Automated reconstruction of dendritic and axonal trees by global optimization with geometric priors

From pixels to connections: exploring in vitro neuron reconstruction software for network graph generation

Digital reconstruction has been instrumental in deciphering how in vitro neuron architecture shapes information flow. Emerging approaches reconstruct neural systems as networks with the aim of understanding their organization through graph theory. Computational tools dedicated to this objective build models of nodes and edges based on key cellular features such as somata, axons, and dendrites. Fully automatic implementations of these tools are readily available, but they may also be purpose-built from specialized algorithms in the form of multi-step pipelines. Here we review software tools informing the construction of network models, spanning from noise reduction and segmentation to full network reconstruction. The scope and core specifications of each tool are explicitly defined to assist bench scientists in selecting the most suitable option for their microscopy dataset. Existing tools provide a foundation for complete network reconstruction, however more progress is needed in establishing morphological bases for directed/weighted connectivity and in software validation.

NeuroEditor: a tool to edit and visualize neuronal morphologies

The digital extraction of detailed neuronal morphologies from microscopy data is an essential step in the study of neurons. Ever since Cajal's work, the acquisition and analysis of neuron anatomy has yielded invaluable insight into the nervous system, which has led to our present understanding of many structural and functional aspects of the brain and the nervous system, well beyond the anatomical perspective. Obtaining detailed anatomical data, though, is not a simple task. Despite recent progress, acquiring neuron details still involves using labor-intensive, error prone methods that facilitate the introduction of inaccuracies and mistakes. In consequence, getting reliable morphological tracings usually needs the completion of post-processing steps that require user intervention to ensure the extracted data accuracy. Within this framework, this paper presents NeuroEditor, a new software tool for visualization, editing and correction of previously reconstructed neuronal tracings. This tool has been developed specifically for alleviating the burden associated with the acquisition of detailed morphologies. NeuroEditor offers a set of algorithms that can automatically detect the presence of potential errors in tracings. The tool facilitates users to explore an error with a simple mouse click so that it can be corrected manually or, where applicable, automatically. In some cases, this tool can also propose a set of actions to automatically correct a particular type of error. Additionally, this tool allows users to visualize and compare the original and modified tracings, also providing a 3D mesh that approximates the neuronal membrane. The approximation of this mesh is computed and recomputed on-the-fly, reflecting any instantaneous changes during the tracing process. Moreover, NeuroEditor can be easily extended by users, who can program their own algorithms in Python and run them within the tool. Last, this paper includes an example showing how users can easily define a customized workflow by applying a sequence of editing operations. The edited morphology can then be stored, together with the corresponding 3D mesh that approximates the neuronal membrane.

Tree Recovery by Dynamic Programming

Tree-like structures are common, naturally occurring objects that are of interest to many fields of study, such as plant science and biomedicine. Analysis of these structures is typically based on skeletons extracted from captured data, which often contain spurious cycles that need to be removed. We propose a dynamic programming algorithm for solving the NP-hard tree recovery problem formulated by (Estrada et al. 2015), which seeks a least-cost partitioning of the graph nodes that yields a directed tree. Our algorithm finds the optimal solution by iteratively contracting the graph via node-merging until the problem can be trivially solved. By carefully designing the merging sequence, our algorithm can efficiently recover optimal trees for many real-world data where (Estrada et al. 2015) only produces sub-optimal solutions. We also propose an approximate variant of dynamic programming using beam search, which can process graphs containing thousands of cycles with significantly improved optimality and efficiency compared with (Estrada et al. 2015).

Super-resolution Segmentation Network for Reconstruction of Packed Neurites

Neuron reconstruction can provide the quantitative data required for measuring the neuronal morphology and is crucial in brain research. However, the difficulty in reconstructing dense neurites, wherein massive labor is required for accurate reconstruction in most cases, has not been well resolved. In this work, we provide a new pathway for solving this challenge by proposing the super-resolution segmentation network (SRSNet), which builds the mapping of the neurites in the original neuronal images and their segmentation in a higher-resolution (HR) space. During the segmentation process, the distances between the boundaries of the packed neurites are enlarged, and only the central parts of the neurites are segmented. Owing to this strategy, the super-resolution segmented images are produced for subsequent reconstruction. We carried out experiments on neuronal images with a voxel size of 0.2 μm × 0.2 μm × 1 μm produced by fMOST. SRSNet achieves an average F1 score of 0.88 for automatic packed neurites reconstruction, which takes both the precision and recall values into account, while the average F1 scores of other state-of-the-art automatic tracing methods are less than 0.70.

Querying Representative and Informative Super-Pixels for Filament Segmentation in Bioimages

Segmenting bioimage based filaments is a critical step in a wide range of applications, including neuron reconstruction and blood vessel tracing. To achieve an acceptable segmentation performance, most of the existing methods need to annotate amounts of filamentary images in the training stage. Hence, these methods have to face the common challenge that the annotation cost is usually high. To address this problem, we propose an interactive segmentation method to actively select a few super-pixels for annotation, which can alleviate the burden of annotators. Specifically, we first apply a Simple Linear Iterative Clustering (i.e., SLIC) algorithm to segment filamentary images into compact and consistent super-pixels, and then propose a novel batch-mode based active learning method to select the most representative and informative (i.e., BMRI) super-pixels for pixel-level annotation. We then use a bagging strategy to extract several sets of pixels from the annotated super-pixels, and further use them to build different Laplacian Regularized Gaussian Mixture Models (Lap-GMM) for pixel-level segmentation. Finally, we perform the classifier ensemble by combining multiple Lap-GMM models based on a majority voting strategy. We evaluate our method on three public available filamentary image datasets. Experimental results show that, to achieve comparable performance with the existing methods, the proposed algorithm can save 40 percent annotation efforts for experts.

Deep iterative vessel segmentation in OCT angiography

This paper addresses retinal vessel segmentation on optical coherence tomography angiography (OCT-A) images of the human retina. Our approach is motivated by the need for high precision image-guided delivery of regenerative therapies in vitreo-retinal surgery. OCT-A visualizes macular vasculature, the main landmark of the surgically targeted area, at a level of detail and spatial extent unattainable by other imaging modalities. Thus, automatic extraction of detailed vessel maps can ultimately inform surgical planning. We address the task of delineation of the Superficial Vascular Plexus in 2D Maximum Intensity Projections (MIP) of OCT-A using convolutional neural networks that iteratively refine the quality of the produced vessel segmentations. We demonstrate that the proposed approach compares favourably to alternative network baselines and graph-based methodologies through extensive experimental analysis, using data collected from 50 subjects, including both individuals that underwent surgery for structural macular abnormalities and healthy subjects. Additionally, we demonstrate generalization to 3D segmentation and narrower field-of-view OCT-A. In the future, the extracted vessel maps will be leveraged for surgical planning and semi-automated intraoperative navigation in vitreo-retinal surgery.

Automated Neuron Reconstruction from 3D Fluorescence Microscopy Images Using Sequential Monte Carlo Estimation

Microscopic images of neuronal cells provide essential structural information about the key constituents of the brain and form the basis of many neuroscientific studies. Computational analyses of the morphological properties of the captured neurons require first converting the structural information into digital tree-like reconstructions. Many dedicated computational methods and corresponding software tools have been and are continuously being developed with the aim to automate this step while achieving human-comparable reconstruction accuracy. This pursuit is hampered by the immense diversity and intricacy of neuronal morphologies as well as the often low quality and ambiguity of the images. Here we present a novel method we developed in an effort to improve the robustness of digital reconstruction against these complicating factors. The method is based on probabilistic filtering by sequential Monte Carlo estimation and uses prediction and update models designed specifically for tracing neuronal branches in microscopic image stacks. Moreover, it uses multiple probabilistic traces to arrive at a more robust, ensemble reconstruction. The proposed method was evaluated on fluorescence microscopy image stacks of single neurons and dense neuronal networks with expert manual annotations serving as the gold standard, as well as on synthetic images with known ground truth. The results indicate that our method performs well under varying experimental conditions and compares favorably to state-of-the-art alternative methods.

ROOTS: An Algorithm to Generate Biologically Realistic Cortical Axons and an Application to Electroceutical Modeling

Advances in computation and neuronal modeling have enabled the study of entire neural tissue systems with an impressive degree of biological realism. These efforts have focused largely on modeling dendrites and somas while largely neglecting axons. The need for biologically realistic explicit axonal models is particularly clear for applications involving clinical and therapeutic electrical stimulation because axons are generally more excitable than other neuroanatomical subunits. While many modeling efforts can rely on existing repositories of reconstructed dendritic/somatic morphologies to study real cells or to estimate parameters for a generative model, such datasets for axons are scarce and incomplete. Those that do exist may still be insufficient to build accurate models because the increased geometric variability of axons demands a proportional increase in data. To address this need, a Ruled-Optimum Ordered Tree System (ROOTS) was developed that extends the capability of neuronal morphology generative methods to include highly branched cortical axon terminal arbors. Further, this study presents and explores a clear use-case for such models in the prediction of cortical tissue response to externally applied electric fields. The results presented herein comprise (i) a quantitative and qualitative analysis of the generative algorithm proposed, (ii) a comparison of generated fibers with those observed in histological studies, (iii) a study of the requisite spatial and morphological complexity of axonal arbors for accurate prediction of neuronal response to extracellular electrical stimulation, and (iv) an extracellular electrical stimulation strength-duration analysis to explore probable thresholds of excitation of the dentate perforant path under controlled conditions. ROOTS demonstrates a superior ability to capture biological realism in model fibers, allowing improved accuracy in predicting the impact that microscale structures and branching patterns have on spatiotemporal patterns of activity in the presence of extracellular electric fields.

ShuTu: Open-Source Software for Efficient and Accurate Reconstruction of Dendritic Morphology

Neurons perform computations by integrating inputs from thousands of synapses-mostly in the dendritic tree-to drive action potential firing in the axon. One fruitful approach to studying this process is to record from neurons using patch-clamp electrodes, fill the recorded neurons with a substance that allows subsequent staining, reconstruct the three-dimensional architectures of the dendrites, and use the resulting functional and structural data to develop computer models of dendritic integration. Accurately producing quantitative reconstructions of dendrites is typically a tedious process taking many hours of manual inspection and measurement. Here we present ShuTu, a new software package that facilitates accurate and efficient reconstruction of dendrites imaged using bright-field microscopy. The program operates in two steps: (1) automated identification of dendritic processes, and (2) manual correction of errors in the automated reconstruction. This approach allows neurons with complex dendritic morphologies to be reconstructed rapidly and efficiently, thus facilitating the use of computer models to study dendritic structure-function relationships and the computations performed by single neurons.

Gotta Trace 'em All: A Mini-Review on Tools and Procedures for Segmenting Single Neurons Toward Deciphering the Structural Connectome

Decoding the morphology and physical connections of all the neurons populating a brain is necessary for predicting and studying the relationships between its form and function, as well as for documenting structural abnormalities in neuropathies. Digitizing a complete and high-fidelity map of the mammalian brain at the micro-scale will allow neuroscientists to understand disease, consciousness, and ultimately what it is that makes us humans. The critical obstacle for reaching this goal is the lack of robust and accurate tools able to deal with 3D datasets representing dense-packed cells in their native arrangement within the brain. This obliges neuroscientist to manually identify the neurons populating an acquired digital image stack, a notably time-consuming procedure prone to human bias. Here we review the automatic and semi-automatic algorithms and software for neuron segmentation available in the literature, as well as the metrics purposely designed for their validation, highlighting their strengths and limitations. In this direction, we also briefly introduce the recent advances in tissue clarification that enable significant improvements in both optical access of neural tissue and image stack quality, and which could enable more efficient segmentation approaches. Finally, we discuss new methods and tools for processing tissues and acquiring images at sub-cellular scales, which will require new robust algorithms for identifying neurons and their sub-structures (e.g., spines, thin neurites). This will lead to a more detailed structural map of the brain, taking twenty-first century cellular neuroscience to the next level, i.e., the Structural Connectome.

FMST: an Automatic Neuron Tracing Method Based on Fast Marching and Minimum Spanning Tree

Neuron reconstruction is an important technique in computational neuroscience. Although there are many reconstruction algorithms, few can generate robust results. In this paper, we propose a reconstruction algorithm called fast marching spanning tree (FMST). FMST is based on a minimum spanning tree method (MST) and improve its performance in two aspects: faster implementation and no loss of small branches. The contributions of the proposed method are as follows. Firstly, the Euclidean distance weight of edges in MST is improved to be a more reasonable value, which is related to the probability of the existence of an edge. Secondly, a strategy of pruning nodes is presented, which is based on the radius of a node's inscribed ball. Thirdly, separate branches of broken neuron reconstructions can be merged into a single tree. FMST and many other state of the art reconstruction methods were implemented on two datasets: 120 Drosophila neurons and 163 neurons with gold standard reconstructions. Qualitative and quantitative analysis on experimental results demonstrates that the performance of FMST is good compared with many existing methods. Especially, on the 91 fruitfly neurons with gold standard and evaluated by five metrics, FMST is one of two methods with best performance among all 27 state of the art reconstruction methods. FMST is a good and practicable neuron reconstruction algorithm, and can be implemented in Vaa3D platform as a neuron tracing plugin.

Brain-Wide Shape Reconstruction of a Traced Neuron Using the Convex Image Segmentation Method

Neuronal shape reconstruction is a helpful technique for establishing neuron identity, inferring neuronal connections, mapping neuronal circuits, and so on. Advances in optical imaging techniques have enabled data collection that includes the shape of a neuron across the whole brain, considerably extending the scope of neuronal anatomy. However, such datasets often include many fuzzy neurites and many crossover regions that neurites are closely attached, which make neuronal shape reconstruction more challenging. In this study, we proposed a convex image segmentation model for neuronal shape reconstruction that segments a neurite into cross sections along its traced skeleton. Both the sparse nature of gradient images and the rule that fuzzy neurites usually have a small radius are utilized to improve neuronal shape reconstruction in regions with fuzzy neurites. Because the model is closely related to the traced skeleton point, we can use this relationship for identifying neurite with crossover regions. We demonstrated the performance of our model on various datasets, including those with fuzzy neurites and neurites with crossover regions, and we verified that our model could robustly reconstruct the neuron shape on a brain-wide scale.

A Multiscale Ray-Shooting Model for Termination Detection of Tree-Like Structures in Biomedical Images

Digital reconstruction (tracing) of tree-like structures, such as neurons, retinal blood vessels, and bronchi, from volumetric images and 2D images is very important to biomedical research. Many existing reconstruction algorithms rely on a set of good seed points. The 2D or 3D terminations are good candidates for such seed points. In this paper, we propose an automatic method to detect terminations for tree-like structures based on a multiscale ray-shooting model and a termination visual prior. The multiscale ray-shooting model detects 2D terminations by extracting and analyzing the multiscale intensity distribution features around a termination candidate. The range of scale is adaptively determined according to the local neurite diameter estimated by the Rayburst sampling algorithm in combination with the gray-weighted distance transform. The termination visual prior is based on a key observation-when observing a 3D termination from three orthogonal directions without occlusion, we can recognize it in at least two views. Using this prior with the multiscale ray-shooting model, we can detect 3D terminations with high accuracies. Experiments on 3D neuron image stacks, 2D neuron images, 3D bronchus image stacks, and 2D retinal blood vessel images exhibit average precision and recall rates of 87.50% and 90.54%. The experimental results confirm that the proposed method outperforms other the state-of-the-art termination detection methods.

Artery-vein segmentation in fundus images using a fully convolutional network

Epidemiological studies demonstrate that dimensions of retinal vessels change with ocular diseases, coronary heart disease and stroke. Different metrics have been described to quantify these changes in fundus images, with arteriolar and venular calibers among the most widely used. The analysis often includes a manual procedure during which a trained grader differentiates between arterioles and venules. This step can be time-consuming and can introduce variability, especially when large volumes of images need to be analyzed. In light of the recent successes of fully convolutional networks (FCNs) applied to biomedical image segmentation, we assess its potential in the context of retinal artery-vein (A/V) discrimination. To the best of our knowledge, a deep learning (DL) architecture for simultaneous vessel extraction and A/V discrimination has not been previously employed. With the aim of improving the automation of vessel analysis, a novel application of the U-Net semantic segmentation architecture (based on FCNs) on the discrimination of arteries and veins in fundus images is presented. By utilizing DL, results are obtained that exceed accuracies reported in the literature. Our model was trained and tested on the public DRIVE and HRF datasets. For DRIVE, measuring performance on vessels wider than two pixels, the FCN achieved accuracies of 94.42% and 94.11% on arteries and veins, respectively. This represents a decrease in error of 25% over the previous state of the art reported by Xu et al. (2017). Additionally, we introduce the HRF A/V ground truth, on which our model achieves 96.98% accuracy on all discovered centerline pixels. HRF A/V ground truth validated by an ophthalmologist, predicted A/V annotations and evaluation code are available at https://github.com/rubenhx/av-segmentation.

Reconnection of Interrupted Curvilinear Structures via Cortically Inspired Completion for Ophthalmologic Images

OBJECTIVE

In this paper, we propose a robust, efficient, and automatic reconnection algorithm for bridging interrupted curvilinear skeletons in ophthalmologic images.

METHODS

This method employs the contour completion process, i.e., mathematical modeling of the direction process in the roto-translation group to achieve line propagation/completion. The completion process can be used to reconstruct interrupted curves by considering their local consistency. An explicit scheme with finite-difference approximation is used to construct the three-dimensional (3-D) completion kernel, where we choose the Gamma distribution for time integration. To process structures in , the orientation score framework is exploited to lift the 2-D curvilinear segments into the 3-D space. The propagation and reconnection of interrupted segments are achieved by convolving the completion kernel with orientation scores via iterative group convolutions. To overcome the problem of incorrect skeletonization of 2-D structures at junctions, a 3-D segment-wise thinning technique is proposed to process each segment separately in orientation scores.

RESULTS

Validations on 4 datasets with different image modalities show that our method achieves an average success rate of in reconnecting gaps of sizes from to , including challenging junction structures.

CONCLUSION

The reconnection approach can be a useful and reliable technique for bridging complex curvilinear interruptions.

SIGNIFICANCE

The presented method is a critical work to obtain more complete curvilinear structures in ophthalmologic images. It provides better topological and geometric connectivities for further analysis.

Optimization of Traced Neuron Skeleton Using Lasso-Based Model

Reconstruction of neuronal morphology from images involves mainly the extraction of neuronal skeleton points. It is an indispensable step in the quantitative analysis of neurons. Due to the complex morphology of neurons, many widely used tracing methods have difficulties in accurately acquiring skeleton points near branch points or in structures with tortuosity. Here, we propose two models to solve these problems. One is based on an L1-norm minimization model, which can better identify tortuous structure, namely, a local structure with large curvature skeleton points; the other detects an optimized branch point by considering the combination patterns of all neurites that link to this point. We combined these two models to achieve optimized skeleton detection for a neuron. We validate our models in various datasets including MOST and BigNeuron. In addition, we demonstrate that our method can optimize the traced skeletons from large-scale images. These characteristics of our approach indicate that it can reduce manual editing of traced skeletons and help to accelerate the accurate reconstruction of neuronal morphology.

Identifying Weak Signals in Inhomogeneous Neuronal Images for Large-Scale Tracing of Sparsely Distributed Neurites

Tracing neurites constitutes the core of neuronal morphology reconstruction, a key step toward neuronal circuit mapping. Modern optical-imaging techniques allow observation of nearly complete mouse neuron morphologies across brain regions or even the whole brain. However, high-level automation reconstruction of neurons, i.e., the reconstruction with a few of manual edits requires discrimination of weak foreground points from the inhomogeneous background. We constructed an identification model, where empirical observations made from neuronal images were summarized into rules for designing feature vectors that to classify foreground and background, and a support vector machine (SVM) was used to learn these feature vectors. We embedded this constructed SVM classifier into a previously developed tool, SparseTracer, to obtain SparseTracer-Learned Feature Vector (ST-LFV). ST-LFV can trace sparsely distributed neurites with weak signals (contrast-to-noise ratio < 1.5) against an inhomogeneous background in datasets imaged by widely used light-microscopy techniques like confocal microscopy and two-photon microscopy. Moreover, 12 sub-blocks were extracted from different brain regions. The average recall and precision rates were 99% and 97%, respectively. These results indicated that ST-LFV is well suited for weak signal identification with varying image characteristics. We also applied ST-LFV to trace long-range neurites from images where neurites are sparsely distributed but their image intensities are weak in some cases. When tracing this long-range neurites, manual edit was required once to obtain results equivalent to the ground truth, compared with 20 times of manual edits required by SparseTracer. This improvement in the level of automatic reconstruction indicates that ST-LFV has the potential to rapidly reconstruct sparsely distributed neurons at the large scale.

Visualization of Neuronal Structures in Wide-Field Microscopy Brain Images

Wide-field microscopes are commonly used in neurobiology for experimental studies of brain samples. Available visualization tools are limited to electron, two-photon, and confocal microscopy datasets, and current volume rendering techniques do not yield effective results when used with wide-field data. We present a workflow for the visualization of neuronal structures in wide-field microscopy images of brain samples. We introduce a novel gradient-based distance transform that overcomes the out-of-focus blur caused by the inherent design of wide-field microscopes. This is followed by the extraction of the 3D structure of neurites using a multi-scale curvilinear filter and cell-bodies using a Hessian-based enhancement filter. The response from these filters is then applied as an opacity map to the raw data. Based on the visualization challenges faced by domain experts, our workflow provides multiple rendering modes to enable qualitative analysis of neuronal structures, which includes separation of cell-bodies from neurites and an intensity-based classification of the structures. Additionally, we evaluate our visualization results against both a standard image processing deconvolution technique and a confocal microscopy image of the same specimen. We show that our method is significantly faster and requires less computational resources, while producing high quality visualizations. We deploy our workflow in an immersive gigapixel facility as a paradigm for the processing and visualization of large, high-resolution, wide-field microscopy brain datasets.

Automated Neuron Tracing Methods: An Updated Account

The reconstruction of neuron morphology allows to investigate how the brain works, which is one of the foremost challenges in neuroscience. This process aims at extracting the neuronal structures from microscopic imaging data. The great advances in microscopic technologies have made a huge amount of data available at the micro-, or even lower, resolution where manual inspection is time consuming, prone to error and utterly impractical. This has motivated the development of methods to automatically trace the neuronal structures, a task also known as neuron tracing. This paper surveys the latest neuron tracing methods available in the scientific literature as well as a selection of significant older papers to better place these proposals into context. They are categorized into global processing, local processing and meta-algorithm approaches. Furthermore, we point out the algorithmic components used to design each method and we report information on the datasets and the performance metrics used.

Rivulet: 3D Neuron Morphology Tracing with Iterative Back-Tracking

The digital reconstruction of single neurons from 3D confocal microscopic images is an important tool for understanding the neuron morphology and function. However the accurate automatic neuron reconstruction remains a challenging task due to the varying image quality and the complexity in the neuronal arborisation. Targeting the common challenges of neuron tracing, we propose a novel automatic 3D neuron reconstruction algorithm, named Rivulet, which is based on the multi-stencils fast-marching and iterative back-tracking. The proposed Rivulet algorithm is capable of tracing discontinuous areas without being interrupted by densely distributed noises. By evaluating the proposed pipeline with the data provided by the Diadem challenge and the recent BigNeuron project, Rivulet is shown to be robust to challenging microscopic imagestacks. We discussed the algorithm design in technical details regarding the relationships between the proposed algorithm and the other state-of-the-art neuron tracing algorithms.

Curvature Integration in a 5D Kernel for Extracting Vessel Connections in Retinal Images

Tree-like structures, such as retinal images, are widely studied in computer-aided diagnosis systems for large-scale screening programs. Despite several segmentation and tracking methods proposed in the literature, there still exist several limitations specifically when two or more curvilinear structures cross or bifurcate, or in the presence of interrupted lines or highly curved blood vessels. In this paper, we propose a novel approach based on multi-orientation scores augmented with a contextual affinity matrix, which both are inspired by the geometry of the primary visual cortex (V1) and their contextual connections. The connectivity is described with a 5D kernel obtained as the fundamental solution of the Fokker-Planck equation modeling the cortical connectivity in the lifted space of positions, orientations, curvatures, and intensity. It is further used in a self-tuning spectral clustering step to identify the main perceptual units in the stimuli. The proposed method has been validated on several easy as well as challenging structures in a set of artificial images and actual retinal patches. Supported by quantitative and qualitative results, the method is capable of overcoming the limitations of current state-of-the-art techniques.

Unsupervised Learning and Pattern Recognition of Biological Data Structures with Density Functional Theory and Machine Learning

By introducing the methods of machine learning into the density functional theory, we made a detour for the construction of the most probable density function, which can be estimated by learning relevant features from the system of interest. Using the properties of universal functional, the vital core of density functional theory, the most probable cluster numbers and the corresponding cluster boundaries in a studying system can be simultaneously and automatically determined and the plausibility is erected on the Hohenberg-Kohn theorems. For the method validation and pragmatic applications, interdisciplinary problems from physical to biological systems were enumerated. The amalgamation of uncharged atomic clusters validated the unsupervised searching process of the cluster numbers and the corresponding cluster boundaries were exhibited likewise. High accurate clustering results of the Fisher’s iris dataset showed the feasibility and the flexibility of the proposed scheme. Brain tumor detections from low-dimensional magnetic resonance imaging datasets and segmentations of high-dimensional neural network imageries in the Brainbow system were also used to inspect the method practicality. The experimental results exhibit the successful connection between the physical theory and the machine learning methods and will benefit the clinical diagnoses.

Automated neuron tracing using probability hypothesis density filtering

Motivation

The functionality of neurons and their role in neuronal networks is tightly connected to the cell morphology. A fundamental problem in many neurobiological studies aiming to unravel this connection is the digital reconstruction of neuronal cell morphology from microscopic image data. Many methods have been developed for this, but they are far from perfect, and better methods are needed.

Results

Here we present a new method for tracing neuron centerlines needed for full reconstruction. The method uses a fundamentally different approach than previous methods by considering neuron tracing as a Bayesian multi-object tracking problem. The problem is solved using probability hypothesis density filtering. Results of experiments on 2D and 3D fluorescence microscopy image datasets of real neurons indicate the proposed method performs comparably or even better than the state of the art.

Availability and Implementation

Software implementing the proposed neuron tracing method was written in the Java programming language as a plugin for the ImageJ platform. Source code is freely available for non-commercial use at https://bitbucket.org/miroslavradojevic/phd .

Contact

meijering@imagescience.org.

Supplementary information

Supplementary data are available at Bioinformatics online.

Semi-automatic 3D morphological reconstruction of neurons with densely branching morphology: Application to retinal AII amacrine cells imaged with multi-photon excitation microscopy

BACKGROUND

Accurate reconstruction of the morphology of single neurons is important for morphometric studies and for developing compartmental models. However, manual morphological reconstruction can be extremely time-consuming and error-prone and algorithms for automatic reconstruction can be challenged when applied to neurons with a high density of extensively branching processes.

NEW METHOD

We present a procedure for semi-automatic reconstruction specifically adapted for densely branching neurons such as the AII amacrine cell found in mammalian retinas. We used whole-cell recording to fill AII amacrine cells in rat retinal slices with fluorescent dyes and acquired digital image stacks with multi-photon excitation microscopy. Our reconstruction algorithm combines elements of existing procedures, with segmentation based on adaptive thresholding and reconstruction based on a minimal spanning tree. We improved this workflow with an algorithm that reconnects neuron segments that are disconnected after adaptive thresholding, using paths extracted from the image stacks with the Fast Marching method.

RESULTS

By reducing the likelihood that disconnected segments were incorrectly connected to neighboring segments, our procedure generated excellent morphological reconstructions of AII amacrine cells.

COMPARISON WITH EXISTING METHODS

Reconstructing an AII amacrine cell required about 2h computing time, compared to 2-4days for manual reconstruction. To evaluate the performance of our method relative to manual reconstruction, we performed detailed analysis using a measure of tree structure similarity (DIADEM score), the degree of projection area overlap (Dice coefficient), and branch statistics.

CONCLUSIONS

We expect our procedure to be generally useful for morphological reconstruction of neurons filled with fluorescent dyes.

Segment 2D and 3D Filaments by Learning Structured and Contextual Features

We focus on the challenging problem of filamentary structure segmentation in both 2D and 3D images, including retinal vessels and neurons, among others. Despite the increasing amount of efforts in learning based methods to tackle this problem, there still lack proper data-driven feature construction mechanisms to sufficiently encode contextual labelling information, which might hinder the segmentation performance. This observation prompts us to propose a data-driven approach to learn structured and contextual features in this paper. The structured features aim to integrate local spatial label patterns into the feature space, thus endowing the follow-up tree classifiers capability to grouping training examples with similar structure into the same leaf node when splitting the feature space, and further yielding contextual features to capture more of the global contextual information. Empirical evaluations demonstrate that our approach outperforms state-of-the-arts on well-regarded testbeds over a variety of applications. Our code is also made publicly available in support of the open-source research activities.

Fuzzy-Logic Based Detection and Characterization of Junctions and Terminations in Fluorescence Microscopy Images of Neurons

Digital reconstruction of neuronal cell morphology is an important step toward understanding the functionality of neuronal networks. Neurons are tree-like structures whose description depends critically on the junctions and terminations, collectively called critical points, making the correct localization and identification of these points a crucial task in the reconstruction process. Here we present a fully automatic method for the integrated detection and characterization of both types of critical points in fluorescence microscopy images of neurons. In view of the majority of our current studies, which are based on cultured neurons, we describe and evaluate the method for application to two-dimensional (2D) images. The method relies on directional filtering and angular profile analysis to extract essential features about the main streamlines at any location in an image, and employs fuzzy logic with carefully designed rules to reason about the feature values in order to make well-informed decisions about the presence of a critical point and its type. Experiments on simulated as well as real images of neurons demonstrate the detection performance of our method. A comparison with the output of two existing neuron reconstruction methods reveals that our method achieves substantially higher detection rates and could provide beneficial information to the reconstruction process.

Reconstructing Curvilinear Networks Using Path Classifiers and Integer Programming

We propose a novel approach to automated delineation of curvilinear structures that form complex and potentially loopy networks. By representing the image data as a graph of potential paths, we first show how to weight these paths using discriminatively-trained classifiers that are both robust and generic enough to be applied to very different imaging modalities. We then present an Integer Programming approach to finding the optimal subset of paths, subject to structural and topological constraints that eliminate implausible solutions. Unlike earlier approaches that assume a tree topology for the networks, ours explicitly models the fact that the networks may contain loops, and can reconstruct both cyclic and acyclic ones. We demonstrate the effectiveness of our approach on a variety of challenging datasets including aerial images of road networks and micrographs of neural arbors, and show that it outperforms state-of-the-art techniques.

Neurite Tracing With Object Process

In this paper we present a pipeline for automatic analysis of neuronal morphology: from detection, modeling to digital reconstruction. First, we present an automatic, unsupervised object detection framework using stochastic marked point process. It extracts connected neuronal networks by fitting special configuration of marked objects to the centreline of the neurite branches in the image volume giving us position, local width and orientation information. Semantic modeling of neuronal morphology in terms of critical nodes like bifurcations and terminals, generates various geometric and morphology descriptors such as branching index, branching angles, total neurite length, internodal lengths for statistical inference on characteristic neuronal features. From the detected branches we reconstruct neuronal tree morphology using robust and efficient numerical fast marching methods. We capture a mathematical model abstracting out the relevant position, shape and connectivity information about neuronal branches from the microscopy data into connected minimum spanning trees. Such digital reconstruction is represented in standard SWC format, prevalent for archiving, sharing, and further analysis in the neuroimaging community. Our proposed pipeline outperforms state of the art methods in tracing accuracy and minimizes the subjective variability in reconstruction, inherent to semi-automatic methods.

A Graph-Theoretical Approach for Tracing Filamentary Structures in Neuronal and Retinal Images

The aim of this study is about tracing filamentary structures in both neuronal and retinal images. It is often crucial to identify single neurons in neuronal networks, or separate vessel tree structures in retinal blood vessel networks, in applications such as drug screening for neurological disorders or computer-aided diagnosis of diabetic retinopathy. Both tasks are challenging as the same bottleneck issue of filament crossovers is commonly encountered, which essentially hinders the ability of existing systems to conduct large-scale drug screening or practical clinical usage. To address the filament crossovers' problem, a two-step graph-theoretical approach is proposed in this paper. The first step focuses on segmenting filamentary pixels out of the background. This produces a filament segmentation map used as input for the second step, where they are further separated into disjointed filaments. Key to our approach is the idea that the problem can be reformulated as label propagation over directed graphs, such that the graph is to be partitioned into disjoint sub-graphs, or equivalently, each of the neurons (vessel trees) is separated from the rest of the neuronal (vessel) network. This enables us to make the interesting connection between the tracing problem and the digraph matrix-forest theorem in algebraic graph theory for the first time. Empirical experiments on neuronal and retinal image datasets demonstrate the superior performance of our approach over existing methods.

Retinal Artery-Vein Classification via Topology Estimation

We propose a novel, graph-theoretic framework for distinguishing arteries from veins in a fundus image. We make use of the underlying vessel topology to better classify small and midsized vessels. We extend our previously proposed tree topology estimation framework by incorporating expert, domain-specific features to construct a simple, yet powerful global likelihood model. We efficiently maximize this model by iteratively exploring the space of possible solutions consistent with the projected vessels. We tested our method on four retinal datasets and achieved classification accuracies of 91.0%, 93.5%, 91.7%, and 90.9%, outperforming existing methods. Our results show the effectiveness of our approach, which is capable of analyzing the entire vasculature, including peripheral vessels, in wide field-of-view fundus photographs. This topology-based method is a potentially important tool for diagnosing diseases with retinal vascular manifestation.

NeuroGPS-Tree: automatic reconstruction of large-scale neuronal populations with dense neurites

The reconstruction of neuronal populations, a key step in understanding neural circuits, remains a challenge in the presence of densely packed neurites. Here we achieved automatic reconstruction of neuronal populations by partially mimicking human strategies to separate individual neurons. For populations not resolvable by other methods, we obtained recall and precision rates of approximately 80%. We also demonstrate the reconstruction of 960 neurons within 3 h.

Neuron anatomy structure reconstruction based on a sliding filter

BACKGROUND

Reconstruction of neuron anatomy structure is a challenging and important task in neuroscience. However, few algorithms can automatically reconstruct the full structure well without manual assistance, making it essential to develop new methods for this task.

METHODS

This paper introduces a new pipeline for reconstructing neuron anatomy structure from 3-D microscopy image stacks. This pipeline is initialized with a set of seeds that were detected by our proposed Sliding Volume Filter (SVF), given a non-circular cross-section of a neuron cell. Then, an improved open curve snake model combined with a SVF external force is applied to trace the full skeleton of the neuron cell. A radius estimation method based on a 2D sliding band filter is developed to fit the real edge of the cross-section of the neuron cell. Finally, a surface reconstruction method based on non-parallel curve networks is used to generate the neuron cell surface to finish this pipeline.

RESULTS

The proposed pipeline has been evaluated using publicly available datasets. The results show that the proposed method achieves promising results in some datasets from the DIgital reconstruction of Axonal and DEndritic Morphology (DIADEM) challenge and new BigNeuron project.

CONCLUSION

The new pipeline works well in neuron tracing and reconstruction. It can achieve higher efficiency, stability and robustness in neuron skeleton tracing. Furthermore, the proposed radius estimation method and applied surface reconstruction method can obtain more accurate neuron anatomy structures.

Tree Topology Estimation

Tree-like structures are fundamental in nature, and it is often useful to reconstruct the topology of a tree - what connects to what - from a two-dimensional image of it. However, the projected branches often cross in the image: the tree projects to a planar graph, and the inverse problem of reconstructing the topology of the tree from that of the graph is ill-posed. We regularize this problem with a generative, parametric tree-growth model. Under this model, reconstruction is possible in linear time if one knows the direction of each edge in the graph - which edge endpoint is closer to the root of the tree - but becomes NP-hard if the directions are not known. For the latter case, we present a heuristic search algorithm to estimate the most likely topology of a rooted, three-dimensional tree from a single two-dimensional image. Experimental results on retinal vessel, plant root, and synthetic tree data sets show that our methodology is both accurate and efficient.

Modeling brain circuitry over a wide range of scales

If we are ever to unravel the mysteries of brain function at its most fundamental level, we will need a precise understanding of how its component neurons connect to each other. Electron Microscopes (EM) can now provide the nanometer resolution that is needed to image synapses, and therefore connections, while Light Microscopes (LM) see at the micrometer resolution required to model the 3D structure of the dendritic network. Since both the topology and the connection strength are integral parts of the brain's wiring diagram, being able to combine these two modalities is critically important. In fact, these microscopes now routinely produce high-resolution imagery in such large quantities that the bottleneck becomes automated processing and interpretation, which is needed for such data to be exploited to its full potential. In this paper, we briefly review the Computer Vision techniques we have developed at EPFL to address this need. They include delineating dendritic arbors from LM imagery, segmenting organelles from EM, and combining the two into a consistent representation.

SPIN: a method of skeleton-based polarity identification for neurons

Directional signal transmission is essential for neural circuit function and thus for connectomic analysis. The directions of signal flow can be obtained by experimentally identifying neuronal polarity (axons or dendrites). However, the experimental techniques are not applicable to existing neuronal databases in which polarity information is not available. To address the issue, we proposed SPIN: a method of Skeleton-based Polarity Identification for Neurons. SPIN was designed to work with large-scale neuronal databases in which tracing-line data are available. In SPIN, a classifier is first trained by neurons with known polarity in two steps: 1) identifying morphological features that most correlate with the polarity and 2) constructing a linear classifier by determining a discriminant axis (a specific combination of the features) and decision boundaries. Each polarity-undefined neuron is then divided into several morphological substructures (domains) and the corresponding polarities are determined using the classifier. Finally, the result is evaluated and warnings for potential errors are returned. We tested this method on fruitfly (Drosophila melanogaster) and blowfly (Calliphora vicina and Calliphora erythrocephala) unipolar neurons using data obtained from the Flycircuit and Neuromorpho databases, respectively. On average, the polarity of 84-92 % of the terminal points in each neuron could be correctly identified. An ideal performance with an accuracy between 93 and 98 % can be achieved if we fed SPIN with relatively "clean" data without artificial branches. Our result demonstrates that SPIN, as a computer-based semi-automatic method, provides quick and accurate polarity identification and is particularly suitable for analyzing large-scale data. We implemented SPIN in Matlab and released the codes under the GPLv3 license.

Population-scale three-dimensional reconstruction and quantitative profiling of microglia arbors

MOTIVATION

The arbor morphologies of brain microglia are important indicators of cell activation. This article fills the need for accurate, robust, adaptive and scalable methods for reconstructing 3-D microglial arbors and quantitatively mapping microglia activation states over extended brain tissue regions.

RESULTS

Thick rat brain sections (100-300 µm) were multiplex immunolabeled for IBA1 and Hoechst, and imaged by step-and-image confocal microscopy with automated 3-D image mosaicing, producing seamless images of extended brain regions (e.g. 5903 × 9874 × 229 voxels). An over-complete dictionary-based model was learned for the image-specific local structure of microglial processes. The microglial arbors were reconstructed seamlessly using an automated and scalable algorithm that exploits microglia-specific constraints. This method detected 80.1 and 92.8% more centered arbor points, and 53.5 and 55.5% fewer spurious points than existing vesselness and LoG-based methods, respectively, and the traces were 13.1 and 15.5% more accurate based on the DIADEM metric. The arbor morphologies were quantified using Scorcioni's L-measure. Coifman's harmonic co-clustering revealed four morphologically distinct classes that concord with known microglia activation patterns. This enabled us to map spatial distributions of microglial activation and cell abundances.

AVAILABILITY AND IMPLEMENTATION

Experimental protocols, sample datasets, scalable open-source multi-threaded software implementation (C++, MATLAB) in the electronic supplement, and website (www.farsight-toolkit.org). http://www.farsight-toolkit.org/wiki/Population-scale_Three-dimensional_Reconstruction_and_Quanti-tative_Profiling_of_Microglia_Arbors

CONTACT

broysam@central.uh.edu

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Efficient Monte Carlo image analysis for the location of vascular entity

Tubular shaped networks appear not only in medical images like X-ray-, time-of-flight MRI- or CT-angiograms but also in microscopic images of neuronal networks. We present EMILOVE (Efficient Monte-carlo Image-analysis for the Location Of Vascular Entity), a novel modeling algorithm for tubular networks in biomedical images. The model is constructed using tablet shaped particles and edges connecting them. The particles encode the intrinsic information of tubular structure, including position, scale and orientation. The edges connecting the particles determine the topology of the networks. For simulated data, EMILOVE was able to accurately extract the tubular network. EMILOVE showed high performance in real data as well; it successfully modeled vascular networks in real cerebral X-ray and time-of-flight MRI angiograms. We also show some promising, preliminary results on microscopic images of neurons.

A novel method for identifying a graph-based representation of 3-D microvascular networks from fluorescence microscopy image stacks

A novel approach to determine the global topological structure of a microvasculature network from noisy and low-resolution fluorescence microscopy data that does not require the detailed segmentation of the vessel structure is proposed here. The method is most appropriate for problems where the tortuosity of the network is relatively low and proceeds by directly computing a piecewise linear approximation to the vasculature skeleton through the construction of a graph in three dimensions whose edges represent the skeletal approximation and vertices are located at Critical Points (CPs) on the microvasculature. The CPs are defined as vessel junctions or locations of relatively large curvature along the centerline of a vessel. Our method consists of two phases. First, we provide a CP detection technique that, for junctions in particular, does not require any a priori geometric information such as direction or degree. Second, connectivity between detected nodes is determined via the solution of a Binary Integer Program (BIP) whose variables determine whether a potential edge between nodes is or is not included in the final graph. The utility function in this problem reflects both intensity-based and structural information along the path connecting the two nodes. Qualitative and quantitative results confirm the usefulness and accuracy of this method. This approach provides a mean of correctly capturing the connectivity patterns in vessels that are missed by more traditional segmentation and binarization schemes because of imperfections in the images which manifest as dim or broken vessels.

Automated computation of arbor densities: a step toward identifying neuronal cell types

The shape and position of a neuron convey information regarding its molecular and functional identity. The identification of cell types from structure, a classic method, relies on the time-consuming step of arbor tracing. However, as genetic tools and imaging methods make data-driven approaches to neuronal circuit analysis feasible, the need for automated processing increases. Here, we first establish that mouse retinal ganglion cell types can be as precise about distributing their arbor volumes across the inner plexiform layer as they are about distributing the skeletons of the arbors. Then, we describe an automated approach to computing the spatial distribution of the dendritic arbors, or arbor density, with respect to a global depth coordinate based on this observation. Our method involves three-dimensional reconstruction of neuronal arbors by a supervised machine learning algorithm, post-processing of the enhanced stacks to remove somata and isolate the neuron of interest, and registration of neurons to each other using automatically detected arbors of the starburst amacrine interneurons as fiducial markers. In principle, this method could be generalizable to other structures of the CNS, provided that they allow sparse labeling of the cells and contain a reliable axis of spatial reference.

Active learning of neuron morphology for accurate automated tracing of neurites

Automating the process of neurite tracing from light microscopy stacks of images is essential for large-scale or high-throughput quantitative studies of neural circuits. While the general layout of labeled neurites can be captured by many automated tracing algorithms, it is often not possible to differentiate reliably between the processes belonging to different cells. The reason is that some neurites in the stack may appear broken due to imperfect labeling, while others may appear fused due to the limited resolution of optical microscopy. Trained neuroanatomists routinely resolve such topological ambiguities during manual tracing tasks by combining information about distances between branches, branch orientations, intensities, calibers, tortuosities, colors, as well as the presence of spines or boutons. Likewise, to evaluate different topological scenarios automatically, we developed a machine learning approach that combines many of the above mentioned features. A specifically designed confidence measure was used to actively train the algorithm during user-assisted tracing procedure. Active learning significantly reduces the training time and makes it possible to obtain less than 1% generalization error rates by providing few training examples. To evaluate the overall performance of the algorithm a number of image stacks were reconstructed automatically, as well as manually by several trained users, making it possible to compare the automated traces to the baseline inter-user variability. Several geometrical and topological features of the traces were selected for the comparisons. These features include the total trace length, the total numbers of branch and terminal points, the affinity of corresponding traces, and the distances between corresponding branch and terminal points. Our results show that when the density of labeled neurites is sufficiently low, automated traces are not significantly different from manual reconstructions obtained by trained users.

Extraction of protein profiles from primary neurons using active contour models and wavelets

The function of complex networks in the nervous system relies on the proper formation of neuronal contacts and their remodeling. To decipher the molecular mechanisms underlying these processes, it is essential to establish unbiased automated tools allowing the correlation of neurite morphology and the subcellular distribution of molecules by quantitative means. We developed NeuronAnalyzer2D, a plugin for ImageJ, which allows the extraction of neuronal cell morphologies from two dimensional high resolution images, and in particular their correlation with protein profiles determined by indirect immunostaining of primary neurons. The prominent feature of our approach is the ability to extract subcellular distributions of distinct biomolecules along neurites. To extract the complete areas of neurons, required for this analysis, we employ active contours with a new distance based energy. For locating the structural parts of neurons and various morphological parameters we adopt a wavelet based approach. The presented approach is able to extract distinctive profiles of several proteins and reports detailed morphology measurements on neurites. We compare the detected neurons from NeuronAnalyzer2D with those obtained by NeuriteTracer and Vaa3D-Neuron, two popular tools for automatic neurite tracing. The distinctive profiles extracted for several proteins, for example, of the mRNA binding protein ZBP1, and a comparative evaluation of the neuron segmentation results proves the high quality of the quantitative data and proves its practical utility for biomedical analyses.

Tracing retinal vessel trees by transductive inference

BACKGROUND

Structural study of retinal blood vessels provides an early indication of diseases such as diabetic retinopathy, glaucoma, and hypertensive retinopathy. These studies require accurate tracing of retinal vessel tree structure from fundus images in an automated manner. However, the existing work encounters great difficulties when dealing with the crossover issue commonly-seen in vessel networks.

RESULTS

In this paper, we consider a novel graph-based approach to address this tracing with crossover problem: After initial steps of segmentation and skeleton extraction, its graph representation can be established, where each segment in the skeleton map becomes a node, and a direct contact between two adjacent segments is translated to an undirected edge of the two corresponding nodes. The segments in the skeleton map touching the optical disk area are considered as root nodes. This determines the number of trees to-be-found in the vessel network, which is always equal to the number of root nodes. Based on this undirected graph representation, the tracing problem is further connected to the well-studied transductive inference in machine learning, where the goal becomes that of properly propagating the tree labels from those known root nodes to the rest of the graph, such that the graph is partitioned into disjoint sub-graphs, or equivalently, each of the trees is traced and separated from the rest of the vessel network. This connection enables us to address the tracing problem by exploiting established development in transductive inference. Empirical experiments on public available fundus image datasets demonstrate the applicability of our approach.

CONCLUSIONS

We provide a novel and systematic approach to trace retinal vessel trees with the present of crossovers by solving a transductive learning problem on induced undirected graphs.