Anisotropic path searching for automatic neuron reconstruction
Graphical abstract
A template-free approach is introduced for automating the 3D reconstruction of neuritis from microscopy volumes. The complex neuronal structures are captured with an efficient adaptive seeding method and the tracing problem is solved by computing the optimal reconstruction from the weighted graph constructed with those optimal seeds. The proposed algorithm is computational efficient and has generated promising results on various sets of microscopy images.■■
Highlights
► A efficient algorithm for automatic neuron reconstruction. ► The algorithm can handle complex structures adaptively and optimize the localization of bifurcations. ► A reliable technique to compare various of neurons for tracing evaluation and neuron retrival.
Introduction
The tasks of extracting neuron structures from microscope images and accurately measuring their topology properties are important for a large number of studies in biology and medicine. In particular, the accurate reconstruction of individual neurons in the system is an essential prerequisite for understanding of how a nervous system functions. However, biologists usually have to rely on time-consuming manual or semi-automatic methods to annotate the neurite structures in practice. Manual tracing is subjective and error-prone given the possible large scale of problem and the variance of neuron image properties in the realistic applications. Therefore, an effective fully-automated reconstruction method is highly-desired. Although there is a long history of attempting to solve this problem in the literature (Cohen et al., 1994, Can et al., 1999) and some commercial products are available (e.g., Neurolucida from MBF Bioscience), no generic automated method has achieved accurate reconstruction that requires no or few manual corrections except on atypical data. This shortcoming is fast becoming the bottleneck in the realization of the high-throughput neuron structure analysis that biologists are contemplating today.
Most existing automatic tracing methods are based upon the fact that a neuron usually forms a branching tree structure. The problem of reconstructing a neuron is thus formulated as determining where the branches go and how they bifurcate. For this reason, the problem is also called neuron tracing. Meijering et al. (2004) suggested a two-dimensional (2D) method that employed local principal ridge direction to guide the live-wire algorithm to trace centerlines. While there are some other 2D methods (e.g., Xiong et al., 2006), they suffer a major drawback that most data today is from 3D confocal scans and generally neuron traces overlap in 2D projections. Therefore a successful strategy for realistic tracing applications has to apply on three-dimensional (3D) images.
In 1994, Cohen et al. (1994) introduced a 3D tracing method based on skeletonization and graph extraction. The same strategy was applied by Koh et al. (2002) but with a modified medial axis to locate dendritic branch centerlines. Bullitt et al. (2001) proposed a seeded central line extraction approach for the vessel tracing problem. Zhang et al. (2007) proposed to generate a complete reconstruction by assembling a set of skeleton segments detected from a neurite structure. However, 3D skeletonization is computationally expensive and the noise in the microscopy data presents a significant challenge for the thinning operation that is at the heart of such approaches.
More recently proposed methods tend to use parametric models for filament tracing (e.g., Shen et al., 2001, Zana and Klein, 2001, Yim et al., 2000, Quek and Kirbas, 2001, Kirbas and Quek, 2004). Al-kofahi et al. (2002) applied a predetermined deformable template to detect short, local segments of neurite structures and their orientations, and used these to generate the final reconstruction. He et al. (2003) proposed to combine local estimates of the “filament probability” with a graph-theoretic approach that attempts to join and prune detected filaments into a single-tree structure. If the image was high-contrast and the neurite structure is well connected, then template based tracing (e.g., tubular or sphere (Al-kofahi et al., 2003)) performs quite well. However, for many often used imaging protocols, significant noise would present in the recorded images and there are significant drops in signal in some sections due to the uneven distribution of the contrast agent within neurites.
In this work, we follow the optimal tree idea to reconstruct neuron morphology in 3D microscopy data. Since the morphological structure is of primary interest, we focus on reliably reconstructing the complete structure. An accurate segmentation of neurite body is plus but not the emphasis of this paper. Our method first detects a set of significant points, or seeds, on the structures of interest in the image volume. An effective technique is developed so that seeds are dense enough to describe the major characteristics of the neuronal structures such as branches and terminals, but also as compact as possible, in order to avoid redundancies and to improve computational efficiency. A tree structure is then constructed from those seeds by finding a minimum spanning tree connecting them, where the edge length between seeds is a geodesic distance between the seeds in question.
The accurate evaluation of the automatic reconstructions is an important issue for the development of the automatic tracing system. Given a ground-truth generated from human annotation or with some semi-automatic tools (e.g., Peng et al., 2010), visual examination of an automated result is straight-forward but prone to subjective errors and cannot provide a comprehensive assessment. Vasilkoski and Stepanyants (2009) proposed to measure the difference between two traces in terms of five features of neuron morphology, including the total arbor length, the tortuosity of neuronal branches, the number of end-points, the proximity of the arbors, and the placement of branch-points. However, those feature statistics can provide only a preliminary evaluation and are not scale-invariant. Nonetheless, it is admirable to know where those differences in their statistics occur in local corresponding regions of the reconstruction and the grand-truth. This requires the piecewise correspondences among different instances of the reconstruction. To this end, Al-kofahi et al. (2003) proposed to compute the average Euclidean distance between closest nodes (within a pre-selected distance) on different traces. This soft-matching strategy is intuitive but vulnerable to the structural complexity due to the lack of a constraint on spatial ordering.
In this paper, we present a fully-automatic neuron comparison method which can be used to establish the global optimal matching between ground-truth and automatic trace effectively. In addition, two metrics are introduced based on the resulting correspondences to show how to produce the quantitative assessment of the automatic tracing system.
The paper is organized as follows. The proposed template-free tracing framework is presented in Section 2, including the global thresholding strategy for background removal and de-noising, an adaptive seeding technique to capture the spread of the single, and the anisotropic path searching (APS) method to determine the optimal connections among the seeds. The automatic neuron comparison method will be introduced in Section 3. The metrics for tracing evaluation will also be presented. Section 4 illustrates and discusses the experimental results of our algorithm on various microscopy data sets. Finally, we conclude in Section 5.
Section snippets
Method
The tracing approach involves (1) automatic seeding of neurite structures from microscopy data, (2) definition of connectivity among the seeds and (3) the construction of the optimal neuron tree structure. Also the evaluation of results against ground-truth generated from experts is addressed in this section. The approach is applicable to extract fiber-like objects from any type of 3D image data. In this paper, we employed three different data sets of three-dimensional microscopy images. The
Trace comparison and tracing evaluation
In order to quantitatively study the performance of the tracing system, it is essential to select reliable metrics to validate the automatic traces in comparison with some gold-standard or ground-truth such as manual annotation. It is the major interest of neuroscientists to determine the topology of the neurite structure, such as the bifurcation locations and branch sizes. Thus the matching of those critical nodes in the traces is a top priority. In addition, establishing the correspondences
Experimental results
We tested the proposed APS tracing algorithm on microscopy images with various image quality and structural complexity. One of the tracing results on a challenging image is demonstrated in Fig. 9. The figure at left shows the Maximum Intensity Projection along the Z-axis of the 3D microscopy stack of a projection neuron of adult Drosophila. The figure at right shows the automatic trace overlapped with the image. The proposed tracing method generated a clean reconstruction covering most of the
Conclusion
In this paper, we presented an automated tracing algorithm, APS, for reconstructing neuronal structures in 3D microscopy images. Since it works only on the foreground structures rather than the entire image volume, the proposed method is adaptive and efficient. Instead of assuming particular morphological structures, an anisotropic path searching technique is applied in the proposed method to detect the optimal traces. The optimal reconstruction is based on the visual significance of the
Acknowledgments
We thank Aljoscha Nern for generating the presynaptic site brain images and Margaret Jefferies for helping text edit the manuscript.
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