Three-dimensional reconstruction of curves from pairs of projection views in the presence of error. I. Algorithms

Using temporal and structural data to reconstruct 3D cerebral vasculature from a pair of 2D digital subtraction angiography sequences

PURPOSE

The purpose of this work is to present a new method for reconstructing patient-specific three-dimensional (3D) vasculature of the brain from a pair of digital subtraction angiography (DSA) image sequences from different viewpoints, e.g., from bi-plane angiography. Our long-term goal is to provide high resolution visualization of 3D vasculature with dynamic flow of contrast agent from limited data that is readily available during surgical procedures. The proposed method is the second of a three-stage process composed of 1) augmenting vessel segmentation with vessel radii and timing of the arrival of a bolus of contrast agent, 2) reconstructing a volumetric representation of the augmented vessel data from the augmented 2D segmentations, and 3) generating a 3D model of vessels and flow of contrast agent from the volumetric reconstruction. Unlike previous methods, which are either limited to relatively simple vessel structures or rely on multiple views and/or prior models of the vasculature, our method requires only a single pair of 2D DSA sequences taken from different view directions.

METHODS

We developed a new mathematical algorithm that augments vessel centerlines with vessel radii and bolus arrival times derived directly from the 2D DSA sequences to constrain the 3D reconstruction. We validated this method on digital phantoms derived from clinical data and from fractal models of branching tree structures.

RESULTS

In standard reconstruction methods, reconstruction by projection of two views into 3D space results in 'ghosting' artifacts, i.e., false 3D structure that occurs where vessels or vessel segments overlap in the 2D images. For the complex vascular of the brain, this ghosting is severe and is a major hurdle for methods that attempt to generate 3D structure from 2D images. We show that our approach reduces ghosting by up to 99% in digital phantoms derived from clinical data.

CONCLUSION

Our dramatic reduction in ghosting artifacts in 3D reconstructions from a pair of 2D image sequences is an important step towards generating high resolution 3D vasculature with dynamic flow information from a single DSA sequence acquired using bi-plane angiography.

Reconstructing the Curve-Skeletons of 3D Shapes Using the Visual Hull

Curve-skeletons are the most important descriptors for shapes, capable of capturing in a synthetic manner the most relevant features. They are useful for many different applications: from shape matching and retrieval, to medical imaging, to animation. This has led, over the years, to the development of several different techniques for extraction, each trying to comply with specific goals. We propose a novel technique which stems from the intuition of reproducing what a human being does to deduce the shape of an object holding it in his or her hand and rotating. To accomplish this, we use the formal definitions of epipolar geometry and visual hull. We show how it is possible to infer the curve-skeleton of a broad class of 3D shapes, along with an estimation of the radii of the maximal inscribed balls, by gathering information about the medial axes of their projections on the image planes of the stereographic vision. It is definitely worth to point out that our method works indifferently on (even unoriented) polygonal meshes, voxel models, and point clouds. Moreover, it is insensitive to noise, pose-invariant, resolution-invariant, and robust when applied to incomplete data sets.

3D stereo interactive medical visualization

Transjugular intrahepatic portosystemic shunt formation (TIPS) is an effective treatment for portal hypertension [LaBerge 1995]. The procedure requires the insertion of a needle through the liver to connect the hepatic and portal veins. This operation is traditionally guided by fluoroscopic images that do not show the location of the target veins during needle insertion. We propose to provide the clinician an interactive, three-dimensional (3D), stereo display so that the position and orientation of the clinician’s needle can be seen relative to the target vasculature intraoperatively. This paper describes the visualizations we are providing for intraoperative guidance.

Three-dimensional representation of curved nanowires

Nanostructures, such as nanowires, nanotubes and nanocoils, can be described in many cases as quasi one-dimensional curved objects projecting in three-dimensional space. A parallax method to construct the correct three-dimensional geometry of such one-dimensional nanostructures is presented. A series of scanning electron microscope images was acquired at different view angles, thus providing a set of image pairs that were used to generate three-dimensional representations using a matlab program. An error analysis as a function of the view angle between the two images is presented and discussed. As an example application, the importance of knowing the true three-dimensional shape of boron nanowires is demonstrated; without the nanowire's correct length and diameter, mechanical resonance data cannot provide an accurate estimate of Young's modulus.

Three-dimensional guide-wire reconstruction from biplane image sequences for integrated display in 3-D vasculature

Using three-dimensional rotational X-ray angiography (3DRA), three-dimensional (3-D) information of the vasculature can be obtained prior to endovascular interventions. However, during interventions, the radiologist has to rely on fluoroscopy images to manipulate the guide wire. In order to take full advantage of the 3-D information from 3DRA data during endovascular interventions, a method is presented that yields an integrated display of the position of the guide wire and vasculature in 3-D. The method relies on an automated method that tracks the guide wire simultaneously in biplane fluoroscopy images. Based on the calibrated geometry of the C-arm, the 3-D guide-wire position is determined and visualized in the 3-D coordinate system of the vasculature. The method is evaluated in an intracranial anthropomorphic vascular phantom. The influence of the angle between projections, distortion correction of the projection images, and accuracy of geometry knowledge on the accuracy of 3-D guide-wire reconstruction from biplane images is determined. If the calibrated geometry information is used and the images are corrected for distortion, a mean distance to the reference standard of 0.42 mm and a tip distance of 0.65 mm is found, which means that accurate guide-wire reconstruction from biplane images can be performed.

Symbolic description of intracerebral vessels segmented from magnetic resonance angiograms and evaluation by comparison with X-ray angiograms

We describe and evaluate methods that create detailed vessel trees by linking vessels that have been segmented from magnetic resonance angiograms (MRA). The tree-definition process can automatically exclude erroneous vessel segmentations. The parent-child connectivity information provided by our vessel trees is important to both surgical planning and to guidance of endovascular procedures. We evaluated the branch connection accuracy of our 3D vessel trees by asking two neuroradiologists to evaluate 140 parent-child connections comprising seven vascular trees against 17 digital subtraction angiography (DSA) views. Each reviewer rated each connection as (1) Correct, (2) Incorrect, (3) Partially correct (a minor error without clinical significance), or (4) Indeterminate. Analysis was summarized for each evaluator by calculating 95% confidence intervals for both the proportion completely correct and the proportion clinically acceptable (completely or partially correct). In order to protect the overall Type I error rate, alpha-splitting was done using a top down strategy. We additionally evaluated segmentation completeness by examining each slice in 11 MRA datasets in order to determine unlabeled vessels identifiable in cross-section following segmentation. Results indicate that only one vascular parent-child connection was judged incorrect by both reviewers. MRA segmentations appeared complete within MRA resolution limits. We conclude that our methods permit creation of detailed vascular trees from segmented 3D image data. We review the literature and compare other approaches to our own. We provide examples of clinically useful visualizations enabled by our methodology and taken from a visualization program now in clinical use.

CT imaging based digitally reconstructed radiographs and their application in brachytherapy

The aim of our study was to develop an algorithm to simulate the digitally reconstructed radiograph (DRR) calculation process for different beam qualities (photon energies) in the range 50 keV to 12 MeV. This was achieved using volumetric anatomical data for the patient obtained from three-dimensional diagnostic CT images. These DRR images can be used in three-dimensional treatment planning for external beam radiotherapy as well as for brachytherapy in the same way as conventional radiographic films. The advantages of using such DRRs in modern 3D brachytherapy treatment planning are shown. A number of tools are described, illustrating that the application of DRRs in brachytherapy is very useful.

A localization algorithm and error analysis for stereo x-ray image guidance

Stereo x-ray radiography attracts increasing attention in major clinical applications. The purpose of this paper is to analyze the 3D localization error for breast biopsy procedures and provide guidelines for improving its accuracy. Our prototype is a CCD based digital stereo x-ray imaging system. The mathematical model consists of two x-ray sources and one stationary detector plane. A closed form least-squares solution is derived for 3D localization of feature points, particularly a biopsy needle tip, from a pair of 2D digital radiographs. Based on the least-squares formula and its first order approximation, the 3D localization error is analyzed in terms of object location, measurement error, separation between the two x-ray sources, and distance from the source to the detector. The stereo imaging and error estimation formulas are numerically simulated and experimentally validated. The data are in agreement with theoretical prediction. These results can be used for the purpose of system design and protocol optimization.

Three-dimensional reconstruction of curves from pairs of projection views in the presence of error. II. Analysis of error

We have previously described an approach to 3D intracerebral vascular reconstruction that uses an MRA as a reconstruction base. Additional vessels seen only by angiography are added by segmenting 2D curves from projection angiograms and reconstructing these curves into 3D, building upon the MRA. This paper is the second of two that discuss the specific problem of reconstructing a 3D curve from a given pair of 2D curves in the presence of error. The method presented is capable of detecting and handling many errors produced by misregistration, image distortion, or misdefinition of 2D curves. The first paper gives an algorithm. The current paper discusses factors affecting the accuracy of a reconstructed curve, with emphasis upon registration error. We analyze the spatial accuracy of a reconstructed point in terms of the relationships between pixel size, relative viewing angle, 3D point location, and registration error. We provide a theoretical framework that, given the known error properties of a registration algorithm, allows optimization of the viewing geometry so as to produce the highest precision of point reconstruction. A major focus is the effect of registration error upon the reconstruction of a curve. We subdivide registration error into two types, one of which produces smoothly continuous point placement errors and the other of which produces pixel pairing errors. We test our ability to reconstruct a 3D curve in the presence of both. Finally, we summarize approaches to other sources of error. We conclude with a list of recommendations to optimize reconstruction accuracy. When projection points are associated by the rules of epipolar geometry, viewplane point displacements should not exceed 1.5-2 mm along the axis perpendicular to epipolar planes.