Evaluation of center-line extraction algorithms in quantitative coronary angiography

Diagnostic performance of angiography-derived fractional flow reserve analysis based on bifurcation fractal law for assessing hemodynamic significance of coronary stenosis

OBJECTIVES

Blood flow into the side branch affects the calculation of coronary angiography-derived fractional flow reserve (FFR), called Angio-FFR. Neglecting or improperly compensating for the side branch flow may decrease the diagnostic accuracy of Angio-FFR. This study aims to evaluate the diagnostic accuracy of a novel Angio-FFR analysis that considers the side branch flow based on the bifurcation fractal law.

METHODS

A one-dimensional reduced-order model based on the vessel segment was used to perform Angio-FFR analysis. The main epicardial coronary artery was divided into several segments according to the bifurcation nodes. Side branch flow was quantified using the bifurcation fractal law to correct the blood flow in each vessel segment. In order to verify the diagnostic performance of our Angio-FFR analysis, two other computational methods were taken as control groups: (i) FFR_s: FFR calculated by delineating the coronary artery tree to consider side branch flow, (ii) FFR_n: FFR calculated by just delineating the main epicardial coronary artery and neglecting the side branch flow.

RESULTS

The analysis of 159 vessels from 119 patients showed that our Anio-FFR calculation method had comparable diagnostic accuracy to FFR_s and provided significantly higher diagnostic accuracy than that of FFR_n. In addition, using invasive FFR as a reference, the Pearson correlation coefficients of Angio-FFR and FFRs were 0.92 and 0.91, respectively, while that of FFR_n was only 0.85.

CONCLUSIONS

Our Angio-FFR analysis has demonstrated good diagnostic performance in assessing the hemodynamic significance of coronary stenosis by using the bifurcation fractal law to compensate for side branch flow.

CLINICAL RELEVANCE STATEMENT

Bifurcation fractal law can be used to compensate for side branch flow during the Angio-FFR calculation of the main epicardial vessel. Compensating for side branch flow can improve the ability of Angio-FFR to diagnose stenosis functional severity.

KEY POINTS

• The bifurcation fractal law could accurately estimate the blood flow from the proximal main vessel into the main branch, thus compensating for the side branch flow. • Angiography-derived FFR based on the bifurcation fractal law is feasible to evaluate the target diseased coronary artery without delineating the side branch.

A robust construction algorithm of the centerline skeleton for complex aortic vascular structure using computational fluid dynamics

Centerlines of blood vessels are useful tools to make important anatomical measurements (length, diameter, area), which cannot be accurately obtained using 2D images. In this paper a brand new method for centerline extraction of vascular trees is presented. By using computational fluid dynamics (CFD) we are able to obtain a robust and purely functional centerline allowing us to support better measurements than classic purely geometrical-based centerlines. We show that the CFD-based centerline is within a few pixels from the geometrical centerline where the latter is defined (far away from inlet/outlets and from the branches). We show that the centerline computed with our method is not affected by traditional errors of other classical volume-based algorithms such as topological thinning, and could be a potential alternative to be considered for future studies.

Automatic Morphological Reconstruction of Neurons from Multiphoton and Confocal Microscopy Images Using 3D Tubular Models

The challenges faced in analyzing optical imaging data from neurons include a low signal-to-noise ratio of the acquired images and the multiscale nature of the tubular structures that range in size from hundreds of microns to hundreds of nanometers. In this paper, we address these challenges and present a computational framework for an automatic, three-dimensional (3D) morphological reconstruction of live nerve cells. The key aspects of this approach are: (i) detection of neuronal dendrites through learning 3D tubular models, and (ii) skeletonization by a new algorithm using a morphology-guided deformable model for extracting the dendritic centerline. To represent the neuron morphology, we introduce a novel representation, the Minimum Shape-Cost (MSC) Tree that approximates the dendrite centerline with sub-voxel accuracy and demonstrate the uniqueness of such a shape representation as well as its computational efficiency. We present extensive quantitative and qualitative results that demonstrate the accuracy and robustness of our method.

Geometrical force constraint method for vessel and x-ray angiogram simulation

This study proposes a novel geometrical force constraint method for 3-D vasculature modeling and angiographic image simulation. For this method, space filling force, gravitational force, and topological preserving force are proposed and combined for the optimization of the topology of the vascular structure. The surface covering force and surface adhesion force are constructed to drive the growth of the vasculature on any surface. According to the combination effects of the topological and surface adhering forces, a realistic vasculature can be effectively simulated on any surface. The image projection of the generated 3-D vascular structures is simulated according to the perspective projection and energy attenuation principles of X-rays. Finally, the simulated projection vasculature is fused with a predefined angiographic mask image to generate a realistic angiogram. The proposed method is evaluated on a CT image and three generally utilized surfaces. The results fully demonstrate the effectiveness and robustness of the proposed method.

Digital Topology and Geometry in Medical Imaging: A Survey

Digital topology and geometry refers to the use of topologic and geometric properties and features for images defined in digital grids. Such methods have been widely used in many medical imaging applications, including image segmentation, visualization, manipulation, interpolation, registration, surface-tracking, object representation, correction, quantitative morphometry etc. Digital topology and geometry play important roles in medical imaging research by enriching the scope of target outcomes and by adding strong theoretical foundations with enhanced stability, fidelity, and efficiency. This paper presents a comprehensive yet compact survey on results, principles, and insights of methods related to digital topology and geometry with strong emphasis on understanding their roles in various medical imaging applications. Specifically, this paper reviews methods related to distance analysis and path propagation, connectivity, surface-tracking, image segmentation, boundary and centerline detection, topology preservation and local topological properties, skeletonization, and object representation, correction, and quantitative morphometry. A common thread among the topics reviewed in this paper is that their theory and algorithms use the principle of digital path connectivity, path propagation, and neighborhood analysis.

Computer Vision Techniques for Transcatheter Intervention

Minimally invasive transcatheter technologies have demonstrated substantial promise for the diagnosis and the treatment of cardiovascular diseases. For example, transcatheter aortic valve implantation is an alternative to aortic valve replacement for the treatment of severe aortic stenosis, and transcatheter atrial fibrillation ablation is widely used for the treatment and the cure of atrial fibrillation. In addition, catheter-based intravascular ultrasound and optical coherence tomography imaging of coronary arteries provides important information about the coronary lumen, wall, and plaque characteristics. Qualitative and quantitative analysis of these cross-sectional image data will be beneficial to the evaluation and the treatment of coronary artery diseases such as atherosclerosis. In all the phases (preoperative, intraoperative, and postoperative) during the transcatheter intervention procedure, computer vision techniques (e.g., image segmentation and motion tracking) have been largely applied in the field to accomplish tasks like annulus measurement, valve selection, catheter placement control, and vessel centerline extraction. This provides beneficial guidance for the clinicians in surgical planning, disease diagnosis, and treatment assessment. In this paper, we present a systematical review on these state-of-the-art methods. We aim to give a comprehensive overview for researchers in the area of computer vision on the subject of transcatheter intervention. Research in medical computing is multi-disciplinary due to its nature, and hence, it is important to understand the application domain, clinical background, and imaging modality, so that methods and quantitative measurements derived from analyzing the imaging data are appropriate and meaningful. We thus provide an overview on the background information of the transcatheter intervention procedures, as well as a review of the computer vision techniques and methodologies applied in this area.

A Robust and Efficient Curve Skeletonization Algorithm for Tree-Like Objects Using Minimum Cost Paths

Conventional curve skeletonization algorithms using the principle of Blum's transform, often, produce unwanted spurious branches due to boundary irregularities, digital effects, and other artifacts. This paper presents a new robust and efficient curve skeletonization algorithm for three-dimensional (3-D) elongated fuzzy objects using a minimum cost path approach, which avoids spurious branches without requiring post-pruning. Starting from a root voxel, the method iteratively expands the skeleton by adding new branches in each iteration that connects the farthest quench voxel to the current skeleton using a minimum cost path. The path-cost function is formulated using a novel measure of local significance factor defined by the fuzzy distance transform field, which forces the path to stick to the centerline of an object. The algorithm terminates when dilated skeletal branches fill the entire object volume or the current farthest quench voxel fails to generate a meaningful skeletal branch. Accuracy of the algorithm has been evaluated using computer-generated phantoms with known skeletons. Performance of the method in terms of false and missing skeletal branches, as defined by human experts, has been examined using in vivo CT imaging of human intrathoracic airways. Results from both experiments have established the superiority of the new method as compared to the existing methods in terms of accuracy as well as robustness in detecting true and false skeletal branches. The new algorithm makes a significant reduction in computation complexity by enabling detection of multiple new skeletal branches in one iteration. Specifically, this algorithm reduces the number of iterations from the number of terminal tree branches to the worst case performance of tree depth. In fact, experimental results suggest that, on an average, the order of computation complexity is reduced to the logarithm of the number of terminal branches of a tree-like object.

A New Approach of Arc Skeletonization for Tree-Like Objects Using Minimum Cost Path

Traditional arc skeletonization algorithms using the principle of Blum's transform, often, produce unwanted spurious branches due to boundary irregularities and digital effects on objects and other artifacts. This paper presents a new robust approach of extracting arc skeletons for three-dimensional (3-D) elongated fuzzy objects, which avoids spurious branches without requiring post-pruning. Starting from a root voxel, the method iteratively expands the skeleton by adding a new branch in each iteration that connects the farthest voxel to the current skeleton using a minimum-cost geodesic path. The path-cost function is formulated using a novel measure of local significance factor defined by fuzzy distance transform field, which forces the path to stick to the centerline of the object. The algorithm terminates when dilated skeletal branches fill the entire object volume or the current farthest voxel fails to generate a meaningful branch. Accuracy of the algorithm has been evaluated using computer-generated blurred and noisy phantoms with known skeletons. Performance of the method in terms of false and missing skeletal branches, as defined by human expert, has been examined using in vivo CT imaging of human intrathoracic airways. Experimental results from both experiments have established the superiority of the new method as compared to a widely used conventional method in terms of accuracy of medialness as well as robustness of true and false skeletal branches.

Automatic vasculature identification in coronary angiograms by adaptive geometrical tracking

As the uneven distribution of contrast agents and the perspective projection principle of X-ray, the vasculatures in angiographic image are with low contrast and are generally superposed with other organic tissues; therefore, it is very difficult to identify the vasculature and quantitatively estimate the blood flow directly from angiographic images. In this paper, we propose a fully automatic algorithm named adaptive geometrical vessel tracking (AGVT) for coronary artery identification in X-ray angiograms. Initially, the ridge enhancement (RE) image is obtained utilizing multiscale Hessian information. Then, automatic initialization procedures including seed points detection, and initial directions determination are performed on the RE image. The extracted ridge points can be adjusted to the geometrical centerline points adaptively through diameter estimation. Bifurcations are identified by discriminating connecting relationship of the tracked ridge points. Finally, all the tracked centerlines are merged and smoothed by classifying the connecting components on the vascular structures. Synthetic angiographic images and clinical angiograms are used to evaluate the performance of the proposed algorithm. The proposed algorithm is compared with other two vascular tracking techniques in terms of the efficiency and accuracy, which demonstrate successful applications of the proposed segmentation and extraction scheme in vasculature identification.

Coronary artery center-line extraction using second order local features

Of interest is the accurate and robust delineation of vessel center-lines for complete arterial tree structure in coronary angiograms which is an imperative step towards 3D reconstruction of coronary tree and feature-based registration of multiple view angiograms. Most existing center-line tracking methods encounter limitations in coping with abrupt variations in local artery direction and sudden changes of lumen diameter that occur in the vicinity of arterial lesions. This paper presents an improved center-line tracing algorithm for automatic extraction of coronary arterial tree based on robust local features. The algorithm employs an improved scanning schema based on eigenvalues of Hessian matrix for reliable identification of true vessel points as well as an adaptive look-ahead distance schema for calculating the magnitude of scanning profile. In addition to a huge variety of clinical examples, a well-established vessel simulation tool was used to create several synthetic angiograms for objective comparison and performance evaluation. The experimental results on the accuracy and robustness of the proposed algorithm and its counterparts under difficult situations such as poor image quality and complicated vessel geometry are presented.

Sequential reconstruction of vessel skeletons from X-ray coronary angiographic sequences

X-ray coronary angiography (CAG) is one of widely used imaging modalities for diagnosis and interventional treatment of cardiovascular diseases. Dynamic CAG sequences acquired from several viewpoints record coronary arterial morphological information as well as dynamic performances. The aim of this work is to propose a semi-automatic method for sequentially reconstructing coronary arterial skeletons from a pair of CAG sequences covering one or several cardiac cycles acquired from different views based on snake model. The snake curve deforms directly in 3D through minimizing a predefined energy function and ultimately stops at the global optimum with the minimal energy, which is the desired 3D vessel skeleton. The energy function combines intrinsic properties of the curve and acquired image data with a priori knowledge of coronary arterial morphology and dynamics. Consequently, 2D extraction, 3D sequential reconstruction and tracking of coronary arterial skeletons are synchronously implemented. The main advantage of this method is that matching between a pair of angiographic projections in point-by-point manner is avoided and the reproducibility and accuracy are improved. Results are given for clinical image data of patients in order to validate the proposed method.

Novel approach for 3-d reconstruction of coronary arteries from two uncalibrated angiographic images

Three-dimensional reconstruction of vessels from digital X-ray angiographic images is a powerful technique that compensates for limitations in angiography. It can provide physicians with the ability to accurately inspect the complex arterial network and to quantitatively assess disease induced vascular alterations in three dimensions. In this paper, both the projection principle of single view angiography and mathematical modeling of two view angiographies are studied in detail. The movement of the table, which commonly occurs during clinical practice, complicates the reconstruction process. On the basis of the pinhole camera model and existing optimization methods, an algorithm is developed for 3-D reconstruction of coronary arteries from two uncalibrated monoplane angiographic images. A simple and effective perspective projection model is proposed for the 3-D reconstruction of coronary arteries. A nonlinear optimization method is employed for refinement of the 3-D structure of the vessel skeletons, which takes the influence of table movement into consideration. An accurate model is suggested for the calculation of contour points of the vascular surface, which fully utilizes the information in the two projections. In our experiments with phantom and patient angiograms, the vessel centerlines are reconstructed in 3-D space with a mean positional accuracy of 0.665 mm and with a mean back projection error of 0.259 mm. This shows that the algorithm put forward in this paper is very effective and robust.

Three-dimensional blood vessel quantification via centerline deformation

It is clinically important to quantify the geometric parameters of an abnormal vessel, as this information can aid radiologists in choosing appropriate treatments or apparatuses. Centerline and cross-sectional diameters are commonly used to characterize the morphology of vessel in various clinical applications. Due to the existence of stenosis or aneurysm, the associated vessel centerline is unable to truly portray the original, healthy vessel shape and may result in inaccurate quantitative measurement. To remedy such a problem, a novel method using an active tube model is proposed. In the method, a smoothened centerline is determined as the axis of a deformable tube model that is registered onto the vessel lumen. Three types of regions, normal, stenotic, and aneurysmal regions, are defined to classify the vessel segment under-analyzed by use of the algorithm of a cross-sectional-based distance field. The registration process used on the tube model is governed by different region-adaptive energy functionals associated with the classified vessel regions. The proposed algorithm is validated on the 3-D computer-generated phantoms and 3-D rotational digital subtraction angiography (DSA) datasets. Experimental results show that the deformed centerline provides better vessel quantification results compared with the original centerline. It is also shown that the registered model is useful for measuring the volume of aneurysmal regions.

A model-based consecutive scanline tracking method for extracting vascular networks from 2-D digital subtraction angiograms

We propose a new model-based algorithm for the automated tracking of vascular networks in 2-D digital subtraction angiograms. Consecutive scanline profiles are fitted by a parametric imaging model to estimate local vessel center point, radius, edge locations and direction. An adaptive tracking strategy is applied with appropriate termination criteria to track each vessel segment. When tracking stops, to prevent premature termination and to detect bifurcations, a look ahead detection scheme is used to search for possible continuation points of the same vessel segment or those of its bifurcated segments. The proposed algorithm can automatically extract the majority of the vascular network without human interaction other than initializing the start point and direction. Compared to other tracking methods, the proposed method highlights accurate estimation of local vessel geometry. Accurate geometric information and a hierarchical vessel network are obtained which can be used for further quantitative analysis of arterial networks to obtain flow conductance estimates.

On concise 3-D simple point characterizations: a marching cubes paradigm

The centerlines of tubular structures are useful for medical image visualization and computer-aided diagnosis applications. They can be effectively extracted by using a thinning algorithm that erodes an object layer by layer until only a skeleton is left. An object point is "simple" and can be safely deleted only if the resultant image is topologically equivalent to the original. Numerous characterizations of 3-D simple points based on digital topology already exist. However, little work has been done in the context of marching cubes (MC). This paper reviews several concise 3-D simple point characterizations in a MC paradigm. By using the Euler characteristic and a few newly observed properties in the context of connectivity-consistent MC, we present concise and more self-explanatory proofs. We also present an efficient method for computing the Euler characteristic locally for MC surfaces. Performance evaluations on different implementations are conducted on synthetic data and multidetector computed tomography examination of virtual colonoscopy and angiography.

Automatic generation of time resolved motion vector fields of coronary arteries and 4D surface extraction using rotational x-ray angiography

Rotational coronary angiography provides a multitude of x-ray projections of the contrast agent enhanced coronary arteries along a given trajectory with parallel ECG recording. These data can be used to derive motion information of the coronary arteries including vessel displacement and pulsation. In this paper, a fully automated algorithm to generate 4D motion vector fields for coronary arteries from multi-phase 3D centerline data is presented. The algorithm computes similarity measures of centerline segments at different cardiac phases and defines corresponding centerline segments as those with highest similarity. In order to achieve an excellent matching accuracy, an increasing number of bifurcations is included as reference points in an iterative manner. Based on the motion data, time-dependent vessel surface extraction is performed on the projections without the need of prior reconstruction. The algorithm accuracy is evaluated quantitatively on phantom data. The magnitude of longitudinal errors (parallel to the centerline) reaches approx. 0.50 mm and is thus more than twice as large as the transversal 3D extraction errors of the underlying multi-phase 3D centerline data. It is shown that the algorithm can extract asymmetric stenoses accurately. The feasibility on clinical data is demonstrated on five different cases. The ability of the algorithm to extract time-dependent surface data, e.g. for quantification of pulsating stenosis is demonstrated.

An improved algorithm for vessel centerline tracking in coronary angiograms

For automated visualization and quantification of artery diseases, the accurate determination of the arterial centerline is a prerequisite. Existing tracking-based approaches usually suffer from the inaccuracy, inflexion and discontinuity in the extracted centerlines, and they may even fail in complicated situations. In this paper, an improved algorithm for coronary arterial centerline extraction is proposed, which incorporates a new tracking direction updating scheme, a self-adaptive magnitude of linear extrapolation and a dynamic-size search window for matched filtering. A simulation study is conducted for the determination of the optimal weighting factor which is used to combine the geometrical topology information and intensity distribution information to obtain the proposed tracking direction. Synthetic and clinical examples, representing some difficult situations that may occur in coronary angiograms, are presented. Results show that the proposed algorithm outperforms the conventional methods. By adopting the proposed algorithm, centerlines are successfully extracted under these complicated situations, and with satisfactory accuracy.

Three-dimensional analysis of complex branching vessels in confocal microscopy images

The characteristic of confocal microscopy (CM) vascular data is that it contains many tiny vessels with branching and complex structure. In this work, an automated method for quantitative analysis and reconstruction of cerebral vessels from CM images is presented in which the extracted centerline of the vessels plays the key role. To assess the efficiency and accuracy of different centerline extraction methods, a comparison among three fully automated approaches is given. The centerline extraction methods studied in this work are a snake model, a path planning approach, and a distance transform-based method. To evaluate the accuracy of the quantitative parameters of vessels such as length and diameter, we apply the method to synthetic data. These results indicate that the snake model and the path planning method are more accurate in extracting the quantitative parameters. The efficiency of the approach in clinical applications is then confirmed by applying the method to real CM images. All three methods investigated in this work are accurate enough to correctly distinguish between normal and stroke brain data, while the snake model is the fastest for clinical applications. In addition, three-dimensional visualization, reconstruction, and characterization of CM vascular images of rat brains are presented.

Evaluation of an improved technique for automated center lumen line definition in cardiovascular image data

The aim of the study was to evaluate a new method for automated definition of a center lumen line in vessels in cardiovascular image data. This method, called VAMPIRE, is based on improved detection of vessel-like structures. A multiobserver evaluation study was conducted involving 40 tracings in clinical CTA data of carotid arteries to compare VAMPIRE with an established technique. This comparison showed that VAMPIRE yields considerably more successful tracings and improved handling of stenosis, calcifications, multiple vessels, and nearby bone structures. We conclude that VAMPIRE is highly suitable for automated definition of center lumen lines in vessels in cardiovascular image data.

An automated method for analysis of flow characteristics of circulating particles from in vivo video microscopy

The behavior of white and red blood cells, platelets, and circulating injected particles is one of the most studied areas of physiology. Most methods used to analyze the circulatory patterns of cells are time consuming. We describe a system named CellTrack, designed for fully automated tracking of circulating cells and micro-particles and retrieval of their behavioral characteristics. The task of automated blood cell tracking in vessels from in vivo video is particularly challenging because of the blood cells' nonrigid shapes, the instability inherent in in vivo videos, the abundance of moving objects and their frequent superposition. To tackle this, the CellTrack system operates on two levels: first, a global processing module extracts vessel borders and center lines based on color and temporal patterns. This enables the computation of the approximate direction of the blood flow in each vessel. Second, a local processing module extracts the locations and velocities of circulating cells. This is performed by artificial neural network classifiers that are designed to detect specific types of blood cells and micro-particles. The motion correspondence problem is then resolved by a novel algorithm that incorporates both the local and the global information. The system has been tested on a series of in vivo color video recordings of rat mesentery. Our results show that the synergy between the global and local information enables CellTrack to overcome many of the difficulties inherent in tracking methods that rely solely on local information. A comparison was made between manual measurements and the automatically extracted measurements of leukocytes and fluorescent microspheres circulatory velocities. This comparison revealed an accuracy of 97%. CellTrack also enabled a much larger volume of sampling in a fraction of time compared to the manual measurements. All these results suggest that our method can in fact constitute a reliable replacement for manual extraction of blood flow characteristics from in vivo videos.

A quantitative analysis of 3-D coronary modeling from two or more projection images

A method is introduced to examine the geometrical accuracy of the three-dimensional (3-D) representation of coronary arteries from multiple (two and more) calibrated two-dimensional (2-D) angiographic projections. When involving more then two projections, (multiprojection modeling) a novel procedure is presented that consists of fully automated centerline and width determination in all available projections based on the information provided by the semi-automated centerline detection in two initial calibrated projections. The accuracy of the 3-D coronary modeling approach is determined by a quantitative examination of the 3-D centerline point position and the 3-D cross sectional area of the reconstructed objects. The measurements are based on the analysis of calibrated phantom and calibrated coronary 2-D projection data. From this analysis a confidence region (alpha degrees approximately equal to [35 degrees - 145 degrees]) for the angular distance of two initial projection images is determined for which the modeling procedure is sufficiently accurate for the applied system. Within this angular border range the centerline position error is less then 0.8 mm, in terms of the Euclidean distance to a predefined ground truth. When involving more projections using our new procedure, experiments show that when the initial pair of projection images has an angular distance in the range alpha degrees approximately equal to [35 degrees - 145 degrees], the centerlines in all other projections (gamma = 0 degrees - 180 degrees) were indicated very precisely without any additional centering procedure. When involving additional projection images in the modeling procedure a more realistic shape of the structure can be provided. In case of the concave segment, however, the involvement of multiple projections does not necessarily provide a more realistic shape of the reconstructed structure.

Endpoint localization in guide wire tracking during endovascular interventions1

RATIONALE AND OBJECTIVES

A method is presented to track guide wires during endovascular interventions under X-ray fluoroscopy. Accurate guide wire tracking can be used to improve guide wire visualization in the low quality fluoroscopic images, and to estimate the position of the guide wire in world coordinates for navigation purposes.

MATERIALS AND METHODS

A two-step procedure is used to track the guide wire in subsequent frames. First, the position of the guide wire is obtained by fitting a spline to the image. Subsequently, the spline is iteratively moved toward the tip of the guide wire for accurate tip localization. For both steps, a feature image is used in which line-like structures are enhanced. The method is validated using a reference standard, obtained by manual tracings of three observers.

RESULTS

The method is evaluated on 20 image sequences, 10 sequences with a J-tipped guide wire and 10 with a straight guide wire. The tracking success was 96% for J-tipped and 100% for straight guide wires, whereas accurate endpoint localization could be performed in 91.3% and 94.4% of the frames respectively, with a tip localization error of less than 1.5 mm.

CONCLUSIONS

Accurate endpoint localization can be performed for both J-tipped and straight guide wires and therefore the presented tracking method can be used for navigation purposes.

Adaptive edge localisation approach for quantitative coronary analysis

Lack of reliability, user dissatisfaction and errors in determining coronary vessel wall characteristics are challenging issues in quantitative coronary analysis (QCA). A new approach is proposed for QCA that tackles these issues. The proposed approach extracts the coronary vessel edges by applying dynamic programming techniques that use human-based decision criteria, adaptive edge detection and feature-based cost minimisation. This approach uses image gradient, image intensity, boundary continuity and adaptive thresholding to gain maximum quality assurance. The validation of this approach was conducted through modelled phantoms and real X-ray angiograms. The results show that the accuracies obtained were 0.0116mm and 0.06mm, respectively, and the precisions were 0.0263mm, and 0.04mm, respectively. The proposed approach is reliable, reproducible and user friendly and provides high precision compared with recently published results. Furthermore, the significance of the proposed approach and its limitations are also discussed.

Predictive (un)distortion model and 3-D reconstruction by biplane snakes

This paper is concerned with the three-dimensional (3-D) reconstruction of coronary vessel centerlines and with how distortion of X-ray angiographic images affects it. Angiographies suffer from pincushion and other geometrical distortions, caused by the peripheral concavity of the image intensifier (II) and the nonlinearity of electronic acquisition devices. In routine clinical practice, where a field-of-view (FOV) of 17-23 cm is commonly used for the acquisition of coronary vessels, this distortion introduces a positional error of up to 7 pixels for an image matrix size of 512 x 512 and an FOV of 17 cm. This error increases with the size of the FOV. Geometrical distortions have a significant effect on the validity of the 3-D reconstruction of vessels from these images. We show how this effect can be reduced by integrating a predictive model of (un)distortion into the biplane snakes formulation for 3-D reconstruction. First, we prove that the distortion can be accurately modeled using a polynomial for each view. Also, we show that the estimated polynomial is independent of focal length, but not of changes in anatomical angles, as the II is influenced by the earth's magnetic field. Thus, we decompose the polynomial into two components: the steady and the orientation-dependent component. We determine the optimal polynomial degree for each component, which is empirically determined to be five for the steady component and three for the orientation-dependent component. This fact simplifies the prediction of the orientation-dependent polynomial, since the number of polynomial coefficients to be predicted is lower. The integration of this model into the biplane snakes formulation enables us to avoid image unwarping, which deteriorates image quality and therefore complicates vessel centerline feature extraction. Moreover, we improve the biplane snake behavior when dealing with wavy vessels, by means of using generalized gradient vector flow. Our experiments show that the proposed methods in this paper decrease up to 88% the reconstruction error obtained when geometrical distortion effects are ignored. Tests on imaged phantoms and real cardiac images are presented as well.