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Cerebrovascular Network Registration via An Efficient Attributed Graph Matching Technique
... The graph matching is used in several fields of research and applications such as computer vision, molecular biology or medicine (Almasi et al. 2018). The road network matching problem has been studied for a long time, and several tools were proposed to solve it. ...
... Another solution is to reduce the problem complexity by only solving the linear part of (1) but using edges information into the node descriptor (Almasi et al. 2018). Thus, the problem is reduced to a Linear Assignment Problem (LAP) that has a well known optimal algorithm. ...
In this paper, we propose an approach for cooperative mapping of traversable ground from aerial and ground views in structured outdoor and indoor environments. The presented approach achieves a hybrid map building based on traversable ground skeletonization and graph matching. The obtained map is an augmented ground traversability map, represented as a hybrid topological/metric graph from heterogeneous sources. This approach provides a very suitable representation for ground navigation and planning. To validate this approach, the proposed algorithm is applied between aerial views, provided by a UAV flying over an experimental site, and ground maps from ground robots at different exploration stages, in realistic simulation and real-world environments.
... To reduce the cost of time to match the large graph [22], and [23] proposed two high-efficiency algorithms, respectively. For some specific application areas, Almasi et al. in Ref. [24] studied the application of attributed graph matching in cerebrovascular network. And Liu et al. in Ref. [25] proposed an attributed graph matching algorithm for image retrieval. ...
Attributed graph is a typical class of graphs with a set of attributes on nodes, edges, even high‐order structure. Objects in the fields are naturally represented as attributed graphs with considerable noise and a large number of nodes, which make traditional graphs matching techniques confront with some new challenges, such as optimization difficulty, inability to match and so on. In order to solve these problems, we propose a new approach, called Attributed Graph Matching via Seeds Guiding (AGM‐SG) in this paper. Our approach introduces seed nodes to guide attributed graph matching, and considers explicitly the first‐order characteristics difference in the problem formulation. It is formulated as a quadratic optimization, and solved by Frank‐Wolfe algorithm with continuous relaxation. It only has O(n²) space complexity, and is suitable to apply to super‐large graphs under different types. We evaluate the proposed approach on the synthetic dataset and three different real datasets including Wikipedia dataset, Enron mail dataset, and Caenorhabditis elegans dataset. Compared with the existing graph matching algorithms, the proposed algorithm outperforms original SGM, RGM and AGMLG significantly, which has more than 5% matching accuracy improvement on all datasets. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.
... In general, feature-based methods mainly contain two steps: feature extraction and feature matching. In recent years, some feature-based methods [13][14][15][16][17][18][19][20][21][22] have been proposed. These algorithms have some common steps including keypoint detection, keypoint description, and keypoint matching. ...
Seeking reliable correspondence between multispectral images is a fundamental and important task in computer vision. To overcome the nonlinearity problem occurring in multispectral image matching, a novel, edge-feature-based maximum clique-matching frame (EMCM) is proposed, which contains three main parts: (1) a novel strong edge binary feature descriptor, (2) a new correspondence-ranking algorithm based on keypoint distinctiveness analysis algorithms in the feature space of the graph, and (3) a false match removal algorithm based on maximum clique searching in the correspondence space of the graph considering both position and angle consistency. Extensive experiments are conducted on two standard multispectral image datasets with respect to the three parts. The feature-matching experiments suggest that the proposed feature descriptor is of high descriptiveness, robustness, and efficiency. The correspondence-ranking experiments validate the superiority of our correspondences-ranking algorithm over the nearest neighbor algorithm, and the coarse registration experiments show the robustness of EMCM with varied interferences.
... In addition, the extracted graphs allow to make observation of structural or morphological changes in neural systems [4]. Registration of graph structures is an indispensable element of prognostic and diagnostic studies that require structural analysis and comparison over time, among different samples, and to some gold standard [5], [6]. ...
The extraction of graph structures in Euclidean vector space is a topic of interest with applications in many fields, such as the analysis of vascular networks in the biomedical domain. While a number of approaches have been proposed to tackle the problem of graph extraction, a quantitative evaluation of those algorithms remains a challenging task: In many cases, manual generation of ground truth for real-world data is time-consuming, error-prone, and thus not feasible. While tools for generating synthetic datasets with corresponding ground truth exist, the resulting data often does not reflect the complexity that real-world scenarios show in morphology and topology. As a complementary or even alternative approach, we propose GERoMe, the Graph Extraction Robustness Measure, which provides a means of quantifying the stability of algorithms that extract (multi-)graphs with associated node positions from non-graph structures. Our method takes edge-associated properties into consideration and does not necessarily require ground truth data, although available ground truth information can be incorporated to additionally evaluate the correctness of the graph extraction algorithm. We evaluate the behavior of the proposed graph similarity measure and demonstrate the usefulness and applicability of our method in an exemplary study on both synthetic and real-world data.
With the closer life rhythm of college students and closer contact with social life, these aspects may increase the pressure of college students' life. Some students have not experienced professional psychological counseling, which will cause extreme psychological stress. When faced with a variety of everyday life demands such as study, love and friendship, job, and future career design, college students should have an optimistic, positive, and courageous mentality. Most of the problems of mental health are the result of college students' excessive stress, trivial family life events and other social factors. In this paper, a spatiotemporal graph neural network college student psychological prediction model for information augmentation transmission is proposed and an information augmentation transmission mechanism is designed to capture the complex dependencies of data. The adaptive graph learning structure can dynamically learn the dependencies between nodes and the enhanced information transmission mechanism can increase the area of information transmission to capture richer spatial information and select the effective information through the attention mechanism, and eliminate the invalid information; and design a data linear and nonlinear fusion mechanism, the mechanism includes linear and nonlinear parts, the two parts capture the linear and nonlinear characteristics of the data, and then Fusion.
Industrial cell culture processes are inherently expensive, time-consuming, and variable. These limitations have become a critical bottleneck for the industrial translation of human cell and tissue biomanufacturing, as few human cell culture products deliver sufficient benefit, value, and consistency to offset their high manufacturing costs to produce useful clinical or biomedical solutions. Recent advances in biomedical image analysis and computational modelling can enhance the design and operation of high-efficiency tissue biomanufacturing platforms, as well as the high-content characterisation and monitoring of culture performance to enable bioprocess control, optimisation, and automation. These computational technologies aim to maximize culture outcomes while minimizing variability and process development expense. In this review, we outline current resources and approaches which harness biomedical imaging and image-based computational models to design and operate efficient and robust human tissue biomanufacturing platforms.
Combining Dirichlet Mixture Models (DMM) with deep learning models for road extraction is an attractive study topic. Benefiting from DMM, the manually labeling work is alleviated. However, DMM suffers from high computational complexity due to pixel by pixel computations. Also, traditional constant parameter settings of DMM may not be suitable for different target images. To address the above problems, we propose an improved DMM which embeds superpixel strategy and sparse representation into DMM. In our road extraction framework, we first use improved DMM to filter out most backgrounds. Then, a trained deep CNN model is used for further precise road area recognition. To further promote the processing speed, we also apply the superpixel scanning strategy for CNN models. We tested our method on a Shaoshan dataset and proved that our method not only can achieve better results than other compared state-of-the-art image segmentation methods, but the processing speed and accuracy of DMM are also improved.
Background and objective:
Intra-operative X-ray angiography, the current standard method for visualizing and diagnosing cardiovascular disease, is limited in its ability to provide essential 3D information. These limitations are disadvantages in treating patients. For example, it is a cause of lowering the success rate of interventional procedures. Here, we propose a novel 2D-3D non-rigid registration method to understand vascular geometry during percutaneous coronary intervention.
Methods:
The proposed method uses the local bijection pair distance as a cost function to minimize the effect of inconsistencies from center-line extraction. Moreover, novel cage-based 3D deformation and multi-threaded particle swarm optimization are utilized to implement real-time registration. We evaluated the proposed method for 154 examinations from 10 anonymous patients by coverage percentage, comparing the average distance of the 2D extracted center-line with that of the registered 3D center-line.
Results:
The proposed 2D-3D non-rigid registration method achieved an average distance of 1.98 mm with a 0.54 s computation time. Additionally, in aiming to reduce the uncertainty of XA images, we used the proposed method to retrospectively visualize the connections between 2D vascular segments and the distal part of occlusions.
Conclusions:
Ultimately, the proposed 2D/3D non-rigid registration method can successfully register the 3D center-line of coronary arteries with corresponding 2D XA images, and is computationally sufficient for online usage. Therefore, this method can improve the success rate of such procedures as a percutaneous coronary intervention and provide the information necessary to diagnose cardiovascular diseases better.
We present a new approach for matching sets of branching curvilinear structures that form graphs embedded in ${mathbb {R}}^2$ or ${mathbb {R}}^3$ and may be subject to deformations. Unlike earlier methods, ours does not rely on local appearance similarity nor does require a good initial alignment. Furthermore, it can cope with non-linear deformations, topological differences, and partial graphs. To handle arbitrary non-linear deformations, we use Gaussian process regressions to represent the geometrical mapping relating the two graphs. In the absence of appearance information, we iteratively establish correspondences between points, update the mapping accordingly, and use it to estimate where to find the most likely correspondences that will be used in the next step. To make the computation tractable for large graphs, the set of new potential matches considered at each iteration is not selected at random as with many RANSAC-based algorithms. Instead, we introduce a so-called Active Testing Search strategy that performs a priority search to favor the most likely matches and speed-up the process. We demonstrate the effectiveness of our approach first on synthetic cases and then on angiography data, retinal fundus images, and microscopy image stacks acquired at very different resolutions.
Measurement of volume flow rates in major cerebral vessels can be used to evaluate the hemodynamic effects of cerebrovascular disease. However, both age and vascular anatomy can affect flow rates independent of disease. We prospectively evaluated 325 healthy adult volunteers using phase contrast quantitative magnetic resonance angiography to characterize these effects on cerebral vessel flow rates and establish clinically useful normative reference values. Flows were measured in the major intracranial and extracranial vessels. The cohort ranged from 18 to 84 years old, with 157 (48%) females. All individual vessel flows and total cerebral blood flow (TCBF) declined with age, at 2.6 mL/minute per year for TCBF. Basilar artery (BA) flow was significantly decreased in individuals with one or both fetal posterior cerebral arteries (PCAs). Internal carotid artery flows were significantly higher with a fetal PCA and decreased with a hypoplastic anterior cerebral artery. Indexing vessel flows to TCBF neutralized the age effect, but anatomic variations continued to impact indexed flow in the BA and internal carotid artery. Variability in normative flow ranges were reduced in distal vessels and by examining regional flows. Cerebral vessel flows are affected by age and cerebrovascular anatomy, which has important implications for interpretation of flows in the disease state.Journal of Cerebral Blood Flow & Metabolism advance online publication, 12 November 2014; doi:10.1038/jcbfm.2014.203.
Graph matching plays an essential role in many real applications. In this paper, we study how to match two large graphs by maximizing the number of matched edges, which is known as maximum common subgraph matching and is NP-hard. To find exact matching, it cannot handle a graph with more than 30 nodes. To find an approxi-mate matching, the quality can be very poor. We propose a novel two-step approach that can efficiently match two large graphs over thousands of nodes with high matching quality. In the first step, we propose an anchor-selection/expansion approach to compute a good initial matching. In the second step, we propose a new approach to refine the initial match-ing. We give the optimality of our refinement and discuss how to randomly refine the matching with different combinations. We further show how to extend our solution to handle labeled graphs. We conducted extensive testing using real and syn-thetic datasets and report our findings in this paper.
Background and purpose:
The middle cerebral artery (MCA) bifurcation is a preferred site for aneurysm formation. Wider bifurcation angles have been correlated with increased risk of aneurysm formation. We hypothesized a link between the presence of MCA aneurysms and the angle morphology of the bifurcation.
Methods:
Three-dimensional rotational angiography volumes of 146 MCA bifurcations (62 aneurysmal) were evaluated for angle morphology: parent-daughter angles (larger daughter Ф1, smaller daughter Ф2), bifurcation angle (Ф1+Ф2), and inclination angle (γ) between the parent vessel axis and the plane determined by daughter vessel axes. Statistics were evaluated using Wilcoxon rank-sum analysis and area under the receiver operator characteristic curve.
Results:
Aneurysmal bifurcations had wider inclination angle γ (median 57.8° versus 15.4°; P<0.0001). Seventy-five percent of aneurysmal MCAs had γ >10°, compared with 25% nonaneurysmal. Ф1 and Ф2, but especially Ф1+Ф2, were significantly larger in aneurysmal bifurcations (median 171.3° versus 98.1°; P<0.0001). Sixty-seven percent of aneurysmal bifurcations had Ф1+Ф2 >161°, compared with 0% nonaneurysmal MCAs. An optimal threshold of 140° was established for Ф1+Ф2 (area under the curve, 0.98). Sixty-eight percent of aneurysms originated off the daughter branches. Seventy-six percent of them originated off the branch with the largest branching angle, specifically if this was the smaller daughter branch. Wider Ф1+Ф2 correlated with aneurysm neck width, but not dome size.
Conclusions:
MCA bifurcations harboring aneurysms have significantly larger branching angles and more often originate off the branch with the largest angle. Wider inclination angle is strongly correlated with aneurysm presence, a novel finding. The results point to altered wall shear stress regulation as a possible factor in aneurysm development and progression.
Aneurysm formation in locations not involving vascular bifurcations has not been thoroughly analyzed. This study evaluated the relationship between the degree of vessel curvature and the presence of intracranial sidewall aneurysms of the internal carotid artery (ICA).
Catheter-based 3D-rotational angiographic volumes and demographic data were available for 130 ICAs. Mean and peak curvatures were evaluated for the intracranial ICA (50 mm caudal from ICA bifurcation) and for its distal segment (from ICA bifurcation to carotid siphon). Four ICA groups, statistically matched for age, were identified: non-aneurysmal women (n=33) and men (n=25), aneurysmal women (n=58) and men (n=14). Univariate and multivariate analyses were employed to evaluate statistical performance.
Aneurysmal ICAs had significantly higher mean curvatures than non-aneurysmal ICAs in both the intracranial (p<0.001) and the distal ICA (p<0.001) for both genders. Peak curvature was significantly higher in aneurysmal versus non-aneurysmal men (p=0.008) but not in aneurysmal versus non-aneurysmal women (p=0.12). Mean curvature in non-aneurysmal ICAs was lower in men than in women but higher in aneurysmal ICAs in men than in women. In multivariate analysis, curvature was highly correlated with aneurysm presence but was independent of age, hypertension, hypercholesterolemia and smoking status.
The presence of a sidewall aneurysm on the ICA is associated with high curvature in both genders. High curvature of the intracranial ICA, as well as of the distal segment, may indicate a higher risk for aneurysm formation. Non-aneurysmal ICAs are less curved in men than in women, which may explain the gender predisposition to aneurysm formation.
Endovascular image-guided interventions (EIGI) involve navigation of a catheter through the vasculature followed by application of treatment at the site of anomaly using live 2D projection images for guidance. 3D images acquired prior to EIGI are used to quantify the vascular anomaly and plan the intervention. If fused with the information of live 2D images they can also facilitate navigation and treatment. For this purpose 3D- 2D image registration is required. Although several 3D-2D registration methods for EIGI achieve registration accuracy below 1 mm, their clinical application is still limited by insufficient robustness or reliability. In this paper, we propose a 3D-2D registration method based on matching a 3D vasculature model to intensity gradients of live 2D images. To objectively validate 3D-2D registration methods, we acquired a clinical image database of ten patients undergoing cerebral EIGI and established ¿gold standard¿ registrations by aligning fiducial markers in 3D and 2D images. The proposed method had mean registration accuracy below 0.65 mm, which was comparable to tested state-of-the-art methods, and execution time below 1 second. With the highest rate of successful registrations and the highest capture range the proposed method was the most robust and thus a good candidate for application in EIGI.
ISSN: 1051-4651
Print ISBN: 0-7695-2521-0
We consider the problem of finding a matching between two sets of features, given complex relations among them, going beyond pairwise. Each feature set is modeled by a hypergraph where the complex relations are represented by hyper-edges. A match between the feature sets is then modeled as a hypergraph matching problem. We derive the hyper-graph matching problem in a probabilistic setting represented by a convex optimization. First, we formalize a soft matching criterion that emerges from a probabilistic in- terpretation of the problem input and output, as opposed to previous methods that treat soft matching as a mere relax- ation of the hard matching problem. Second, the model in- duces an algebraic relation between the hyper-edge weight matrix and the desired vertex-to-vertex probabilistic match- ing. Third, the model explains some of the graph match- ing normalization proposed in the past on a heuristic ba- sis such as doubly stochastic normalizations of the edge weights. A key benefit of the model is that the global op- timum of the matching criteria can be found via an iterative successive projection algorithm. The algorithm reduces to the well known Sinkhorn (15) row/column matrix normal- ization procedure in the special case when the two graphs have the same number of vertices and a complete matching is desired. Another benefit of our model is the straightfor- ward scalability from graphs to hyper-graphs.
Graph matching is an essential problem in computer vision and machine learning. In this paper, we introduce a random walk
view on the problem and propose a robust graph matching algorithm against outliers and deformation. Matching between two graphs
is formulated as node selection on an association graph whose nodes represent candidate correspondences between the two graphs.
The solution is obtained by simulating random walks with reweighting jumps enforcing the matching constraints on the association
graph. Our algorithm achieves noise-robust graph matching by iteratively updating and exploiting the confidences of candidate
correspondences. In a practical sense, our work is of particular importance since the real-world matching problem is made
difficult by the presence of noise and outliers. Extensive and comparative experiments demonstrate that it outperforms the
state-of-the-art graph matching algorithms especially in the presence of outliers and deformation.
A recent paper posed the question: "Graph Matching: What are we really talking about?". Far from providing a definite answer to that question, in this paper we will try to characterize the role that graphs play within the Pattern Recognition field. To this aim two taxonomies are presented and discussed. The first includes almost all the graph matching algorithms proposed from the late seventies, and describes the different classes of algorithms. The second taxonomy considers the types of common applications of graph-based techniques in the Pattern Recognition and Machine Vision field.
We propose a convex-concave programming approach for the labeled weighted graph matching problem. The convex-concave programming formulation is obtained by rewriting the weighted graph matching problem as a least-square problem on the set of permutation matrices and relaxing it to two different optimization problems: a quadratic convex and a quadratic concave optimization problem on the set of doubly stochastic matrices. The concave relaxation has the same global minimum as the initial graph matching problem, but the search for its global minimum is also a hard combinatorial problem. We, therefore, construct an approximation of the concave problem solution by following a solution path of a convex-concave problem obtained by linear interpolation of the convex and concave formulations, starting from the convex relaxation. This method allows to easily integrate the information on graph label similarities into the optimization problem, and therefore, perform labeled weighted graph matching. The algorithm is compared with some of the best performing graph matching methods on four data sets: simulated graphs, QAPLib, retina vessel images, and handwritten Chinese characters. In all cases, the results are competitive with the state of the art.
We present an algorithm for graph matching in a pattern recognition context. This algorithm deals with weighted graphs, based on new structural and topological node signatures. Using these signatures, we compute an optimum solution for node-to-node assignment with the Hungarian method and propose a distance formula to compute the distance between weighted graphs. The experiments demonstrate that the newly presented algorithm is well suited to pattern recognition applications. Compared with four well-known methods, our algorithm gives good results for clustering and retrieving images. A sensitivity analysis reveals that the proposed method is also insensitive to weak structural changes.
The angles of arterial bifurcations are governed by principles of work minimization (optimality principle). This determines the relationship between the angle of a bifurcation and the radii of the vessels. Nevertheless, the model is predicated on an absence of significant communication between these branches. The circle of Willis changes this relationship because the vessels proximal to the ring of vessels have additional factors that determine work minimization compared with more distal branches. This must have an impact on understanding of the relationship between shear stress and aneurysm formation. The authors hypothesized that normal bifurcations of cerebral arteries beyond the circle of Willis would follow optimality principles of minimum work and that the presence of aneurysms would be associated with deviations from optimum bifurcation geometry. Nevertheless, the vessels participating in (or immediately proximal to) the circle of Willis may not follow the geometric model as it is generally applied and this must also be investigated.
One hundred seven bifurcations of the middle cerebral artery (MCA), distal internal carotid artery (ICA), and basilar artery (BA) were studied in 55 patients. The authors analyzed three-dimensional reconstructions of digital subtraction angiography images with respect to vessel radii and bifurcation angles. The junction exponent (that is, a calculated measure of the division of flow at the bifurcation) and the difference between the predicted optimal and observed branch angles were used as measures of deviation from the geometry thought best to minimize work. The mean junction exponent for MCA bifurcations was 2.9 +/- 1.2 (mean +/- standard deviation [SD]), which is close to the theoretical optimum of 3, but it was significantly smaller (p < 0.001; 1.7 +/- 0.8, mean +/- SD) for distal ICA bifurcations. In a multilevel multivariate logistic regression analysis, only the observed branch angles were significant independent predictors for the presence of an aneurysm. The odds ratio (OR) (95% confidence interval) for the presence of an aneurysm was 3.46 (1.02-11.74) between the lowest and highest tertile of the observed angle between the parent vessel and the largest branch. The corresponding OR for the smallest branch was 48.06 (9.7-238.2).
The bifurcation beyond the circle of Willis (that is, the MCA) closely approximated optimality principles, whereas the bifurcations within the circle of Willis (that is, the distal ICA and BA) did not. This indicates that the confluence of hemodynamic forces plays an important role in the distribution of work at bifurcations within the circle of Willis. In addition, the observed branch angles were predictors for the presence of aneurysms.
A graduated assignment algorithm for graph matching is presented
which is fast and accurate even in the presence of high noise. By
combining graduated nonconvexity, two-way (assignment) constraints, and
sparsity, large improvements in accuracy and speed are achieved. Its low
order computational complexity [O(lm), where l and m are the number of
links in the two graphs] and robustness in the presence of noise offer
advantages over traditional combinatorial approaches. The algorithm, not
restricted to any special class of graph, is applied to subgraph
isomorphism, weighted graph matching, and attributed relational graph
matching. To illustrate the performance of the algorithm, attributed
relational graphs derived from objects are matched. Then, results from
twenty-five thousand experiments conducted on 100 mode random graphs of
varying types (graphs with only zero-one links, weighted graphs, and
graphs with node attributes and multiple link types) are reported. No
comparable results have been reported by any other graph matching
algorithm before in the research literature. Twenty-five hundred control
experiments are conducted using a relaxation labeling algorithm and
large improvements in accuracy are demonstrated
We have been developing a theory for the generic representation of 2-D shape, where structural descriptions are derived from the shocks (singularities) of a curve evolution process, acting on bounding contours. We now apply the theory to the problem of shape matching. The shocks are organized into a directed, acyclic shock graph, and complexity is managed by attending to the most significant (central) shape components first. The space of all such graphs is highly structured and can be characterized by the rules of a shock graph grammar. The grammar permits a reduction of a shock graph to a unique rooted shock tree. We introduce a novel tree matching algorithm which finds the best set of corresponding nodes between two shock trees in polynomial time. Using a diverse database of shapes, we demonstrate our system's performance under articulation, occlusion, and changes in viewpoint. Acknowledgements We thank Jonas August and Allen Tannenbaum for many helpful discussions. Kaleem Siddiqi an...
. The problem of matching shapes parameterized as a set of points is frequently encountered in medical imaging tasks. When the point-sets are derived from landmarks, there is usually no problem of determining the correspondences or homologies between the two sets of landmarks. However, when the point sets are automatically derived from images, the difficult problem of establishing correspondence and rejecting non-homologies as outliers remains. The Procrustes method is a well-known method of shape comparison and can always be pressed into service when homologies between point-sets are known in advance. This paper presents a powerful extension of the Procrustes method to pointsets of differing point counts with correspondences unknown. The result is the softassign Procrustes matching algorithm which iteratively establishes correspondence, rejects non-homologies as outliers, determines the Procrustes rescaling and the spatial mapping between the point-sets. 1 Introduction ...
This chapter introduces quadratic assignment problems (QAP) as models for finding an optimal assignment among two sets of interrelated objects. References to many applications of QAPs, like in location theory, are given. Moreover, several classical combinatorial optimization problems are identified as special cases of the QAP, like the traveling salesman problem, graph partitioning, max clique problem, minimum-weight feedback arc set problem, (FASP) and packing problems in graphs. These subproblems show that the QAP is NP-hard. Several different formulations of the QAP are presented in detail as being basic for different solution approaches. Special emphasis is laid to the different possibilities for describing QAPs as (mixed-)integer linear programs. Moreover, QAP polyhedra are discussed. Crucial for exact solution approaches are lower bounding procedures. The paradigm of admissible transformations is introduced for describing several variants of Gilmore-Lawler type bounds. Moreover, bounds based on eigenvalues and bounds found by semidefinite programming are discussed in detail. Among exact solution methods, special emphasis is laid on branch-and-bound approaches. With respect to heuristics, not only simple construction heuristics and improvement heuristics are described, but also several metaheuristics like simulated annealing, tabu search, greedy randomized search, genetic algorithms, and ant systems are discussed. Links to available computer programs are delivered. © Springer Science+Business Media New York 2013. All rights are reserved.
The complexity of the interaction between the blood and brain is well known since the hemato-encephalic barrier (BEE) was firstly described. Most of the neurological diseases lead to BEE disruption. In this chapter, we will focus the attention on the neurological deficits due to vascular impairment.
In particular we will analyse the clinical manifestation, pathogenic mechanisms and therapy of stroke, transient ischaemic attack (TIA), microvascular disease and migraine.
Stroke and TIA are the most frequent neurological diseases. Stroke is the third leading cause of death and the first cause of disability in western countries. TIA is a risk factor for stroke development and might be considered itself a microscopic stroke.
Small-vessel diseases are the first cause of vascular dementia and may also play a role in neurodegenerative diseases.
Finally migraine, a common benign neurological disease, represents a good example of the interaction between arterial cells (endothelial and blood cells) and neurons.
Vascular diseases are one of the most challenging health problems in developed countries. Past as well as ongoing research activities often focus on efficient, robust and fast aorta segmentation, and registration techniques. According to this needs our study targets an abdominal aorta registration method. The investigated algorithms make it possible to efficiently segment and register abdominal aorta in pre- and post-operative Computed Tomography (CT) data. In more detail, a registration technique using the Path Similarity Skeleton Graph Matching (PSSGM), as well as Maximum Weight Cliques (MWCs) are employed to realise the matching based on Computed Tomography data. The presented approaches make it possible to match characteristic voxels belonging to the aorta from different Computed Tomography (CT) series. It is particularly useful in the assessment of the abdominal aortic aneurysm treatment by visualising the correspondence between the pre- and post-operative CT data. The registration results have been tested on the database of 18 contrast-enhanced CT series, where the cross-registration analysis has been performed producing 153 matching examples. All the registration results achieved with our system have been verified by an expert. The carried out analysis has highlighted the advantage of the MWCs technique over the PSSGM method. The verification phase proves the efficiency of the MWCs approach and encourages to further develop this methods.
Copyright © 2015 Elsevier Ltd. All rights reserved.
Fusing preoperative and intra-operative information into a single space aims at taking advantage of two complementary modalities and necessitates a step of registration that must provide good alignment and relevant correspondences. This paper addresses both purposes in the case of 3D/2D vessel tree matching.
We propose a registration algorithm endorsing this vascular tree nature by providing a pairing procedure that preserves the tree topology and by integrating this pairing into an iterative algorithm maintaining pairing coherence. In addition, we define two complementary error measures quantifying the resulting alignment error and pairing error, and both are based on manual ground-truth that is independent of the type of transformation to retrieve.
Experiments were conducted on a database of 63 clinical cases, evaluating robustness and accuracy of our approach with respect to the iterative closest point algorithm.
The proposed method exhibits good results in terms of both pairing and alignment as well as low sensitivity to rotations to be compensated (up to 30[Formula: see text]).
The problem of graph matching in general is NPcomplete and many approximate pairwise matching techniques have been proposed. For a general setting in real applications, it typically requires to find the consistent matchings across a batch of graphs. Sequentially performing pairwise matching is prone to error propagation along the pairwise matching sequence, and the sequences generated in different pairwise matching orders can lead to contradictory solutions. Motivated by devising a robust and consistent multiple-graph matching model, we propose a unified alternating optimization framework for multigraph matching. In addition, we define and use two metrics related to graph-wise and pairwise consistencies. The former is used to find an appropriate reference graph which induces a set of basis variables and launches the iteration procedure. The latter defines the order in which the considered graphs in the iterations are manipulated. We show two embodiments under the proposed framework that can cope with the nonfactorized and factorized affinity matrix, respectively. Our multigraph matching model has two major characters: i) the affinity information across multiple graphs are explored in each iteration by fixing part of the matching variables via a consistencydriven mechanism; ii) the framework is flexible to incorporate various existing pairwise graph matching solvers in an "outof- box" fashion, and also can proceed with the output of other multi-graph matching methods. The experimental results on both synthetic data and real images empirically show that the proposed framework performs competitively with the state-of-the-art.
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.
Object:
Arterial bifurcations represent preferred locations for aneurysm formation, especially when they are associated with variations in divider geometry. The authors hypothesized a link between basilar apex aneurysms and basilar bifurcation (α) and vertebrobasilar junction (VBJ) angles.
Methods:
The α and VBJ angles were measured in 3D MR and rotational angiographic volumes using a coplanar 3-point technique. Angle α was compared between age-matched cohorts in 45 patients with basilar artery (BA) aneurysms, 65 patients with aneurysms in other locations (non-BA), and 103 nonaneurysmal controls. Additional analysis was performed in 273 nonaneurysmal controls. Computational fluid dynamics (CFD) simulations were performed on parametric BA models with increasing angles.
Results:
Angle α was significantly wider in patients with BA aneurysms (146.7° ± 20.5°) than in those with non-BA aneurysms (111.7° ± 18°) and in controls (103° ± 20.6°) (p < 0.0001), whereas no difference was observed for the VBJ angle. A wider angle α correlated with BA aneurysm neck width but not dome size, which is consistent with CFD results showing a widening of the impingement zone at the bifurcation apex. BA bifurcations hosting even small aneurysms (< 5 mm) had a significantly larger α angle compared with matched controls (p < 0.0001). In nonaneurysmal controls, α increased with age (p < 0.0001), with a threshold effect above 35 years of age and a steeper dependence in females (p = 0.002) than males (p = 0.04).
Conclusions:
The α angle widens with age during adulthood, especially in females. This angular widening is associated with basilar bifurcation aneurysms and may predispose individuals to aneurysm initiation by diffusing the flow impingement zone away from the protective medial band region of the flow divider.
In this paper, we consider the weighted graph matching problem with partially disclosed correspondences between a number of anchor nodes. Our construction exploits recently introduced node signatures based on graph Laplacians, namely the Laplacian family signature (LFS) on the nodes, and the pair wise heat kernel map on the edges. In this paper, without assuming an explicit form of parametric dependence nor a distance metric between node signatures, we formulate an optimization problem which incorporates the knowledge of anchor nodes. Solving this problem gives us an optimized proximity measure specific to the graphs under consideration. Using this as a first order compatibility term, we then set up an integer quadratic program (IQP) to solve for a near optimal graph matching. Our experiments demonstrate the superior performance of our approach on randomly generated graphs and on two widely-used image sequences, when compared with other existing signature and adjacency matrix based graph matching methods.
We present a new robust point matching algorithm (RPM) that can
jointly estimate the correspondence and non-rigid transformations
between two point-sets that may be of different sizes. The algorithm
utilizes the soft assign for the correspondence and the thin-plate
spline for the non-rigid mapping. Embedded within a deterministic
annealing framework, the algorithm can automatically reject a fraction
of the points as outliers. Experiments on both 2D synthetic point-sets
with varying degrees of deformation, noise and outliers, and on real 3D
sulcal point-sets (extracted from brain MRI) demonstrate the robustness
of the algorithm
We introduce a convex relaxation approach for the quadratic assignment problem to the field of computer vision. Due to convexity, a favourable property of this approach is the absence of any tuning parameters and the computation of high-quality combinatorial solutions by solving a mathematically simple optimization problem. Furthermore, the relaxation step always computes a tight lower bound of the objective function and thus can additionally be used as an efficient subroutine of an exact search algorithm. We report the results of both established benchmark experiments from combinatorial mathematics and random ground-truth experiments using computer-generated graphs. For comparison, a deterministic annealing approach is investigated as well. Both approaches show similarly good performance. In contrast to the convex approach, however, the annealing approach yields no problem relaxation, and four parameters have to be tuned by hand for the annealing algorithm to become competitive.
Graph matching and MAP inference are essential problems in computer vision and machine learning. We introduce a novel algorithm that can accommodate both problems and solve them efficiently. Recent graph matching algorithms are based on a general quadratic programming formulation, which takes in consid- eration both unary and second-order terms reflecting the similarities in local ap- pearance as well as in the pairwise geometric relationships between the matched features. This problem is NP-hard, therefore most algorithms find approximate solutions by relaxing the original problem. They find the optimal continuous so- lution of the modified problem, ignoring during optimization the original discrete constraints. Then the continuous solution is quickly binarized at the end, but very little attention is put into this final discretization step. In this paper we argue that the stage in which a discrete solution is found is crucial for good performance. We propose an efficient algorithm, with climbing and convergence properties, that optimizes in the discrete domain the quadratic score, and it gives excellent results either by itself or by starting from the solution returned by any graph matching algorithm. In practice it outperforms state-or-the art graph matching algorithms and it also significantly improves their performance if used in combination. When applied to MAP inference, the algorithm is a parallel extension of Iterated Con- ditional Modes (ICM) with climbing and convergence properties that make it a compelling alternative to the sequential ICM. In our experiments on MAP infer- ence our algorithm proved its effectiveness by significantly outperforming (13), ICM and Max-Product Belief Propagation.
List of Algorithms. Preface. Possible Course Outlines. 1. Introduction. 2. The Image, Its Representations and Properties. 3. The Image, Its Mathematical and Physical Background. 4. Data Structures for Image Analysis. 5. Image Pre-Processing. 6. Segmentation I. 7. Segmentation II. 8. Shape Representation and Description. 9. Object Recognition. 10. Image Understanding. 11. 3d Geometry, Correspondence, 3d from Intensities. 12. Reconstruction from 3d. 13. Mathematical Morphology. 14. Image Data Compression. 15. Texture. 16. Motion Analysis. Index.
Graph matching is an essential problem in computer vision that has been successfully applied to 2D and 3D feature matching and object recognition. Despite its importance, little has been published on learning the parameters that control graph matching, even though learning has been shown to be vital for improving the matching rate. In this paper we show how to perform parameter learning in an unsupervised fashion, that is when no correct correspondences between graphs are given during training. Our experiments reveal that unsupervised learning compares favorably to the supervised case, both in terms of efficiency and quality, while avoiding the tedious manual labeling of ground truth correspondences. We verify experimentally that our learning method can improve the performance of several state-of-the art graph matching algorithms. We also show that a similar method can be successfully applied to parameter learning for graphical models and demonstrate its effectiveness empirically.
Many medical applications require a registration of different images of the same organ. In many cases, such a registration is accomplished by manually placing landmarks in the images. In this paper we propose a method which is able to find reasonable landmarks automatically. To achieve this, nodes of the vessel systems, which have been extracted from the images by a segmentation algorithm, will be assigned by the so-called association graph method and the coordinates of these matched nodes can be used as landmarks for a non-rigid registration algorithm.
The author (2) has shown that corresponding to each positive square matrix A (i.e. every a ij > 0) is a unique doubly stochastic matrix of the form D 1 AD 2 , where the D i are diagonal matrices with positive diagonals. This doubly stochastic matrix can be obtained as the limit of the iteration defined by alternately normalizing the rows and columns of A.
In this paper, it is shown that with a sacrifice of one diagonal D it is still possible to obtain a stochastic matrix. Of course, it is necessary to modify the iteration somewhat. More precisely, it is shown that corresponding to each positive square matrix A is a unique stochastic matrix of the form DAD where D is a diagonal matrix with a positive diagonal. It is shown further how this stochastic matrix can be obtained as a limit to an iteration on A.
The management of unruptured intracranial aneurysms is controversial. Investigators from the International Study of Unruptured Intracranial Aneurysms aimed to assess the natural history of unruptured intracranial aneurysms and to measure the risk associated with their repair.
Centres in the USA, Canada, and Europe enrolled patients for prospective assessment of unruptured aneurysms. Investigators recorded the natural history in patients who did not have surgery, and assessed morbidity and mortality associated with repair of unruptured aneurysms by either open surgery or endovascular procedures.
4060 patients were assessed-1692 did not have aneurysmal repair, 1917 had open surgery, and 451 had endovascular procedures. 5-year cumulative rupture rates for patients who did not have a history of subarachnoid haemorrhage with aneurysms located in internal carotid artery, anterior communicating or anterior cerebral artery, or middle cerebral artery were 0%, 2. 6%, 14 5%, and 40% for aneurysms less than 7 mm, 7-12 mm, 13-24 mm, and 25 mm or greater, respectively, compared with rates of 2 5%, 14 5%, 18 4%, and 50%, respectively, for the same size categories involving posterior circulation and posterior communicating artery aneurysms. These rates were often equalled or exceeded by the risks associated with surgical or endovascular repair of comparable lesions. Patients' age was a strong predictor of surgical outcome, and the size and location of an aneurysm predict both surgical and endovascular outcomes.
Many factors are involved in management of patients with unruptured intracranial aneurysms. Site, size, and group specific risks of the natural history should be compared with site, size, and age-specific risks of repair for each patient.
We present a visual analytics technique to explore graphs using the concept of a data signature. A data signature, in our context, is a multidimensional vector that captures the local topology information surrounding each graph node. Signature vectors extracted from a graph are projected onto a low-dimensional scatterplot through the use of scaling. The resultant scatterplot, which reflects the similarities of the vectors, allows analysts to examine the graph structures and their corresponding real-life interpretations through repeated use of brushing and linking between the two visualizations. The interpretation of the graph structures is based on the outcomes of multiple participatory analysis sessions with intelligence analysts conducted by the authors at the Pacific Northwest National Laboratory. The paper first uses three public domain data sets with either well-known or obvious features to explain the rationale of our design and illustrate its results. More advanced examples are then used in a customized usability study to evaluate the effectiveness and efficiency of our approach. The study results reveal not only the limitations and weaknesses of the traditional approach based solely on graph visualization, but also the advantages and strengths of our signature-guided approach presented in the paper.
We present an efficient spectral method for finding consistent correspondences between two sets of features. We build the adjacency matrix M of a graph whose nodes represent the potential correspondences and the weights on the links represent pairwise agreements between potential correspondences. Correct assignments are likely to establish links among each other and thus form a strongly connected cluster. Incorrect correspondences establish links with the other correspondences only accidentally, so they are unlikely to belong to strongly connected clusters. We recover the correct assignments based on how strongly they belong to the main cluster of M, by using the principal eigenvector of M and imposing the mapping constraints required by the overall correspondence mapping (one-to-one or one-to-many). The experimental evaluation shows that our method is robust to outliers, accurate in terms of matching rate, while being much faster than existing methods.
In this paper, we propose a general framework for graph matching which is suitable for different problems of pattern recognition. The pattern representation we assume is at the same time highly structured, like for classic syntactic and structural approaches, and of subsymbolic nature with real-valued features, like for connectionist and statistic approaches. We show that random walk based models, inspired by Google's PageRank, give rise to a spectral theory that nicely enhances the graph topological features at node level. As a straightforward consequence, we derive a polynomial algorithm for the classic graph isomorphism problem, under the restriction of dealing with Markovian spectrally distinguishable graphs (MSD), a class of graphs that does not seem to be easily reducible to others proposed in the literature. The experimental results that we found on different test-beds of the TC-15 graph database show that the defined MSD class "almost always" covers the database, and that the proposed algorithm is significantly more efficient than top scoring VF algorithm on the same data. Most interestingly, the proposed approach is very well-suited for dealing with partial and approximate graph matching problems, derived for instance from image retrieval tasks. We consider the objects of the COIL-100 visual collection and provide a graph-based representation, whose node's labels contain appropriate visual features. We show that the adoption of classic bipartite graph matching algorithms offers a straightforward generalization of the algorithm given for graph isomorphism and, finally, we report very promising experimental results on the COIL-100 visual collection.
The type of representation used in describing shape can have a significant impact on the effectiveness of a recognition strategy. Shape has been represented by its bounding curve as well as by the medial axis representation which captures the regional interaction of the boundaries. Shape matching with the former representation is achieved by curve matching, while the latter is achieved by matching skeletal graphs. In this paper, we compare the effectiveness of these two methods using approaches which we have developed recently for each. The results indicate that skeletal matching involves a higher degree of computational complexity, but is better than curve matching in the presence of articulation or rearrangement of parts. However, when these variations are not present, curve matching is a better strategy due to its lower complexity and roughly equivalent recognition rate.
Path similarity skeleton graph matching, pattern analysis and machine intelligence
- X Bai
- L J Latecki
Bai, X., Latecki, L.J., 2008. Path similarity skeleton graph matching, pattern analysis
and machine intelligence. Trans. IEEE 30 (7), 1282-1292.
Robust matching of 3d lung vessel trees
- D Smeets
- P Bruyninckx
- J Keustermans
- D Vandermeulen
- P Suetens
Smeets, D., Bruyninckx, P., Keustermans, J., Vandermeulen, D., Suetens, P., 2010. Robust matching of 3d lung vessel trees. In: Proceedings of the MICCAI Workshop
on Pulmonary Image Analysis.