## 3 Results
### Automated Segmentation of Layer Thickness  
We now calculate the thickness of the clear coat and base coat layers of the paint samples across the whole B-scan image. We first partition the image to identify the layers automatically using the graph search approach described in the previous section. Using forward first order finite differences as a discrete approximation to the derivative, we calculate the energy functional as an important step in  
Figure 4: **(Top)** LF-FD-OCT image of silver metallic paint sampler (Figure 3b) with two (blue and red) A-Scan locations marked. (**Bottom**) Plot of the red and blue A-Scans, with the apparent thickness measured using only the single A-Scan data. The arrows show the correspondence of the A-Scan peaks with location in the B-Scan image. identifying the contours. An example of this using the silver sample is shown for \(j=0\) and \(j=1\) in Figure 5a,b respectively. The lower values corresponding to the minimiser appear as the darker colour in the figure and are to be traced automatically. While the lowest intensity path may appear clear in each figure, the remaining paths are difficult to trace by sight. Proceeding hierarchically with the graph search approach, we obtain a set of potential interface contours (Figure 5c) which closely match the visible edges. An additional phantom contour is also found which does not represent a layer boundary but does correspond to a solution of the graph-search problem. We now employ our data-fitting step to remove this contour (Figure 5d). At this point, we have a close segmentation of each layer given the presentation of the paint samples in the image. As a final step, we compensate for the visible blurring of the air-clear coat layer interface by replacing the two boundary contours with their mean value to obtain the final segmentation of the silver sample shown in Figure 6a. The same procedure is applied to the blue paint sample and the contours are correctly identified in Figure 6c. It is now a simple procedure to obtain the thickness measurements of each layer across the whole B-Scan (Figure 6b,d). Table 2 gives the mean and standard deviation of these measured thicknesses of the clear coating and base coat, within a B-Scan measurement, for the two samples with both OCT instruments. However, it should be noted that this standard deviation does not have a clear relationship with accuracy or precision of the mean value. The variance is caused by the apparent interface texture in the image, which may be real or, as quite likely in this case, a result of the volume scattering properties of one of the layers. Here reflections from the semi-sparse metallic flakes within the base coat layer dominate giving a lumpy image signal, which the graph search algorithm traces over. The repeatability (precision), for the LF-OCT, of the mean clear and base coat thickness values was quantified by measuring at eight locations on the Indus silver sample, the standard deviation was 2 and 5 nG.m, respectively. The accuracy is determined by the axial resolution (systematic biasing of graph search algorithm to one side of the interface will be of this order  
Figure 5: Segmentation process of LF-OCT B-scan of silver car paint sample. (**a,b**) The joint energy functional used to find the initial contours; (**c**) The initial result using graph-search segmentation; (**d**) The result after automated removal of the phantom contour. of magnitude) and/or scattering homogeneity of the layers (non-homogeneous properties causing the apparent profile undulate into the layer, as is likely in these results). If we treat these as standard error, the accuracy for the given Indus Silver sample LF-OCT measurement is then calculated to be 3 and 4 nG: \(\upmu\)m for the clear and base coat, respectively. In Table 2, the largest difference in mean thickness of both techniques is 3 nG: \(\upmu\)m for the base coat, which is within the measured undulation, precision, and calculated accuracy values of the LF-OCT.