Segmentation procedure

When a nerve section is correctly preserved, fixed and stained, it shows the myelin appearing darker in the images (see figure ). Therefore, we can define nerve fibers in our images as objects where a clear region is surrounded by a dark myelin sheath of constant thickness. Beyond this basic definition, let us review a few properties that can be used to differentiate fibers from other structures.
Fibers have a round or ellipsoidal shape, but it is quite frequent to observe some kind of deformation [141,129]. A shape parameter, such as perimeter²/surface, for the axon and myelin sheath - can be used as a helpful criterion, but only in a loose fashion.

  

Figure 4.4: Typical irregularities in fibers. Left: size can vary from 2 to $20 \mu m$ (diameters). Center: densely packed axons are connected. Right: bad fixation and coloration leaves bright rings in the myelin sheath.

Rushton [137] established that the ratio d/D, between the diameter of the axon and that of the whole fiber, is close to 0.6, a value that optimizes the nerve impulse transmission in the myelinated axon.
Unfortunately, the fibers also present a number of highly variable features that can hinder the efficiency of detection algorithms (see figure ). For instance, for mixed nerves containing both sensitive and motor axons, the diameter of the fibers can vary between $1 \mu m$ (the light microscope resolution limit) and $20 \mu m$. Another difficulty comes from the spatial distribution of the fibers: they can be either isolated or densely packed together, which can makes their separation a crucial problem. Finally, fixation and coloration problems can create bright spots within the myelin sheaths, multiple rings, etc.
The method we propose is divided in five steps. First, pixels are classified into myelin (black) or non-myelin (white) pixels according to their luminance. Secondly, the resulting binary image is filtered with connected morphological operators, using rules derived from the above description. Axon candidates are identified in the equivalent zonal graph. Thirdly, the thickness of the myelin sheath around each axon is evaluated, which discards inappropriate candidates and separates adjacent fibers. Fourth, additional morphological criteria are used to detect and discard false fibers. Finally, oblique cuts are detected and a geometrical correction is performed when needed.