Repulsive force based snake model to segment and track neuronal axons in 3D microscopy image stacks
Introduction
Three-dimensional reconstruction of images of tubular biological objects, such as blood vessels and neuronal processes, has become an active research topic. Such reconstruction can reveal geometrical features (e.g., length, diameter, and orientation) and topological characteristics (e.g., connectivity and branch order) of the biological circuits, which are crucial in understanding the physiology or development of a biological system. One area where this kind of reconstruction is particularly useful is the arbors of individual axons. For example, a “motor unit” which are the axon and muscle fiber targets innervated by a motor axon has been analyzed by tracing the entire arbor of the axon and identifying all the innervated muscle fibers (Keller-Peck et al., 2001, Kasthuri and Lichtman, 2003). Such reconstruction has been made possible by the development of transgenic mice in which only small subsets of motor axons express fluorescent proteins (Feng et al., 2000, Walsh and Lichtman, 2003). Reconstructing larger numbers of axons has not been possible because of the difficulty of segmenting and extracting individual axons when many are running in a tightly fasciculated bundle. It is thus important to develop computational algorithms that will segment individual axons from both the background and other nearby axons. We are particularly interested in making these approaches fully automatic because of the large size of fully resolved confocal data sets of neuromuscular connections (tens of GB).
The absolute requirement for reconstruction is to correctly segment individual objects contained in the specimen. The segmentation process faces several obstacles: each axonal profile usually has irregular shape, orientation, light intensity, and contrast. In addition, different axons are frequently intertwined into tight bundles with limited space between their boundaries, which tends to make the space between objects often brighter than the background. Moreover, the resolution of the images is limited by physical laws of diffraction, leading to ambiguous borders when axons are closer than 0.25 ìm. In order to overcome these problems, several schemes of segmentation have been proposed in the literature, including adaptive thresholding, region growing (grassfire), watershed, active contours (snakes), algorithms based on the variational principles, wavelets, and combination of multiple approaches (Jiang and Mojon, 2003, Mahadevan et al., 2004). However, all these methods suffer from various shortcomings that make them insufficient to segment axons in fasciculated bundles. For instance, watershed algorithm tends to over-segment; region growing, on the other hand, tends to under-segment. Ordinary active contour methods also perform unsatisfactorily when the image contains nearby objects whose intensities are added up at their mutual boundary.
Once segmented in a single 2D plane, each individual axon then needs to be traced throughout the image stack, for which several methods have been suggested. For example, rank statistics-based method has been developed to trace neuronal processes and vasculature from two-dimensional confocal microscope images (Al-Kofahi et al., 2003). Al-Kofahi et al. (2002) presented a different 3D tracing method to locate axons in confocal image stacks. Wavelet based segmentation has been proposed to segment axons based on multiscale edges in 3D (Dima et al., 2002). Fuzzy logic based method has also been developed to process airway in 3D (Park et al., 1998).
In this paper, we propose a snake-based algorithm to segment and trace the 3D objects in an image stack. The advantage of this approach is that it retrieves the topological information robustly from the data. Since the classic snake model is prone to give incorrect segmentation when objects of interest are close to each other, a repulsive force based approach is deployed to address this problem and improve the segmentation performance. To improve image quality, we preprocess raw images by morphological operations to enhance contrast, non-linear filtering to remove noise, and anistropic diffusion to enhance edges.
Section snippets
Materials
Fig. 1 shows the maximum intensity projection (MIP) of motor axons in a peripheral muscle nerve connecting to the omohyoid muscle on the x–y, x–z, and y–z planes. The axons express YFP (Yellow Florescence Protein) in their cytoplasm under the control of the regulatory element of the ubiquitous nervous system gene Thy-1 (Feng et al., 2000). Three-dimensional stacks of images of fluorescently labeled processes are obtained by using confocal microscope.
Preprocessing
As discussed above, methods have been
Results
In this section, we present the results by applying our method to segment and track axons. Our raw data consist of an image stack obtained from a confocal microscope and resampled along the x axis, which gave 200 image slices. There are six axons in the data set. We use different examples to illustrate the effectiveness of our repulsive snake in segmenting and tracking axons. The first example shows that our method can adequately correct error made by the GVF snake in the intermediate steps and
Discussions and conclusions
In this paper, we introduced a snake method based on repulsive force to detect the boundaries of the cross-sections of axons in 2D image and connect the boundaries in 3D to track the axons. The evolution of the snakes is controlled by the two parameters, namely, α and β of (1) where a large α creates a snake of large contraction while a large β favors a final contour of high rigidity and a small β allows the snake to deform toward a corner. The adjustment of the two parameters needs to be
Acknowledgments
X. Xu and S.T.C. Wong were supported by Harvard Center for Neurodegeneration and Repair, Harvard Medical School, Boston, MA, USA.
S.P. Yung was supported by a HKU grant of code 10206889.
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