SURFACE RECONSTRUCTION IN 3D MEDICAL IMAGING
Jonathan C. Carr
This thesis addresses two problems in medical imaging, the development of a system for 3D imaging with ultrasound and a system for making titanium prostheses for cranioplasty. Central to both problems is the construction and depiction of surfaces from volume data where the data is not acquired on a regular grid or is incomplete.
A system for acquiring 3D pulse-echo ultrasound data using a conventional 2D ultrasound scanner equipped with an electro-magnetic spatial locator is described. The non-parallel nature of 2D B-scan slices acquired by the system requires the development of new visualisation algorithms to depict three dimensional structures.
Two methods for visualising iso-valued surfaces from the ultrasound data are presented. One forms an intermediate volume reconstruction suitable for conventional ray-casting while the second method renders surfaces directly from the slice data. In vivo imaging of human anatomy is used to demonstrate reconstructions of tissue surfaces. Filtering and spatial compounding of scan data are used to reduce speckle.
Pulse-echo ultrasound primarily depicts tissue boundaries. These are characterised by incomplete acoustic interfaces contaminated by noise. The problem of reconstructing tissue interfaces from ultrasound data is viewed as an example of the general problem of reconstructing an object's shape from unorganised surface data. A novel method for reconstructing surfaces in the absence of a priori knowledge of the object's shape, is described and applied to 3D ultrasound data. The method uses projections through the surface data taken from many viewpoints to reconstruct surfaces. Aspects of the method are similar to work in computer vision concerning the determination of the shape of 3D objects from their silhouettes. This work is extended by considering the reconstruction of incomplete objects in the presence of noise and through the development of practical algorithms for pixel and voxel data. The reconstruction of realistic, non-convex objects is considered. 2D and 3D ultrasound data derived from phantoms, as well as artificial data, are used to demonstrate reconstructions.
The second problem studied in this thesis concerns designing cranial implants to repair defects in the skull. Skull surfaces are extracted from X-ray CT data by ray-casting iso-valued surfaces. A tensor product B-spline interpolant is used in the ray-caster to reduce ripples in the surface data due to partial voluming and the large spacing between CT slices. The associated surface depth-maps are characterised by large irregular holes which correspond to the defect regions requiring repair. Radial basis function approximation is introduced as a method of interpolating the surface of the skull across these defect regions. The fitted surface is used to produce CNC milling instructions to machine a mould in the shape of the surface from a block of hard plastic resin. A cranial implant is then formed by pressing flat titanium plate into the mould under high pressure in a hydraulic press.
The system improves upon current treatment procedures by avoiding the manual aspects of fashioning an implant. It is also suitable when techniques which use symmetry to reconstruct the skull are inadequate or not possible. Radial basis function (RBF) approximation has previously been restricted to problems where the number of interpolation centres is small. The use of newly developed fast methods for evaluating radial basis interpolants in the surface interpolation software results in a computationally efficient system for designing cranial implants and demonstrates that RBFs are potentially of wide interest in medical imaging and engineering problems where data does not lie on a regular grid. The system has been successfully used to treat patients at Christchurch Hospital.
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