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

Abstract

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 difficulties 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.