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

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towards the center. Similarly, all the seed points in the MIP image are aligned towards the centerof the axon on which they lie.The axons in the MIP image are tracked individually using an iterative process. Thealgorithm is initiated at the first aligned seed point in the image. Using the angle of orientation oftheaxon at this particular location, the next center of the axon is predicted by moving by apredefined step size along this direction. The edges of the axons are then detected as mentionedearlier and any error in prediction is corrected by using the distance of the edges from the center.Since the axon thickness is known to be fairly smooth over small distances, the edge informationof the axon in the previous iteration is used as a constraint to minimize errors. More specifically,the distance of the edges from the center in the current iteration are bounded to lie within acertain limit near the previously detected edge lengths. This limit is set equal to the step size ofthe algorithm, as it can be safely assumed that edge lengths corresponding to close lying centerson an axon have more similarity than those that are far spaced. An axon is said to be completelytraced in the MIP image if the predicted center lies outside the image boundary or in thebackground.During the axon tracking process, seed points are searched in the vicinity of the center, andany seed point found is labeled with the current axon number. Once a particular axon iscompletely traced, the algorithm begins with the next unlabeled seed point in the MIP image. Allthe axons are considered to be traced when every seed point in the image is labeled. Though thismethod is computationally efficient, it cannot track the centerlines when the axons seem to crossoverin the MIP image. Figure 4 shows the cross-over of axons.2.2 Detection of centerlines using cross-sectional informationA cross-over is detected by the algorithm when the centerline of the current axon intersects a12
traced axon in the MIP image. To deal with this situation, we have developed an algorithm thatworks directly on the cross-sectional information. Though this method is accurate, it iscomputationally expensive as compared the method described in the previous section. Therefore,it is applied to only a few sections in the dataset where there is an ambiguity due to the cross-over.An outline of our processing scheme is as follows. First, as mentioned earlier, the crosssectionalimages of axons in the dataset suffer from intensity non-uniformity and blurriness.Hence, all the cross-sectional im ages are preprocessed using the Hessian method of adaptivesmoothing (Carmona et al., 1998). Besides removing noise from the image, this method alsoenhances image features. The axons are then segmented using the seeded watershed algorithm(Gonzalez et al., 1992) to find their centers in the cross-sections. Hence, another set of seedpointsare introduced here that are used as the starting point for the segmentation algorithm.Unlike the previous use of seeds, the ones for this stage of the methods are specified within thecross-sectional images being analyzed and are used to roughly determine the centers of themultiple axons located within the cross section. The mean-shift algorithm (Debeir et al., 2005) isused to find the seed points. Finally, a guided region growing approach is developed toaccurately segment the axons when the seeded watersh ed algorithm fails.The process begins by identifying a cross-sectional slice where the axons in question arewell-separated. Starting from the point of cross-over in the MIP image, a search is initiated tofind a location where the centerlines of the axons are separated by more than a certain distance,d, defined as:d = d current+ d traced(2)where d current and d traced are the diameters of the current and the intersecting axon. They aredetermined by using the left and right edge information from the template based MIP tracking13
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 14 and 15: algorithm. The blue line in Figure
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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