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Confluent Vessel Trees with Accurate Bifurcations
... Zhang et al.explored several unsupervised geometry-based methods for tubular object reconstruction. The divergence prior (Zhang et al., 2019) and confluence property (Zhang et al., 2021b) were incorporated as the explicit constraints to improve reconstruction accuracy. ...
... Zhang et al.explored several unsupervised geometry-based methods for tubular object reconstruction. The divergence prior (Zhang et al., 2019) and confluence property (Zhang et al., 2021b) were incorporated as the explicit constraints to improve reconstruction accuracy. ...
Open international challenges are becoming the de facto standard for assessing computer vision and image analysis algorithms. In recent years, new methods have extended the reach of pulmonary airway segmentation that is closer to the limit of image resolution. Since EXACT'09 pulmonary airway segmentation, limited effort has been directed to quantitative comparison of newly emerged algorithms driven by the maturity of deep learning based approaches and clinical drive for resolving finer details of distal airways for early intervention of pulmonary diseases. Thus far, public annotated datasets are extremely limited, hindering the development of data-driven methods and detailed performance evaluation of new algorithms. To provide a benchmark for the medical imaging community, we organized the Multi-site, Multi-domain Airway Tree Modeling (ATM'22), which was held as an official challenge event during the MICCAI 2022 conference. ATM'22 provides large-scale CT scans with detailed pulmonary airway annotation, including 500 CT scans (300 for training, 50 for validation, and 150 for testing). The dataset was collected from different sites and it further included a portion of noisy COVID-19 CTs with ground-glass opacity and consolidation. Twenty-three teams participated in the entire phase of the challenge and the algorithms for the top ten teams are reviewed in this paper. Quantitative and qualitative results revealed that deep learning models embedded with the topological continuity enhancement achieved superior performance in general. ATM'22 challenge holds as an open-call design, the training data and the gold standard evaluation are available upon successful registration via its homepage.
Computational fluid dynamics (CFD) simulation provides valuable information on blood flow from the vascular geometry. However, it requires extracting precise models of arteries from low-resolution medical images, which remains challenging. Centerline-based representation is widely used to model large vascular networks with small vessels, as it encodes both the geometric and topological information and facilitates manual editing. In this work, we propose an automatic method to generate a structured hexahedral mesh suitable for CFD directly from centerlines. We addressed both the modeling and meshing tasks. We proposed a vessel model based on penalized splines to overcome the limitations inherent to the centerline representation, such as noise and sparsity. The bifurcations are reconstructed using a parametric model based on the anatomy that we extended to planar n-furcations. Finally, we developed a method to produce a volume mesh with structured, hexahedral, and flow-oriented cells from the proposed vascular network model. The proposed method offers better robustness to the common defects of centerlines and increases the mesh quality compared to state-of-the-art methods. As it relies on centerlines alone, it can be applied to edit the vascular model effortlessly to study the impact of vascular geometry and topology on hemodynamics. We demonstrate the efficiency of our method by entirely meshing a dataset of 60 cerebral vascular networks. 92% of the vessels and 83% of the bifurcations were meshed without defects needing manual intervention, despite the challenging aspect of the input data. The source code is released publicly.
Extracting the cerebral anterior vessel tree of patients with an intracranial large vessel occlusion (LVO) is relevant to investigate potential biomarkers that can contribute to treatment decision making. The purpose of our work is to develop a method that can achieve this from routinely acquired computed tomography angiography (CTA) and computed tomography perfusion (CTP) images.
To this end, we regard the anterior vessel tree as a set of bifurcations and connected centerlines. The method consists of a proximal policy optimization (PPO) based deep reinforcement learning (DRL) approach for tracking centerlines, a convolutional neural network based bifurcation detector, and a breadth-first vessel tree construction approach taking the tracking and bifurcation detection results as input. We experimentally determine the added values of various components of the tracker. Both DRL vessel tracking and CNN bifurcation detection were assessed in a cross validation experiment using 115 subjects. The anterior vessel tree formation was evaluated on an independent test set of 25 subjects, and compared to interobserver variation on a small subset of images.
The DRL tracking result achieves a median overlapping rate until the first error (1.8 mm off the reference standard) of 100, [46, 100] % on 8032 vessels over 115 subjects. The bifurcation detector reaches an average recall and precision of 76% and 87% respectively during the vessel tree formation process. The final vessel tree formation achieves a median recall of 68% and precision of 70%, which is in line with the interobserver agreement.
A vectorial representation of the vascular network that embodies quantitative features - location, direction, scale, bifurcations - has many potential cardio- and neuro-vascular applications. We present VTrails, an end-to-end approach to extract geodesic vascular minimum spanning trees from angiographic data by solving a connectivity-optimised anisotropic level-set over a voxel-wise tensor field representing the orientation of the underlying vasculature. Evaluating real and synthetic vascular images, we compare VTrails against the state-of-the-art ridge detectors for tubular structures by assessing the connectedness of the vesselness map and inspecting the synthesized tensor field. The inferred geodesic trees are then quantitatively evaluated within a topologically-aware framework, by comparing the proposed method against popular vascular segmentation tool-kits on clinical angiographies. VTrails potentials are discussed towards integrating group-wise vascular image analyses. The performance of VTrails demonstrates its versatility and usefulness also for patient-specific applications in interventional neuroradiology and vascular surgery.
The analysis of thin curvilinear objects in 3D images is a complex and challenging task. In this article, we introduce a new, nonlinear operator, called RORPO (Ranking Orientation Responses of Path Operators). Inspired by the multidirectional paradigm currently used in linear filtering for thin structure analysis, RORPO is built upon the notion of path operator from mathematical morphology. This operator, unlike most operators commonly used for 3D curvilinear structure analysis, is discrete, non-linear and non-local. From this new operator, two main curvilinear structure characteristics can be estimated: an intensity feature, that can be assimilated to a quantitative measure of curvilinearity; and a directional feature, providing a quantitative measure of the structure's orientation. We provide a full description of the structural and algorithmic details for computing these two features from RORPO, and we discuss computational issues.We experimentally assess RORPO by comparison with three of the most popular curvilinear structure analysis filters, namely Frangi Vesselness, Optimally Oriented Flux, and Hybrid Diffusion with Continuous Switch. In particular, we show that our method provides up to 8% more true positive and 50% less false positives than the next best method, on synthetic and real 3D images.
In this paper, we propose a novel curvature-penalized minimal path model via an orientation-lifted Finsler metric and the Euler elastica curve. The original minimal path model computes the globally minimal geodesic by solving an Eikonal partial differential equation (PDE). Essentially, this first-order model is unable to penalize curvature which is related to the path rigidity property in the classical active contour models. To solve this problem, we present an Eikonal PDE-based Finsler elastica minimal path approach to address the curvature-penalized geodesic energy minimization problem. We were successful at adding the curvature penalization to the classical geodesic energy. The basic idea of this work is to interpret the Euler elastica bending energy via a novel Finsler elastica metric that embeds a curvature penalty. This metric is non-Riemannian, anisotropic and asymmetric, and is defined over an orientation-lifted space by adding to the image domain the orientation as an extra space dimension. Based on this orientation lifting, the proposed minimal path model can benefit from both the curvature and orientation of the paths. Thanks to the fast marching method, the global minimum of the curvature-penalized geodesic energy can be computed efficiently.
We introduce two anisotropic image data-driven speed functions that are computed by steerable filters. Based on these orientation-dependent speed functions, we can apply the proposed Finsler elastica minimal path model to the ap- plications of closed contour detection, perceptual grouping and tubular structure extraction. Numerical experiments on both synthetic and real images show that these applications of the proposed model indeed obtain promising results.
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.
Many applications in vision require estimation of thin structures such as
boundary edges, surfaces, roads, blood vessels, neurons, etc. Unlike most
previous approaches, we simultaneously detect and delineate thin structures
with sub-pixel localization and real-valued orientation estimation. This is an
ill-posed problem that requires regularization. We propose an objective
function combining detection likelihoods with a prior minimizing curvature of
the center-lines or surfaces. Unlike simple block-coordinate descent, we
develop a novel algorithm that is able to perform joint optimization of
location and detection variables more effectively. Our lower bound optimization
algorithm applies to quadratic or absolute curvature. The proposed early vision
framework is sufficiently general and it can be used in many higher-level
applications. We illustrate the advantage of our approach on a range of 2D and
3D examples.
Recently, Fredman and Tarjan invented a new, especially efficient form of heap (priority queue). Their data structure, the Fibonacci heap (or F-heap) supports arbitrary deletion in O(log n) amortized time and other heap operations in O(1) amortized time. In this paper we use F-heaps to obtain fast algorithms for finding minimum spanning trees in undirected and directed graphs. For an undirected graph containing n vertices and m edges, our minimum spanning tree algorithm runs in O(m log β (m, n)) time, improved from O(mβ(m, n)) time, where β(m, n)=min {i|log(i) n ≦m/n}. Our minimum spanning tree algorithm for directed graphs runs in O(n log n + m) time, improved from O(n log n +m log log log(m/n+2) n). Both algorithms can be extended to allow a degree constraint at one vertex.
We present a novel approach to 3D delineation of dendritic networks in noisy image stacks. We achieve a level of automation
beyond that of state-of-the-art systems, which model dendrites as continuous tubular structures and postulate simple appearance
models. Instead, we learn models from the data itself, which make them better suited to handle noise and deviations from expected
appearance.
From very little expert-labeled ground truth, we train both a classifier to recognize individual dendrite voxels and a density
model to classify segments connecting pairs of points as dendrite-like or not. Given these models, we can then trace the dendritic
trees of neurons automatically by enforcing the tree structure of the resulting graph. We will show that our approach performs
better than traditional techniques on brighfield image stacks.
This paper proposes a novel curvilinear structure detector, called Op- timally Oriented Flux (OOF). OOF finds an optimal axis on which image gradi- ents are projected in order to compute the image gradient flux. The computation of OOF is localized at the boundaries of local spherical regions. It avoids con- sidering closely located adjacent structures. The main advantage of OOF is its robustness against the disturbance induced by closely located adjacent objects. Moreover, the analytical formulation of OOF introduces no additional computa- tion load as compared to the calculation of the Hessian matrix which is widely used for curvilinear structure detection. It is experimentally demonstrated that OOF delivers accurate and stable curvilinear structure detection responses under the interference of closely located adjacent structures as well as image noise.
We present a new interactive method for tubular structure extraction. The main application and motivation for this work is
vessel tracking in 2D and 3D images. The basic tools are minimal paths solved using the fast marching algorithm. This allows
interactive tools for the physician by clicking on a small number of points in order to obtain a minimal path between two
points or a set of paths in the case of a tree structure. Our method is based on a variant of the minimal path method that
models the vessel as a centerline and surface. This is done by adding one dimension for the local radius around the centerline.
The crucial step of our method is the definition of the local metrics to minimize. We have chosen to exploit the tubular structure
of the vessels one wants to extract to built an anisotropic metric. The designed metric is well oriented along the direction
of the vessel, admits higher velocity on the centerline, and provides a good estimate of the vessel radius. Based on the optimally
oriented flux this measure is required to be robust against the disturbance introduced by noise or adjacent structures with
intensity similar to the target vessel. We obtain promising results on noisy synthetic and real 2D and 3D images and we present
a clinical validation.
Ordered labeled trees are trees in which the left-to-right order among siblings is significant. The distance between two ordered trees is considered to be the weighted number of edit operations (insert, delete, and modify) to transform one tree to another. The problem of approximate tree matching is also considered. Specifically, algorithms are designed to answer the following kinds of questions: 1. What is the distance between two trees? 2. What is the minimum distance between T 1 and T 2 when zero or more subtrees can be removed from T 2 ? 3. Let the pruning of a tree at node n mean removing all the descendants of node n. The analogous question for prunings as for subtrees is answered. A dynamic programming algorithm is presented to solve the three questions in sequential time O(|T 1 |×|T 2 |×min(depth(T 1 ),leaves(T 1 ))×min(depth(T 2 ),leaves(T 2 ))) and space O(|T 1 |×|T 2 |) compared with O(|T 1 |×|T 2 |×(depth(T 1 )) 2 ×(depth(T 2 )) 2 ) for the best previous published algorithm due to Tai [J. Assoc. Comput. Mach. 26, 422-433 (1979; Zbl 0409.68040)]. Further, the algorithm presented here can be parallelized to give time O(|T 1 |+|T 2 |).
Confluent graphs capture the connection properties of train tracks, offering a very natural generalization of planar graphs, and – as the example of railroad maps shows – are an important tool in graph visualization. In this paper we continue the study of confluent graphs, in- troducing strongly confluent graphs and tree-confluent graphs. We show that strongly confluent graphs can be recognized in NP (the complex- ity of recognizing confluent graphs remains open). We also give a natu- ral elimination ordering characterization of tree-confluent graphs which shows that they form a subclass of the chordal bipartite graphs, and can be recognized in polynomial time.
An approach is described for curve inference that is based on curvature information. The inference procedure is divided into two stages: a trace inference stage, which is the subject of the present work, and a curve synthesis stage. It is shown that recovery of the trace of a curve requires estimating local models for the curve at the same time, and that tangent and curvature information are sufficient. These make it possible to specify powerful constraints between estimated tangents to a curve, in terms of a neighborhood relationship called cocircularity, and between curvature estimates, in terms of a curvature consistency relation. Because all curve information is quantized, special care must be taken to obtain accurate estimates of trace points, tangents, and curvatures. This issue is addressed specifically to the introduction of a smoothness constraint and a maximum curvature constraint. The procedure is applied to two types of images: artificial images designed to evaluate curvature and noise sensitivity, and natural images
Digital reconstruction, or tracing, of 3D neuron structures is critical toward reverse engineering the wiring and functions of a brain. However, despite a number of existing studies, this task is still challenging, especially when a 3D microscopic image has low signal-to-noise ratio (SNR) and fragmented neuron segments. Published work can handle these hard situations only by introducing global prior information, such as where a neurite segment starts and terminates. However, manual incorporation of such global information can be very time consuming. Thus, a completely automatic approach for these hard situations is highly desirable.
We have developed an automatic graph algorithm, called the all-path pruning (APP), to trace the 3D structure of a neuron. To avoid potential mis-tracing of some parts of a neuron, an APP first produces an initial over-reconstruction, by tracing the optimal geodesic shortest path from the seed location to every possible destination voxel/pixel location in the image. Since the initial reconstruction contains all the possible paths and thus could contain redundant structural components (SC), we simplify the entire reconstruction without compromising its connectedness by pruning the redundant structural elements, using a new maximal-covering minimal-redundant (MCMR) subgraph algorithm. We show that MCMR has a linear computational complexity and will converge. We examined the performance of our method using challenging 3D neuronal image datasets of model organisms (e.g. fruit fly).
The software is available upon request. We plan to eventually release the software as a plugin of the V3D-Neuron package at http://penglab.janelia.org/proj/v3d.
pengh@janelia.hhmi.org.
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.
Automated segmentation and analysis of tree-like structures from 3D medical images are important for many medical applications, such as those dealing with blood vasculature or lung airways. However, there is an absence of large databases of expert segmentations and analyses of such 3D medical images, which impedes the validation and training of proposed image analysis algorithms. In this work, we simulate volumetric images of vascular trees and generate the corresponding ground-truth segmentations, bifurcation locations, branch properties, and tree hierarchy. The tree generation is performed by iteratively growing a vascular structure based on a user-defined (possibly spatially varying) oxygen demand map. We describe the details of the algorithm and provide a variety of example results.
Accurate and fully automatic assessment of vessel (stenoses)
dimensions in angiographic images has been sought as a diagnostic tool,
in particular for coronary heart disease. Here, the authors propose a
new technique to estimate vessel borders in angiographic images, a
necessary first step of any automatic analysis system. Unlike in
previous approaches, the obtained edge estimates are not artificially
smoothed; this is extremely important since quantitative analysis is the
goal. Another important feature of the proposed technique is that no
constant background is assumed, this making it well suited for
nonsubtracted angiograms. The key aspect of the authors' approach is
that continuity/smoothness constraints are not used to modify the
estimates directly derived from the image (which would introduce
distortion) but rather to elect (without modifying) candidate estimates.
Robustness against unknown background is provided by the use a
morphological edge operator, instead of some linear operator (such as a
matched filter) which has to assume known background and known vessel
shape
The authors present an efficient architecture to synthesize filters of arbitrary orientations from linear combinations of basis filters, allowing one to adaptively steer a filter to any orientation, and to determine analytically the filter output as a function of orientation. Steerable filters may be designed in quadrature pairs to allow adaptive control over phase as well as orientation. The authors show how to design and steer the filters and present examples of their use in the analysis of orientation and phase, angularly adaptive filtering, edge detection, and shape from shading. One can also build a self-similar steerable pyramid representation. The same concepts can be generalized to the design of 3-D steerable filters
The multiscale second order local structure of an image (Hessian) is examined with the purpose of developing a vessel enhancement filter. A vesselness measure is obtained on the basis of all eigenvalues of the Hessian. This measure is tested on two dimensional DSA and three dimensional aortoiliac and cerebral MRA data. Its clinical utility is shown by the simultaneous noise and background suppression and vessel enhancement in maximum intensity projections and volumetric displays. 1
Curvilinear structure restoration in image processing procedures is a difficult task, which can be compounded when these structures are thin, i.e., when their smallest dimension is close to the resolution of the sensor. Many recent restoration methods involve considering a local gradient-based regularization term as prior, assuming gradient sparsity. An isotropic gradient operator is typically not suitable for thin curvilinear structures, since gradients are not sparse for these. In this paper, we propose a mixed gradient operator that combines a standard gradient in the isotropic image regions, and a directional gradient in the regions where specific orientations are likely. In particular, such information can be provided by curvilinear structure detectors (e.g., RORPO or Frangi filters). Our proposed mixed gradient operator, that can be viewed as a companion tool of such detectors, is proposed in a discrete framework and its formulation/computation holds in any dimension; in other words, it is valid in Z
n
, n≥1. We show how this mixed gradient can be used to construct image priors that take edge orientation, as well as intensity, into account, and then involved in various image processing tasks while preserving curvilinear structures. The experiments carried out on 2D, 3D, real, and synthetic images illustrate the relevance of the proposed gradient, and its use in variational frameworks for both denoising and segmentation tasks.
We propose a new approach to detecting irregular curvilinear structures in noisy image stacks. In contrast to earlier approaches that rely on circular models of the cross-sections, ours allows for the arbitrarily-shaped ones that are prevalent in biological imagery. This is achieved by maximizing the image gradient flux along multiple directions and radii, instead of only two with a unique radius as is usually done. This yields a more complex optimization problem for which we propose a computationally efficient solution. We demonstrate the effectiveness of our approach on a wide range of challenging gray scale and color datasets and show that it outperforms existing techniques, especially on very irregular structures.
A method of mathematically fitting a curve through a given ordered set
of points was developed and programmed in fortran computer language. The fitted
curve, which is made up of a series of normalized cubic polynomials, very nearly
approximates the curve generated by passing an infinitely thin spline through the
sets of points and is, therefore, called a cubic spline''. The curve has the
prop. erties of continuous position, slope, and curvature. The restraints placed
upon the cubic spline may be relaxed by applying an additional feature which
permits the points to be adjusted by, at most, some preset value. This has the
effect of smoothing the curve in the sense that it reduces the strain energy
stored in it while preserving the general shape of the curve. Tool centers for
numerically controlled tools are found with the interpolation and offsetting
methods included. (auth)
Chu and Liu, Edmonds, and Bock have independently devised an efficient algorithm to find an optimum branching in a directed graph. We give an implementation of the algorithm which runs in 0(m logn) time if the problem graph has n vertices and m edges. A modification for dense graphs gives a running time of 0(n2). We also show that the unmodified algorithm runs in 0(n(log n)2 +m) time on an average graph, assuming a uniform probability distribution.
We present a novel technique for the automatic formation of vascular trees from segmented tubular structures. Our method combines
a minimum spanning tree algorithm with a minimization criterion of the Mahalanobis distance. First, a multivariate class of
connected junctions is defined using a set of trained vascular trees and their corresponding image volumes. Second, a minimum
spanning tree algorithm forms the tree using the Mahalanobis distance of each connection from the “connected” class as a cost
function. Our technique allows for the best combination of the discrimination criteria between connected and non-connected
junctions and is also modality, organ and segmentation specific.
An ordered tree is a tree in which each node’s incident edges are cyclically ordered; think of the tree as being embedded
in the plane. Let A and B be two ordered trees. The edit distance between A and B is the minimum cost of a sequence of operations (contract an edge, uncontract an edge, modify the label of an edge) needed
to transform A into B. We give an O(n
3 log n) algorithm to compute the edit distance between two ordered trees.
Digital reconstructions of neuronal morphology are used to study neuron function, development, and responses to various conditions. Although many measures exist to analyze differences between neurons, none is particularly suitable to compare the same arborizing structure over time (morphological change) or reconstructed by different people and/or software (morphological error). The metric introduced for the DIADEM (DIgital reconstruction of Axonal and DEndritic Morphology) Challenge quantifies the similarity between two reconstructions of the same neuron by matching the locations of bifurcations and terminations as well as their topology between the two reconstructed arbors. The DIADEM metric was specifically designed to capture the most critical aspects in automating neuronal reconstructions, and can function in feedback loops during algorithm development. During the Challenge, the metric scored the automated reconstructions of best-performing algorithms against manually traced gold standards over a representative data set collection. The metric was compared with direct quality assessments by neuronal reconstruction experts and with clocked human tracing time saved by automation. The results indicate that relevant morphological features were properly quantified in spite of subjectivity in the underlying image data and varying research goals. The DIADEM metric is freely released open source ( http://diademchallenge.org ) as a flexible instrument to measure morphological error or change in high-throughput reconstruction projects.
Full reconstruction of neuron morphology is of fundamental interest for the analysis and understanding of neuron function. We have developed a novel method capable of tracing neurons in three-dimensional microscopy data automatically. In contrast to template-based methods, the proposed approach makes no assumptions on the shape or appearance of neuron's body. Instead, an efficient seeding approach is applied to find significant pixels almost certainly within complex neuronal structures and the tracing problem is solved by computing an graph tree structure connecting these seeds. In addition, an automated neuron comparison method is introduced for performance evaluation and structure analysis. The proposed algorithm is computationally efficient. Experiments on different types of data show promising results.
Thesis (Ph. D. in Computer Science)--University of California, Berkeley, December 1985. Includes bibliographical references (leaves 151-157).
The aim of this article is to build trajectories for virtual endoscopy inside 3D medical images, using the most automatic way. Usually the construction of this trajectory is left to the clinician who must define some points on the path manually using three orthogonal views. But for a complex structure such as the colon, those views give little information on the shape of the object of interest. The path construction in 3D images becomes a very tedious task and precise a priori knowledge of the structure is needed to determine a suitable trajectory. We propose a more automatic path tracking method to overcome those drawbacks: we are able to build a path, given only one or two end points and the 3D image as inputs. This work is based on previous work by Cohen and Kimmel [Int. J. Comp. Vis. 24 (1) (1997) 57] for extracting paths in 2D images using Fast Marching algorithm. Our original contribution is twofold. On the first hand, we present a general technical contribution which extends minimal paths to 3D images and gives new improvements of the approach that are relevant in 2D as well as in 3D to extract linear structures in images. It includes techniques to make the path extraction scheme faster and easier, by reducing the user interaction. We also develop a new method to extract a centered path in tubular structures. Synthetic and real medical images are used to illustrate each contribution. On the other hand, we show that our method can be efficiently applied to the problem of finding a centered path in tubular anatomical structures with minimum interactivity, and that this path can be used for virtual endoscopy. Results are shown in various anatomical regions (colon, brain vessels, arteries) with different 3D imaging protocols (CT, MR).
In this paper, we propose an innovative approach to the segmentation of tubular structures. This approach combines all of the benefits of minimal path techniques such as global minimizers, fast computation, and powerful incorporation of user input, while also having the capability to represent and detect vessel surfaces directly which so far has been a feature restricted to active contour and surface techniques. The key is to represent the trajectory of a tubular structure not as a 3-D curve but to go up a dimension and represent the entire structure as a 4-D curve. Then we are able to fully exploit minimal path techniques to obtain global minimizing trajectories between two user supplied endpoints in order to reconstruct tubular structures from noisy or low contrast 3-D data without the sensitivity to local minima inherent in most active surface techniques. In contrast to standard purely spatial 3-D minimal path techniques, however, we are able to represent a full tubular surface rather than just a curve which runs through its interior. Our representation also yields a natural notion of a tube's "central curve." We demonstrate and validate the utility of this approach on magnetic resonance (MR) angiography and computed tomography (CT) images of coronary arteries.
This paper presents methods to model complex vasculature in three-dimensional (3-D) images using cylindroidal superellipsoids, along with robust estimation and detection algorithms for automated image analysis. This model offers an explicit, low-order parameterization, enabling joint estimation of boundary, centerlines, and local pose. It provides a geometric framework for directed vessel traversal, and extraction of topological information like branch point locations and connectivity. M-estimators provide robust region-based statistics that are used to drive the superellipsoid toward a vessel boundary. A robust likelihood ratio test is used to differentiate between noise, artifacts, and other complex unmodeled structures, thereby verifying the model estimate. The proposed methodology behaves well across scale-space, shows a high degree of insensitivity to adjacent structures and implicitly handles branching. When evaluated on synthetic imagery mimicking specific structural complexities in tumor microvasculature, it consistently produces ubvoxel accuracy estimates of centerlines and widths in the presence of closely-adjacent vessels, branch points, and noise. An edit-based validation demonstrated a precision level of 96.6% at a recall level of 95.4%. Overall, it is robust enough for large-scale application
Vascular tree structure: Fast curvature regularization and validation
- chesakov
Inference of cerebrovascular topology with geodesic minimum spanning trees
- Stefano Moriconi
- A Maria
- Rolf Zuluaga
- Parashkev Jäger
- Sébastien Nachev
- M Jorge Ourselin
- Cardoso