A frequency-limited waviness and curvature measurement algorithm for composite fibre trackings

Abstract

Given a set of irregularly sampled 3D polygonal curves representing composite fibres within a micro-computed tomography volume, a new approach based on the Frenet–Serret formulas is proposed to measure the point curvature and waviness along a polyline even when its oscillations are not coplanar. However, a direct computation of the measures would lead to ill-formed results depending on variant externalities across acquisitions such as noise, sampling, resolution, fractality, etc. Consequentially, we also propose a decoupling mechanism employing a low-pass Gaussian frequency filter to gradually discard features smaller than a certain user-specified σ wavelength referenced in actual space units. This proposal has been tested, characterized and visualized using both real and synthetic datasets contemplating complex waveform features to assess the filter selectivity and convergence across varying sampling frequencies (i.e. polyline resolution). The C++ VTK implementation, alongside an extra amount of supplementary materials encompassing the execution results and synthetic datasets is provided.