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Fig. 7.6 An illustration of the dual-model enhancement results. The dual-model algorithm was applied on the original CCM image on the left resulting in the response image on the right. Even the structures of small and faint nerve fibers were enhanced

7.4.4 Postprocessing the Enhanced-Contrast Image

Once the CCM image is enhanced, the detection of the nerve fibers becomes a trivial task. The response image of the dual-model has a zero value for a background pixel and a value that is greater than zero, up to unity for everything else. This makes global thresholding of intensities an effective technique of separating background and foreground.

Changing the threshold value of the dual-model detector α in (7.5) and (7.6) will change the sensitivity of the detection as shown in Fig. 7.7. A lower threshold value will produce sensitive detection even for the very faint nerve fibers. However, this will also cause a more noisy response image due to the false positive detected nerve fibers that are represented as small fragments. These fragments can then be easily filtered out by simple postprocessing techniques as shown in Fig. 7.7.

The values that correspond to foreground pixels, that is, pixels on a nerve fiber, represent a confidence measure. The higher the value the more likely this is a nerve fiber pixel. Once the image is thresholded and turned into a binary form, zeros for background and ones for foreground, nerve fibers appear as thick ridges flowing across the image. This is followed by morphological operators to eliminate islands (separate pixels) between nerve fibers and to reduce the number of spurs in the thinned image.

To be able to estimate the center of these ridges, that is, the one-pixel line detection of nerve fibers, the binary linear structures are thinned using [42]. The skeletonized image (e.g., Fig. 7.8) provides a straightforward representation for

7 Detecting and Analyzing Linear Structures in Biomedical Images: A Case Study...

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Fig. 7.7 An illustration of the dual-model enhancement threshold α on the response image. The first column contains the original CCM; the images in the second column are enhanced with a relatively high threshold. The images in the third and the last column are enhanced with the same low threshold but the images in the last column are also postprocessed to remove small fragmented nerve fibers

Fig. 7.8 After the original CCM image is enhanced to exploit the nerve fiber structures, the image is thresholded to produce a binary image which is then thinned to a skeleton image as shown in the last image on the right

defining the image features described in Sect. 7.3.3. NFL is simply the count of pixels with binary value of one. Fully connected lines of detected pixels that have a length greater than a certain threshold are counted to give the number of major nerve fibers in the CCM image and used to compute the NFD.

At each pixel on the skeleton, we can calculate the crossing number [43], which defines the number of neighbors the pixel has on the skeleton. One defines an end point, two is a ridge point, and three or more indicate a branch point. This allows us to recognize and count branch points.