Three-dimensional reconstruction from serial non-contiguous sections using variational implicit techniques.

摘要

Variational implicit surfaces have been widely used in computer graphics and animation and generally provide appropriate solutions for uniformly distributed sparse data. The fields of medicine and biology increasingly rely on accurate three-dimensional reconstructions for data visualization and registration. Despite the fact that biological structures fit perfectly within the scope of variational implicit interpolation (smooth closed surfaces), the structures to model in these fields constitute a computational challenge due to the non-homogeneity of the initial dataset that usually consists in serial distant sections, as well as the presence of local high curvatures in the shapes to reconstruct. This thesis proposes different approaches that address these issues. Solutions based on the utilization of isotropic/anisotropic compactly supported radial basis function and surface regularization are presented. Probabilistic contours are introduced as a direct and useful application of the use of implicit functions in the reconstruction paradigm. Further constraints to the reconstruction are presented in the form of a section-to-section registration, shape transformation and its incorporation as shape of influence within the global interpolation scheme. However optimized for serial non-contiguous sections, this work can be easily generalized to the reconstruction of any biological structure from a non-uniform initial dataset.