The appearance of hair is influenced by the 3D geometric arrangement of hair fibres. An accurate 3D representation of hair is needed for hair research to assess the effect of different treatments. X-ray microtomography (XRT) can be used for the 3D visualisation of hair arrays and the quantitative analysis of volume and shape attributes.

Introduction

The characterisation of the 3D arrangement of hair fibres is needed to understand what happens to hair when different products or treatments are applied (e.g. shampoo, conditioner and hairspray). Hair can be stretched, bent and curled. Human hair is a very complex visual pattern where hundreds of thousands of hairs are grouped into strands and wisps in diverse hair styles. The hair diameters range from 40 to 120 microns with an average density for most adults of 170-300 hairs per square centimetre. Important properties of hair are volume and shape (e.g. curliness). The fibre-fibre interaction within the hair arrays has a significant effect on the overall properties. However imaging systems using cameras or laser scanners obtain only information about the external surface of the hair array. X-ray microtomography (XRT) allows the 3D visualisation of the spatial distribution of chemical constituents within a sample or the 3D surface morphology of a sample [1]. It can probe the microstructure non-invasively into a few millimetres depth with an axial and lateral resolution down to a few micrometers. The contrast in XRT images is based on the difference in absorption of X-rays by the constituents of the sample (e.g. solid and air). It is influenced by the density and composition of the constituents. The XRT method was tested on Caucasian (straight) and Afro (curly) hair.

Methodology

Images were made using a Skyscan 1072 desktop XRT system with X-ray tube with tungsten anode which was set to 50kV and 200 µA. A stack of about 600 flat cross sections was obtained after tomographic reconstruction of images (1024 x 1024) acquired under different rotations over 180 degrees with a step size of 0.225 degrees. The acquisition time for one projection was 2.6 s resulting in a total acquisition and read-out time of about 75 min (825 projection images).

By changing the distance between the sample and the source one can change the magnification of the projection. Magnifying the object allows to increase the spatial resolution. The actual resolution is limited to about 6 µm. Magnification factors between 14 and 40 were selected resulting in pixel sizes ranging from 19.6 µm to 6.5 µm. With a lower magnification a larger field of view can be obtained allowing the imaging of larger samples. With a pixel size of about 20 µm (enough detail) a maximum length of 20 mm of straight hair fibres within a hair array can be imaged. By merging two images 40 mm can be reached. For visualisation in 3-D space, iso-surface and volume rendering was used (Amira software, version 4.1.2 from Mercury Computer Systems). Iso-surface rendering was done by segmentation using thresholding followed by surface generation with constrained smoothing. The surface generation module of the Amira software computes a triangular approximation of the interfaces between the segmented sections. To reduce noise a 3D median filter with a size of 3 x 3 pixels was used. For image processing the image analysis toolbox (DIPlib vers. 1.4.1 from the Delft University of Technology, NL) running under MATlab (vers.7.1 SP3 from MathWorks) was used.

Results

A representative XRT image of a horizontal cross section of straight hair is shown in figure 1. The fibres are visible as circular hollow objects. A clear distinction can be made between the solid fibre and air, making it possible to identify the fibres using thresholding (generating a binary image). Figure 2 shows 3D views of the hair array generated by iso-surface rendering of a stack of 700 horizontal XRT cross sections. In this study the internal structure of the hair fibre is not of interest. It is just important to know exactly where each fibre is at any particular point along the hair switch in 3D, effectively obtaining a co-ordinate set which could be reconstructed. Hair fibres are touching each other in 3D space and have to be separated using image processing using a watershed transform of the distance transform of the labelled XRT image. Figure 3 shows an example of the identification of a single fibre in an XRT image of a hair array.
A representative XRT image of a cross section of Afro hair is shown in figure 4A. The images were obtained with a voxel resolution of 14.6 µm resulting in a field of view of 15 mm. Figure 4B shows a 3D view of the hair array generated by ­volume rendering of a stack of 550 horizontal XRT cross sections. A part of this volume was visualised using iso-surface rendering (fig. 4C).
The hair fibres in the XRT images were segmented using thresholding (labelling the voxels). The grey value of the hair fibres is lower (darker) than the background making thresholding at a fixed grey level possible. The threshold level has to be selected carefully. A too high threshold level caused smearing of the hair fibres making further separation more complicated. Optimal thresholding shows the scale like-cells (cuticles) on the outer surface (fig. 4C). For iso-surface rendering the labelled voxels were used. By using skeleton operators the centre lines of the hair fibres can be extracted (see fig. 5, skeletonisation will thin down binary features to a single pixel line resembling the framework of the feature). From these lines the cross points can be extracted. The orientation distribution of hair fibres can be estimated using a Gradient Square Tensor (GST).