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

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the 3D stack. Several automatic algorithms were introduced in the past for the centerline trackingof elongated tubular objects, such as retinal vasculature (Can et al., 1999) and neurons (Zhang etal., 2006). Though being computationally efficient in tracking the centerlines, they fail to workwhen the objects seem to cross each other in the MIP image.The second category of algorithms tracks the centers by segmenting the objects in a sequenceof cross-sectional images in the dataset. A popular algorithm in practice today is the snake model(Kass et al., 1987). It improves on an initial boundary by minimizing an energy functionalconsisting of internal and external energies. The authors of (Cai et al., 2006) proposed animprovement over the original snake model by incorporating a repulsive force to segment closelying cross-sections of axons. Similar to the snake model, the repulsive snake model is unable toaccurately segment the axons of blurred boundaries. Level-sets represent another approach tosegment and track using cross-sectional information, but they are computationally expensive andcan be slow to converge (Xiong et al., 2006).The final set of algorithms deploys 3D methods to track the objects in volumes ofmicroscopic data. The main advantage of these algorithms is that they can track the objectsregardless of their image orientation. The authors of (Al-Kofahi et al., 2002) built on thetemplate based approach in (Can et al., 1999). The axons over short distances were modeled ascylinders with elliptical cross-sections having a certain curvature. Four sets of directionaltemplates were used to track the centers of the axons in each iteration. Another approach wasintroduced in (Tschirren et al., 2005), where the authors used fuzzy connectivity forsegmentation and analysis of intra-thoracic airway trees. The dataset was analyzed iterativelyinside a moving cylindrical region of interest. Inside this cylinder, two regions, foreground andbackground, were grown simultaneously to compete for voxels. The centerlines could then be4
found by skeletonization process. The authors of (Streekstra et al., 2002) used derivatives of aGaussian kernel to find the direction and the location of the centerlines. The orientation of thecenterline is first found by computing the direction along which the second order derivative isthe least in magnitude. In a plane perpendicular to this direction, a point where the gradientvanishes is declared to be the center. Though the algorithms that fall in this category aretheoretically attractive, their computational costs increase significantly with the size andcomplexity of the datasets.Commercially or publicly available software packages, such as NeuronJ (Meijering et al.,2004) and Reconstruct (Fiala, 2005), on the other hand, track the centerlines in such fluorescentmicroscopic stacks interactively. NeuronJ, a plug-in for the freely available software, ImageJ(Abramoff et al., 2004), uses live-wire (Barrett et al., 1997) method to track the centerlines in theMIP image. The user has to select at least two points for each axon and has to guide thecenterline when there is an ambiguity. Reconstruct also needs user intervention when the axonsare close to each other. Manually segmenting huge stacks of data is a painstaking task and canlead to fatigue related bias.A new and computationally efficient tracking algorithm for extracting the centerlines of theaxons in fluorescent microscopy datasets is presented in this paper. We introduce a robust hybridalgorithm to track the centerlines of the axons in three-dimensional space with minimal userintervention. The basic approach is to track well-separated axons in the MIP plane using a lowcomplexitytwo-dimensional approach developed in (Can et al., 1999) and adopt morecomputationally sophisticated algorithms when the centerlines appear to intersect each other inthe MIP image. In addition, we make use of the cross-sectional information as the cross-over ofcenterlines can be easily resolved using this approach. Our approach can be summarized as: (1)5
Page 2 and 3: AbstractThis paper presents a new a
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 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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