Graph Refinement based Airway Extraction using Mean-Field Networks and Graph Neural Networks

Graph refinement, or the task of obtaining subgraphs of interest from over-complete graphs, can have many varied applications. In this work, we extract trees or collection of sub-trees from image data by, first deriving a graph-based representation of the volumetric data and then, posing the tree extraction as a graph refinement task. We present two methods to perform graph refinement. First, we use mean-field approximation (MFA) to approximate the posterior density over the subgraphs from which the optimal subgraph of interest can be estimated. Mean field networks (MFNs) are used for inference based on the interpretation that iterations of MFA can be seen as feed-forward operations in a neural network. This allows us to learn the model parameters using gradient descent. Second, we present a supervised learning approach using graph neural networks (GNNs) which can be seen as generalisations of MFNs. Subgraphs are obtained by training a GNN-based graph refinement model to directly predict edge probabilities. We discuss connections between the two classes of methods and compare them for the task of extracting airways from 3D, low-dose, chest CT data. We show that both the MFN and GNN models show significant improvement when compared to one baseline method, that is similar to a top performing method in the EXACT'09 Challenge, and a 3D U-Net based airway segmentation model, in detecting more branches with fewer false positives.Comment: Accepted for publication at Medical Image Analysis. 14 page

Model and Appearance Based Analysis of Neuronal Morphology from Different Microscopy Imaging Modalities

The neuronal morphology analysis is key for understanding how a brain works. This process requires the neuron imaging system with single-cell resolution; however, there is no feasible system for the human brain. Fortunately, the knowledge can be inferred from the model organism, Drosophila melanogaster, to the human system. This dissertation explores the morphology analysis of Drosophila larvae at single-cell resolution in static images and image sequences, as well as multiple microscopy imaging modalities. Our contributions are on both computational methods for morphology quantification and analysis of the influence of the anatomical aspect. We develop novel model-and-appearance-based methods for morphology quantification and illustrate their significance in three neuroscience studies. Modeling of the structure and dynamics of neuronal circuits creates understanding about how connectivity patterns are formed within a motor circuit and determining whether the connectivity map of neurons can be deduced by estimations of neuronal morphology. To address this problem, we study both boundary-based and centerline-based approaches for neuron reconstruction in static volumes. Neuronal mechanisms are related to the morphology dynamics; so the patterns of neuronal morphology changes are analyzed along with other aspects. In this case, the relationship between neuronal activity and morphology dynamics is explored to analyze locomotion procedures. Our tracking method models the morphology dynamics in the calcium image sequence designed for detecting neuronal activity. It follows the local-to-global design to handle calcium imaging issues and neuronal movement characteristics. Lastly, modeling the link between structural and functional development depicts the correlation between neuron growth and protein interactions. This requires the morphology analysis of different imaging modalities. It can be solved using the part-wise volume segmentation with artificial templates, the standardized representation of neurons. Our method follows the global-to-local approach to solve both part-wise segmentation and registration across modalities. Our methods address common issues in automated morphology analysis from extracting morphological features to tracking neurons, as well as mapping neurons across imaging modalities. The quantitative analysis delivered by our techniques enables a number of new applications and visualizations for advancing the investigation of phenomena in the nervous system

Automated Reconstruction of Dendritic and Axonal Trees by Global Optimization with Geometric Priors

We present a novel probabilistic approach to fully automated delineation of tree structures in noisy 2D images and 3D image stacks. Unlike earlier methods that rely mostly on local evidence, ours builds a set of candidate trees over many different subsets of points likely to belong to the optimal tree and then chooses the best one according to a global objective function that combines image evidence with geometric priors. Since the best tree does not necessarily span all the points, the algorithm is able to eliminate false detections while retaining the correct tree topology. Manually annotated brightfield micrographs, retinal scans and the DIADEM challenge datasets are used to evaluate the performance of our method. We used the DIADEM metric to quantitatively evaluate the topological accuracy of the reconstructions and showed that the use of the geometric regularization yields a substantial improvemen

Automatic Multi-Model Fitting for Blood Vessel Extraction

Blood vessel extraction and visualization in 2D images or 3D volumes is an essential clinical task. A blood vessel system is an example of a tubular tree like structure, and fully automated reconstruction of tubular tree like structures remains an open computer vision problem. Most vessel extraction methods are based on the vesselness measure. A vesselness measure, usually based on the eigenvalues of the Hessian matrix, assigns a high value to a voxel that is likely to be a part of a blood vessel. After the vesselness measure is computed, most methods extract vessels based on the shortest paths connecting voxels with a high measure of vesselness. Our approach is quite different. We also start with the vesselness measure, but instead of computing shortest paths, we propose to fit a geometric of vessel system to the vesselness measure. Fitting a geometric model has the advantage that we can choose a model with desired properties and the appropriate goodness-of-fit function to control the fitting results. Changing the model and goodness-of-fit function allows us to change the properties of the reconstructed vessel system structure in a principled way. In contrast, with shortest paths, any undesirable reconstruction properties, such as short-cutting, is addressed by developing ad-hock procedures that are not easy to control. Since the geometric model has to be fitted to a discrete set of points, we threshold the vesselness measure to extract voxels that are likely to be vessels, and fit our geometric model to these thresholded voxels. Our geometric model is a piecewise-line segment model. That is we approximate the vessel structure as a collection of 3D straight line segments of various lengths and widths. This can be regarded as the problem of fitting multiple line segments, that is a multi-model fitting problem. We approach the multi-model fitting problem in the global energy optimization framework. That is we formulate a global energy function that reflects the goodness of fit of our piecewise line segment model to the thresholded vesselness voxels and we use the efficient and effective graph cut algorithm to optimize the energy. Our global energy function consists of the data, smoothness and label cost. The data cost encourages a good geometric fit of each voxel to the line segment it is being assigned to. The smoothness cost encourages nearby line segments to have similar angles, thus encouraging smoother blood vessels. The label cost penalizes overly complex models, that is, it encourages to explain the data with fewer line segment models. We apply our algorithm to the challenging 3D data that are micro-CT images of a mouse heart and obtain promising results

Learning Approach to Delineation of Curvilinear Structures in 2D and 3D Images

Detection of curvilinear structures has long been of interest due to its wide range of applications. Large amounts of imaging data could be readily used in many fields, but it is practically not possible to analyze them manually. Hence, the need for automated delineation approaches. In the recent years Computer Vision witnessed a paradigm shift from mathematical modelling to data-driven methods based on Machine Learning. This led to improvements in performance and robustness of the detection algorithms. Nonetheless, most Machine Learning methods are general-purpose and they do not exploit the specificity of the delineation problem. In this thesis, we present learning methods suited for this task and we apply them to various kinds of microscopic and natural images, proving the general applicability of the presented solutions. First, we introduce a topology loss - a new training loss term, which captures higher-level features of curvilinear networks such as smoothness, connectivity and continuity. This is in contrast to most Deep Learning segmentation methods that do not take into account the geometry of the resulting prediction. In order to compute the new loss term, we extract topology features of prediction and ground-truth using a pre-trained network, whose filters are activated by structures at different scales and orientations. We show that this approach yields better results in terms of conventional segmentation metrics and overall topology of the resulting delineation. Although segmentation of curvilinear structures provides useful information, it is not always sufficient. In many cases, such as neuroscience and cartography, it is crucial to estimate the network connectivity. In order to find the graph representation of the structure depicted in the image, we propose an approach for joint segmentation and connection classification. Apart from pixel probabilities, this approach also returns the likelihood of a proposed path being a part of the reconstructed network. We show that segmentation and path classification are closely related tasks and can benefit from the synergy. The aforementioned methods rely on Machine Learning, which requires significant amounts of annotated ground-truth data to train models. The labelling process often requires expertise, it is costly and tiresome. To alleviate this problem, we introduce an Active Learning method that significantly decreases the time spent on annotating images. It queries the annotator only about the most informative examples, in this case the hypothetical paths belonging to the structure of interest. Contrary to conventional Active Learning methods, our approach exploits local consistency of linear paths to pick the ones that stand out from their neighborhood. Our final contribution is a method suited for both Active Learning and proofreading the result, which often requires more time than the automated delineation itself. It investigates edges of the delineation graph and determines the ones that are especially significant for the global reconstruction by perturbing their weights. Our Active Learning and proofreading strategies are combined with a new efficient formulation of an optimal subgraph computation and reduce the annotation effort by up to 80%

Automated Reconstruction of Dendritic and Axonal Trees by Global Optimization with Geometric Priors

We present a novel probabilistic approach to fully automated delineation of tree structures in noisy 2D images and 3D image stacks. Unlike earlier methods that rely mostly on local evidence, ours builds a set of candidate trees over many different subsets of points likely to belong to the optimal tree and then chooses the best one according to a global objective function that combines image evidence with geometric priors. Since the best tree does not necessarily span all the points, the algorithm is able to eliminate false detections while retaining the correct tree topology. Manually annotated brightfield micrographs, retinal scans and the DIADEM challenge datasets are used to evaluate the performance of our method. We used the DIADEM metric to quantitatively evaluate the topological accuracy of the reconstructions and showed that the use of the geometric regularization yields a substantial improvement

3D interactive coronary artery segmentation using random forests and Markov random field optimization

Coronary artery segmentation plays a vital important role in coronary disease diagnosis and treatment. In this paper, we present a machine learning based interactive coronary artery segmentation method for 3D computed tomography angiography images. We first apply vessel diffusion to reduce noise interference and enhance the tubular structures in the images. A few user strokes are required to specify region of interest and background. Various image features for detecting the coronary arteries are then extracted in a multi-scale fashion, and are fed into a random forests classifier, which assigns each voxel with probability values of being coronary artery and background. The final segmentation is carried through an MRF based optimization using primal dual algorithm. A connectivity component analysis is carried out as post processing to remove isolated, small regions to produce the segmented coronary arterial vessels. The proposed method requires limited user interference and achieves robust segmentation results

Automated Reconstruction of Evolving Curvilinear Tree Structures

Curvilinear networks are prevalent in nature and span many different scales, ranging from micron-scale neural structures in the brain to petameter-scale dark-matter arbors binding massive galaxy clusters. Reliably reconstructing them in an automated fashion is of great value in many different scientific domains. However, it remains an open Computer Vision problem. In this thesis we focus on automatically delineating curvilinear tree structures in images of the same object of interest taken at different time instants. Unlike virtually all of the existing methods approaching the task of tree structures delineation we process all the images at once. This is useful in the more ambiguous regions and allows to reason for the tree structure that fits best to all the acquired data. We propose two methods that utilize this principle of temporal consistency to achieve results of higher quality compared to single time instant methods. The first, simpler method starts by building an overcomplete graph representation of the final solution in all time instants while simultaneously obtaining correspondences between image features across time. We then define an objective function with a temporal consistency prior and reconstruct the structures in all images at once by solving a mathematical optimization. The role of the prior is to encourage solutions where for two consecutive time instants corresponding candidate edges are either both retained or both rejected from the final solution. The second multiple time instant method uses the same overcomplete graph principle but handles the temporal consistency in a more robust way. Instead of focusing on the very local consistency of single edges of the overcomplete graph we propose a method for describing topological relationships. This favors solutions whose connectivity is consistent over time. We show that by making the temporal consistency more global we achieve additional robustness to errors in the initial features matching step, which is shared by both the approaches. In the end, this yields superior performance. Furthermore, an added benefit of both our approaches is the ability to automatically detect places where significant changes have occurred over time, which is challenging when considering large amounts of data. We also propose a simple single time instant method for delineating tree structures. It computes a Minimum Spanning Arborescence of an initial overcomplete graph and proceeds to optimally prune spurious branches. This yields results of lower but still competitive quality compared to the mathematical optimization based methods, while keeping low computational complexity. Our methods can applied to both 2D and 3D data. We demonstrate their performance in 3D on microscopy volumes of mouse brain and rat brain. We also test them in 2D on time-lapse images of a growing runner bean and aerial images of a road network

Reconstructing Curvilinear Networks using Path Classifiers and Integer Programming

We propose a novel Bayesian 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

Methods for Automated Neuron Image Analysis

Knowledge of neuronal cell morphology is essential for performing specialized analyses in the endeavor to understand neuron behavior and unravel the underlying principles of brain function. Neurons can be captured with a high level of detail using modern microscopes, but many neuroscientific studies require a more explicit and accessible representation than offered by the resulting images, underscoring the need for digital reconstruction of neuronal morphology from the images into a tree-like graph structure. This thesis proposes new computational methods for automated detection and reconstruction of neurons from fluorescence microscopy images. Specifically, the successive chapters describe and evaluate original solutions to problems such as the detection of landmarks (critical points) of the neuronal tree, complete tracing and reconstruction of the tree, and the detection of regions containing neurons in high-content screens