfaces, acquired from voxel images, to a unit sphere. This method could be used to describe parametrically any closed surface, and overcomes the restriction to just star-shaped objects that is commonly found in literature. A surface meshing algorithm is proposed by applying the parametrisation to map regular surface meshes initially defined on the a unit sphere, by tessellation of an embedded icosahedron, upon the parametrically defined surfaces. This procedure creates regular sampled meshes which is a prerequisite for a good discretisation of a surface, in an automatic procedure. A Boundary Element Method for OT is constructed, for the solution of the diffusion equation on realistic geometrical models, constructed from segmented Magnetic Resonance Images (MRI) or Computed Tomography (CT) scans. In this work we propose a method for reconstruction of the boundaries of piecewise constant regions. The shape description for closed surfaces is used in a novel shape estimation inverse problem in 3D using OT measurements, based on a forward solution constructed from BEM and the regular meshes. Some examples are given that portray the capabilities of the proposed method.
| Type: | Thesis (Doctoral) |
|---|---|
| Title: | Three-dimensional shape-based reconstructions in medical imaging |
| Identifier: | PQ ETD:602764 |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Additional information: | Thesis digitised by ProQuest. |
| UCL classification: | UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1446822 |
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