Automated Axon Tracking of 3D Confocal Laser Scanning ...

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algorithm. The blue line in Figure 4 shows this location.Figure 4 - The phenomenon of axon cross-over. The scale bar in the figure corresponds to 4μm. The figure has beenmagnified for better visualization.Since each point on the centerlines of the axons in the MIP image correspond to a crosssectionalslice, as shown in Figure 1, we pull out the corresponding slice from the dataset to startthe cross-sectional analysis. Once the axons are found to be well separated again in threedimensionalspace, the template based tracking is used again to track the axons in the MIPimage.2.2.1 TrackingThe axons in the cross-sectional slices are segmented in order to find the centerlines of theaxons. Apart from providing a good visualization of the axon boundaries in the cross-sections,segmentation helps in the detection of the centers of axons when they have irregular shapes. Toavoid errors in finding the centerlines, all the axons present in the current slice, including thosethat are not yet tracked in MIP image, are tracked together. In order to find the starting points forthe segmentation algorithm, the approximate center points have to be estimated. Thus we14
introduce another set of seed points that initiate the segmentation.We begin the analysis by finding the centers of the axons in the first cross-sectional slice.The centers of the axons traced in the MIP image can be easily found by searching for localintensity maxima in that slice. But, as seen in Figure 4, not all the axons are usually traced in theMIP image before encountering a cross-over. Therefore, the seed points for the rest of the axonsin the first image are identified manually. These serve as the initial seed points for the next slicein the dataset. The axon cross-sections in the current slice will most likely be shifted from theirpositions in the previous slice. So, the centers from the previous cross-section cannot be directlyused as seeds, and need correction. The mean-shift algorithm is used for this purpose.Mean-ShiftThe mean-shift makes use of the intensity information to find the seed points in the image. Itbasically tries to find the approximate center points by searching for the center inside a movingkernel, which is a disc shaped region. The kernel is first placed at the initial seed points obtaineddirectly from the previous cross-section. The center inside the kernel is calculated based on theweighted mean with the intensity as the weights. The seed point is then updated with the meancalculated in the current iteration. The kernel is now centered at the new seed point and thecomputation is repeated again until the algorithm converges or until the number of iterationsreaches a preset threshold.The mean shift algorithm fails when close-lying axons have a considerable difference in theirintensities. The algorithm tends to move towards the brighter axon in such cases, which results inseed point being placed near the edges or sometimes entirely outside the actual axon. This isshown in Figure 6(a) inside the yellow ellipse. The corresponding segmentation result usingseeded watershed algorithm is shown in Figure 6(b).15
Page 2 and 3: AbstractThis paper presents a new a
Page 4 and 5: the 3D stack. Several automatic alg
Page 6 and 7: Track the centerlines in the MIP im
Page 8 and 9: 2.1 Tracking the Axons in the MIP I
Page 10 and 11: algorithm, and therefore must be in
Page 12 and 13: towards the center. Similarly, all
Page 16 and 17: To avoid this problem, we introduce
Page 18 and 19: (a)(b)(c)Figure 7 - Segmentation of
Page 20 and 21: distribution and used to train the
Page 22 and 23: After the region of interest is ide
Page 24 and 25: The number of cross-sections to be
Page 26 and 27: (e)Figure 10 - Tracking results in
Page 28 and 29: Figure 11 - Tracking results in dat
Page 30 and 31: In comparison with the manual track
Page 32 and 33: algorithm worked for five consecuti
Page 34 and 35: dataset in a direction normal to th
Page 36 and 37: ReferencesAbramoff M.D., Magelhaes,
Page 38: Imaging. 24(12), 1529- 1539.Wang M.

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