Topologically Robust B-spline Reconstruction of Fibers from 3D Images

The micro-structure of wood-based insulation materials is analyzed to gain insight into how features on microscopic scales influence macroscopic thermal conductivity. Three-dimensional (3D) image data obtained by micro-computed tomography reveals a complex structure formed by cellulose fibers. To study the effect of geometry changes, simple B-spline representations of these fibers are highly desirable. A straightforward solution is to extract a triangulated isosurface from the 3D image and partition it into quadrilateral macro-cells with disk-like topology. For each cell, a B-spline surface is constructed by minimizing a least squares error term. However, the physical processing of the material affects the structure of the fibers. The resulting changes in surface topology cause difficultie s for the quadrilateral partitioning. Image processing tools can solve these topological issues, but they also impact geometry. We present a novel approach that splits geometry and topology processing of the data. It allows for topological simplification while still preserving the geometry of a scanned object. Established B-spline approximation methods are used to create a model. The involved mathematical equations are described in detail with a focus on simple implementation. Our presented results demonstrate that smooth and accurate models can be created for challenging data.