Discussion

In the above section, we show that the automatic procedure gives results that are very similar to the manual procedure for a given set of images. Because of the following considerations, we may even claim that the automatic procedure can be more accurate than the manual one, because it is able to process the entirety of the available data set.
Manual procedures use a uniform sampling scheme in order to maintain an equal representation of all locations within the nerve cross section. Mayhew [105] or Fiola [50] consider $10 \%$ of the entire nerve surface as the optimal area to examine. On the other hand, Torch [158] shows that myelin fibers are not randomly distributed within nerves and concludes that it would be necessary to perform measures on at least $50\%$ of the nerve bundle in order to keep an acceptable representation of the fiber populations. This non-random distribution may also be increased by pathological conditions where the fiber loss is either focal, as it has been described for diphtheritic polyneuritis, amyloidosis, leprosy and primary nerve tumors (Fisher [51], Rukaniva [136], Simpson [148] and Rudge [135]) or multi-focal as in diabetic neuropathy ( Thomas [154]).
The computational cost of the method is a critical parameter due to the considerable amount of data to be processed to study a complete cross-section of a nerve. Most of the processing is performed on the zonal graph, not on the image itself. Because this graph is orders of magnitude smaller than the image, the cost of the connected operators filtering is negligible. The main computational costs lie in the thresholding step, in the generation of the zonal graph and in the evaluation of the myelin sheath's thickness. Globally, the method requires less than one minute on a Pentium II, 233MHz computer to process a $1850 \times 1234$ pixels image. This means between one and two hours to process a complete cross-section.
In conclusion, the above procedure is a fast and accurate method for the morphometry of nerve cross-section.