Comparison with the manual procedure

For one nerve, 9 images were selected at different nerve locations. Using standard software (NIH image for Macintosh), contour fibers were manually drawn and measured. A total number of 1936 fibers were found by the manual and 1899 by the automatic method. In figure , the manual and automatic histograms are depicted ( $bin = 0.5 \mu m$) in the upper left panel. The fit between both histograms H₁,H₂ made of n bins is evaluated with the $\chi^2$ test, i.e.

  

Figure 4.10: Comparison of fiber size distribution found by the manual and automatic procedures. $\chi^2$ values are placed on the upper right corner for each histogram. The bin size is $0.5 \mu m$.

$$\chi^2= \sum_{b=1}^{n} \frac{(H_1(b)-H_2(b))^2}{H_1(b)+H_2(b)}$$ (4.6)

This value and the number of bins used determine the goodness of the fit. For the complete histogram, there is no significant difference (p > 0.05; n = 26).
In order to get finer results, the histogram is split into its two lobes. The first lobe shows a negligible difference confirmed by the $\chi^2$ test (p > 0.1; n=10). Interestingly, when the second lobe of the manual histogram is left shifted by $0.5 \mu m$, the fitting is highly improved (p > 0.5; n=16). This indicates a slight underestimation of the size of the large fibers by the automatic method.