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

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