Classifications

• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
  • G06T11/00—2D [Two Dimensional] image generation
  • G06T11/003—Reconstruction from projections, e.g. tomography
  • G06T11/006—Inverse problem, transformation from projection-space into object-space, e.g. transform methods, back-projection, algebraic methods
• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
  • G06T2211/00—Image generation
  • G06T2211/40—Computed tomography
  • G06T2211/404—Angiography

Definitions

• Root-mean-square (RMS) errors in the 3-D position and the 3-D configuration of vessel centerlines and in the angles defining the R matrix and T vector were 0.9 - 5.5 mm, 0.7 - 1.0 mm, and less than 1.5 and 2.0 degrees, respectively, when using 2-D vessel centerlines with RMS normally distributed errors varying from 0.4 - 4.2 pixels (0.25 - 1.26 mm). More specifically, the method for three-dimensional reconstruction of a target object from two-dimensional images involves a target object having a plurality of branch-like vessels.
• FIG. 7 is a schematic view showing two set-ups of a biplane imaging system resulting from the employed two initial conditions yielding two sets of reconstructed 3-D objects A'- D' and A - D (real 3-D object points) as shown in gray and black circles, respectively.
• DETAILED DESCRIPTION OF THE INVENTION Referring now to Fig.
• biplane projection images are acquired using an X-ray based imaging system.
• X-ray based imaging system other non-X-ray based imaging systems may be used, as will be described hereinafter.
• Such X-ray based images are preferably created using a biplane imaging system where two projection images are produced substantially simultaneously.
• the patient is placed in a position so that the target object, in this illustrated embodiment, the heart, is scanned by the imaging system.
• the imaging system preferably includes a plurality of imaging portions where each imaging portion provides a projection image of the coronary structure.
• the identified centerlines and the branching relationships are used to construct the hierarchy in each image by their labeling according to the appropriate anatomy of the primary and secondary coronary arteries.
• the labeling process on the coronary tree is performed automatically by application of the breadth-first search algorithm to traverse identified vessel centerlines, as is known in the art. From each vessel of the coronary tree that is currently visited, this approach searches as broadly as possible by next visiting all of the vessel centerlines that are adjacent to it.
• the geometric orientation of the gantries during exposure may not be available or alternately, if it is available, may require a calibration process.
• the information of a single plane system includes the gantry orientation (LAO and CAUD angles), SID (focal spot to image intensified distance), and magnification.
• LAO and CAUD angles the gantry orientation
• SID focal spot to image intensified distance
• magnification magnification
• such information is defined based on each individual reference system.
• the relative orientation that characterizes the two views is unknown. Therefore, it is necessary to determine the biplane geometry. If the two reference points, which are the location of the iso-centers, are made to coincide, the relative orientation can be calculated directly from the recorded information. However, such coincidence of the reference points is difficult to achieve in a practical environment.
• steps 32-36 of Fig. 1 may be employed to calculate the 3-D coronary arterial structures.
• steps 32-36 of Fig. 1 may be employed to calculate the 3-D coronary arterial structures.
• a significant advantage of the present inventive method is that 3-D reconstruction is accurately rendered from 2-D projection images when such orientation information is unavailable.
• the bifurcation points are calculated, as shown in step 24 of Fig. 1.
• An important step in the present inventive method relies on the accurate establishment of correspondence between image features, such as points or curve segments between projections.
• the bifurcation points on the vascular tree are prominent features and are often recognized in both images to facilitate the determination of biplane imaging geometry.
• Each X-ray source (or focal spot) functions as the origin of 3-D coordinate space and the spatial relationship between each imaging portion of the biplane system can be characterized by a transformation in the form of a rotation matrix R and a translation vector t .
• R rotation matrix
• t translation vector
• -19- ratio of the SID and the approximate distance of the object to the focal spot Item (4), immediately above, is optional but may provide a more accurate estimate if it is available.
• An essential step in feature-based 3-D reconstruction from two views relies on the accurate establishment of correspondence in image features, such as points or curve segments between projections, as is illustrated in step 32 of Fig. 1.
• the bifurcation points on the vascular tree are prominent features and can often be recognized in both images to facilitate the determination of biplane imaging geometry. Because the vessel co ⁇ espondences are maintained based on the hierarchical digraphs, the correspondences of bifurcation points are inherently established and can be retrieved by traversing the associated hierarchical digraphs (data structures).
• the established pairs of bifurcation points are used for the calculation of the biplane imaging geometry.
• the correction of pincushion error can be implemented based on known algorithms. For example, a method described in a publication entitled “Correction of Image Deformation from Lens Distortion Using Bezier Patches", Computer Viusion. Graphics Image Processing. Vol. 47, 1989, pp. 385-394, may be used, as is known in the art.
• the pincushion distortion does not considerably affect the accuracy of the 3-D reconstruction due to the small field of view (i.e., 100 cm SID and 17 cm x 17 cm II).
• the estimated imaging geometry, as well as the 3-D objects by use of the linear algorithm may considerably deviate from the real solution and, therefore are not suitable to serve as the initial estimate for the refinement process.
• Such a situation can be identified if (1) not all of the calculated 3-D points are in front of both (or all) focal spots, (2) the RMS image point errors are large (e.g. , > 50 pixels) or (3) the projections of the calculated 3-D points are not in the image plane. To remedy this problem, the estimates of
• Equ. (2) where t d represents the magnitude of t . If the magnitude of / is not available, an approximated measurement is calculated as follows:
• Fig. 5 illustrates the graphical representation of the predefined initial solutions.
• the scaled 3-D points (r'tting J ⁇ , j',) defined in the *'y'z' coordinate system are initialized as
• an "optimal" estimate of the biplane imaging geometry and 3-D object structures is be obtained by minimizing: mi n F 1 (P,P')- ⁇ ( ⁇ r ⁇ ) 2 -(r ]r ⁇ ) ⁇ ( ⁇ ' 1 - ⁇ ⁇ l) ⁇ m y ⁇
• the first two terms of the objective function F,(P,P') denote the square of distance between the input of image data and the projection of calculated 3-D data at the rth point.
• Equ. (4) Equ. (4) where denotes the respective /rth column vectors of matrix R. From a pair of projections, the 3-D objects can only be recovered up to a scale factor, at best. This fact is reflected by the inspection of each quotient term involving the 3-D points in Equ. (4) as follows:
• constraint C characterizes the quaternion norm
• constraint C 2 ensures a unit translation vector
• constraints C 3 and C Community Force the scaled coordinates £', and £, to be in front of the respective focal spots. If the isocenter distances of employed biplane imaging systems or MF factors are available, the constraints C 3 and C 4 in Eq.(8) can be modified as:
• ⁇ and a' denote the MF factors
• ⁇ h ⁇ 12.5 ⁇ 2.0 cm denotes the maximal length of the heart along a long-axis view at end-diastole, as is known and described by A.E. Weyman in a publication entitled “Cross-Sectional Echocardiography, " Lea & Febiger, Philadelphia, 1982.
• ⁇ c defines the radius of a circular disk (e.g., 20 pixels) centered at ( ⁇ dress ⁇ ,) or (£',, ⁇ ',) and psize represents the pixel size.
• Fig. 6 shows the bounding regions based on the employed constraint C 3 to C 6 in x'y'z' system. If two initial solutions are employed (as described under the subheading of Initial Estimates of Biplane Imaging Geometry), in general, two sets of biplane imaging geometry and their associated 3-D scaled object points will be obtained:
• Fig. 7 illustrates a typical example by use of several object point RMS errors on image points associated with the true solutions defined by one imaging geometry
• the calculated imaging parameters which have a smaller RMS error on the image points, are selected as the optimal solution.
• the magnitude of the translation vector i.e. , the distance between the two focal spots
• the scale factor S f is calculated and employed to obtain the absolute 3-D object point as
• L rf denotes the known 3-D distance associated with the two scaled 3-D object points
• the orientation information is used to establish the point correspondences on vessel centerlines in the pair of images and is further used to calculate 3-D morphologic structures of coronary arterial tree, as is illustrated in step 34 of Fig. 1.
• the calculated imaging geometry in conjunction with the epipolar constraints are employed as the framework for establishing the point correspondences on the vessel centerlines based on the two identified 2-D coronary arterial trees.
• the correspondence of a point in one image must lie on the epipolar line in the other image. Two types of ambiguity may arise in the two-view correspondence problem: (1) the epipolar line may intersect more that one vessel in the coronary arterial tree, and (2) the epipolar line may intersect more than one point on a single vessel.
• the first ambiguity is resolved by means of the constructed hierarchical digraph defining the anatomy of the 2-D coronary arterial tree such that the epipolar constraints are applied iteratively to every pair of corresponding vessels in the two coronary trees. For example, the corresponding centerline points of the left anterior descending artery
• each 2-D vessel centerline is modeled by
• Equ. (10) and r y denotes the component of the rotation matrix R.
• Rendering of Reconstructed 3-D Coronary Tree and Estimation of an Optimal View After the 3-D vessel centerlines are obtained which define the 3-D location of the arterial tree, as shown in step 34 of Fig. 1, the anatomical mo ⁇ hology of the arterial tree is generated by a surface based reproduction technique, as illustrated in step 36 of Fig. 1 , as is known in the art.
• a surface based reproduction technique is described by S.Y. Chen, K.R. Hoffmann, CT. Chen, and J.D. Carroll in a publication entitled "Modeling the Human Heart based on Cardiac Tomography," SPIE, vol. 177 ' 8, 1992, pp. 14-18.
• Equ. (12) subject to the constraints -90° ⁇ ⁇ ⁇ 90°, -40° ⁇ ⁇ ⁇ 40° , where " . " denotes the inner product and 0 ; is the angle between the directional vector / ; and
• Equ. (13) In prior art methods, due to the problem of vessel overlap and vessel foreshortening, multiple projections are necessary to adequately evaluate the coronary arterial tree using arteriography. Hence, the patient may receive additional or unneeded radiation and contrast material during diagnostic and interventional procedures.
• This known traditional trial and error method may provide views in which overlapping and foreshortening are somewhat minimized, but only in terms of the subjective experience -based judgement of the angiographer.
• the reconstructed 3-D coronary arterial tree can be rotated to any selected viewing angle yielding multiple computer-generated projections to determine for each patient which standard views are useful and which are of no clinical value due to excessive overlap. Therefore, the 3-D computer assistance provides a means to improve the quality and utility of the images subsequently acquired.
• RMS errors in angles defining the R matrix and t vector were less than 0.5 (£7), 1.2 (E ⁇ ), and 0.7 (£ 7 ) degrees, respectively, when ten corresponding points were used with RMS normally distributed e ⁇ ors varying from 0.7 - 4.2 pixels (0.21 - 1.32 mm) in fifty configurations; when only the linear based Metz-Fencil method was employed, the respective errors varied from 0.5 - 8.0 degrees, 6.0 - 40.0 degrees, and 3.7 - 34.1 degrees.
• the simulation shows substantial improvement in the estimation of biplane imaging geometry based on the new technique, which facilitates accurate reconstruction of 3-D coronary arterial structures.
• the simulation shows highly accurate results in the estimation of biplane imaging geometry, vessel correspondences (less than 2 mm RMS error), and 3-D coronary arterial structures (less than 2 mm RMS error in configuration and 0.5 cm RMS error in absolute position, respectively) when a computer-simulated coronary arterial tree is used.
• Angiograms of fifteen patients were analyzed where each patient had multiple biplane image acquisitions.
• the biplane imaging geometry was first determined without the need of a calibration object, and the 3-D coronary arterial trees including the left and the right coronary artery systems were reconstructed. Similarity between the real and reconstructed arterial
• the present inventive method is novel in several ways: (1) the 3-D coronary vasculature is reconstructed from a pair of projection angiograms based on a biplane imaging system or multiple pairs of angiograms acquired from a single-plane system in the same phase of the cardiac cycle at different viewing angles without use of a calibration object to achieve accuracies in magnification and imaging geometry of better than 2% and three degrees, respectively; (2) a beating 3-D coronary vasculature can be reproduced throughout the cardiac cycles in the temporal sequences of images to facilitate the study of heart movement; (3) the choice of an optimal view of the vasculature of interest can be achieved on the basis of the capability of rotating the reconstructed 3-D coronary arterial tree; and (4) the inventive method can be implemented on most digital single-plane or biplane systems.
• a calculated 3-D coronary tree for each patient predicts which projections are clinically useful thus providing an optimal visualization strategy which leads to more efficient and successful diagnostic and therapeutic procedures.
• the elimination of coronary artery views with excessive overlap may reduce contrast and radiation.
• the present inventive method is not limited to X-ray based imaging systems.
• suitable imaging systems may include particle-beam imaging systems, radar imaging systems, ultrasound imaging systems, photographic imaging systems, and laser imaging systems.
• imaging systems are suitable when perspective-projection images of the target object are provided by the systems.
• Appendix A for a source code listing of the above-described method.
• the software is written in C Programming Language including GL Graphics Library Functions and Tk. Tel Library functions compiled on a Unix-based C Compiler.

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• 1996
  • 1996-06-19 US US08/665,836 patent/US6047080A/en not_active Expired - Lifetime
• 1997
  • 1997-06-17 WO PCT/US1997/010194 patent/WO1997049065A1/en not_active Application Discontinuation
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• 1999
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