With the enhancement of computer and imaging technology, increasing amounts of biological data are being generated. The data include Magnetic Resonance Imaging (MRI), Computed Tomography (CT), and histological scans of objects. The goal of the work presented in this thesis is to accurately and efficiently reconstruct smooth 3D implicit surface models of the structures that are described by contours from biological cross-section data.
Two methods are presented for performing contour reconstruction that use Multi-level Partition of Unity (MPU) implicit surfaces. A convenient method is proposed to estimate surface normals for contours so that implicit point set-based surface representations can be applied. First, a slice-based approach is discussed. In the slice-based approach, a distance field is generated for each contour slice using MPU implicits. The distance fields are stacked to produce a 3D volume, from which a 3D surface model is extracted. Second, a volume-based approach is presented. This approach treats the points on every contour as a single point set and constructs a smooth but accurate 3D surface.
The techniques presented here are compared to several other reconstruction methods described in the literature. Further, the reconstruction process is shown to be effective at dealing with noise and to generally have sub-voxel accuracy with respect to the input data. The volume-based approach is also invariant under anisotropic sampling of the original data, producing accurate results even in the presence of missing slices.