WO2017188559A1 - Procédé de reconstitution d'images en tomodensitométrie - Google Patents

Procédé de reconstitution d'images en tomodensitométrie Download PDF

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WO2017188559A1
WO2017188559A1 PCT/KR2017/000506 KR2017000506W WO2017188559A1 WO 2017188559 A1 WO2017188559 A1 WO 2017188559A1 KR 2017000506 W KR2017000506 W KR 2017000506W WO 2017188559 A1 WO2017188559 A1 WO 2017188559A1
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sinogram
fixed point
projection
center
image
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Kyung Taek JUN
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Im TechnologyCo ltd
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    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T12/00—Tomographic reconstruction from projections
    • G06T12/20—Inverse problem, i.e. transformations from projection space into object space

Definitions

  • the present invention relates to a method of image reconstruction and, more particularly, to a method of image reconstruction in computed tomography.
  • the first category uses pairs of projection images taken from the reverse viewing angles (at 0-180 degrees). They perform the image registration of these pairs to calculate the offset of CoR. This method is often considered efficient, however, Vo, N. T. , Drakopoulos, M., Atwood, R. C. & Reinhard, C. "Reliable method for calculating the center of rotation in parallel-beam tomography. Opt. Express, 22, 19078 (2014)” argued that it is not feasible especially when the projections have low contrasts or the optics system have fixed defects.
  • the second method evaluates the projection image from the reconstruction using a parameter to measure the quality of image reconstruction and to calibrate the relative offset of the rotation axis (Gursoy, D., De Carlo, F., Xiao, X. & Jacobsen, C. TomoPy: a framework for the analysis of synchrotron tomographic data. J. Synchrotron Rad. 21, 1188-1193 (2014)).
  • This technique is widely used and has its own strength in terms of using all the available information, but it is often time-consuming and inapplicable for the reconstruction with artifacts.
  • the last one considered the center-of-mass (CMXDonath, T., Beckmann, F. & Schreyer, A. Automated determination of the center of rotation in tomography data. J. Opt. Soc. Am. A, 23, 1048-1057 (2006)). To make it work, the sample should be within the field of view, which is not always possible.
  • the object of the present invention is to provide for an improved image reconstruction.
  • fixed point is defined as the point in space that can be discriminated or calculated by analysis of a projection image set.
  • Fixed point is the point in space that can be discriminated or calculated by analysis of a projection image set.
  • the real RA is located on the center line of the sinusoidal trajectory of the FP.
  • a method of reconstructing an image in computed tomography comprises: obtaining a sinogram of an object; determining at least one fixed point of the object; letting the fixed point to be a virtual rotation axis such that the fixed point corresponds to a straight line across a center of the sinogram; calculating relative positions of points other than the fixed point of the object relative to the fixed point in the sinogram; and reconstructing an image based on a calcuation of the relative positions of the points.
  • a computer- implemented method for reconstructing an image in computed tomography includes a processor, and the method comprises: obtaining, by the processor, a sinogram of an object; determining or receiving, by the processor, at least one fixed point of the object; translating, by the processor, the fixed point to be a virtual rotation axis such that the fixed point corresponds to a straight line across a center of the sinogram; calculating, by the processor, relative positions of points other than the fixed point of the object relative to the fixed point in the sinogram; and reconstructing, by the processor, an image based on a calculation of the relative positions of the points.
  • a non-transitory computer-readable medium having stored thereon computer-executable instructions When executed by a computer, the computer-executable instructions cause the computer to: obtain a sinogram of an object; determine or receive at least one fixed point of the object; translate the fixed point to be a virtual rotation axis such that the fixed point corresponds to a straight line across a center of the sinogram; calculate relative positions of points other than the fixed point of the object relative to the fixed point in the sinogram; and reconstruct an image based on a calculation of the relative positions of the points.
  • a system for reconstructing an image in computed tomography comprises: a processor; an input coupled to the processor and configured to receive a parallel projection dataset; and a memory coupled to the processor.
  • the memory includes computer-executable instructions that when executed by the processor cause the processor to: obtain a sinogram of an object; determine or receive at least one fixed point of the object; translate the fixed point to be a virtual rotation axis such that the fixed point corresponds to a straight line across a center of the sinogram; calculate relative positions of points other than the fixed point of the object relative to the fixed point in the sinogram; and reconstruct an image based on a calculation of the relative positions of the points.
  • Fig. 1 schematically shows a flow diagram of a method of image reconstruction in computed tomography according to an exemplary embodiment of the present invention.
  • Figs. 2a-2c are sinograms of specimen placed on several different part of the stage in which we marked the stage with the red dot at the bottom to indicate ⁇ is zero degree.
  • Figs. 3a-3b are sinograms with the translation errors during the beam time.
  • Figs. 4a-4c are sinograms and reconstruction images of a layer of Hanford soil in a polyether ether ketone(PEEK) column from National
  • Synchrotron Light Source (NSLS) X2B beamline at Brookhaven National Laboratory (BNL) .
  • Fig. 5 shows the sinogram and its reconstruction image with which we figured P CA of each column in Fig. 3b sinogram and align them on the function
  • Figs. 6a-6c show analysis of a partial image of human lower jaw including the teeth.
  • Figs. 7a-7d show objects of prolate spheroid located on the rotating stage and their sinograms.
  • Figs. 8a-8c show the sinogram pattern of cylindrical specimen and the CA trajectory, depending on the tilt of the object or the RA.
  • Figs. 9a-9c show shadow changes depending on the location of a cylindrical specimen.
  • Fig. 10 shows a trajectory of a fixed point when there were several errors during beam time.
  • Figs. 11a- lib show the cases when the x-ray density of projection is changed during the beam time.
  • Figs. 12a-12c show optimized reconstruction images with various optimization methods.
  • Figs. 13a-13b show the common layer in the projections and the sinogram.
  • Fig. 1 schematically shows a flow diagram of a method of image reconstruction in computed tomography according to an exemplary embodiment of the present invention.
  • a sinogram of an object is obtained in step SI.
  • a sinogram involves the information about a specific layer of an object and accumulates the projection shadows taken from each angle to build a reconstruction image of the layer. This sinogram will later be transformed into a reconstructed image through the inverse Radon transform or (Fast) Fourier transform with filters. Hence, an errorless reconstructed image will be obtained only with an ideal sinogram or an ideal projection set, and a necessary condition for the ideal sinogram is that its pattern is changed sequentially following the projection angles.
  • the sinogram was constructed by a projection image of the circular image specimen, a cross-sectional image of a cylinder in 2D.
  • the sinogram pattern is linear in this case.
  • the projection shadow from an angle remains the same, even when the specimen was moved to a different spot and had a different sinogram pattern.
  • the error occurring vertically to the beam shows a definite cut-off point as the graph of Fig. 3b illustrates.
  • Fig. 3b the error appeared when the parallel beam was shoot perpendicularly to the stage and the cut-off of the sinogram was reflected at the 90 degrees of ⁇ .
  • the error that arises when the specimen is moved perpendicularly to the beam is always reflected identically on the projection and the discontinuity of equal amount is also found in the sinogram.
  • V n is the distance to which the rth column has to be moved in the sinogram, and it is written as follows:
  • V n v*cos( 9 off-0 e ), n ⁇ e (or n ⁇ e)
  • ⁇ indicates the angle of rth column and Q e is the angle at which the orthogonal translation error occurred in the sinogram, v is the distance that the object is vertically moved to, and can be measured through the two columns 6 e -i and 6 e in the sinogram, for the sinogram exactly reflects the shift.
  • v we used a certain section of e-th column and the section will be compared to the part of Ce-l -t column.
  • a total pixel number m is used in calculation, s is the starting point in the (e-l)-th. column.
  • p,(j) indicates the value of a pixel position at / ' -th column and /-th row in sinogram; Pitt) indicates the initial pixel point.
  • t is an integer and indicates translation.
  • the pixel length is the unit length.
  • Figs. 4a-4c show how we can apply the orthogonal translation algorithm to the real projections.
  • Figs. 4a-4c are sinograms and reconstruction images of a layer of Hanford soil in a polyether ether ketone (PEEK) column from National Synchrotron Light Source (NSLS) X2B beamline at Brookhaven National Laboratory (BNL) .
  • the third pictures in 4a-4c are the magnified images of the white frame of the reconstruction images in the middle.
  • the center of the x-ray impermeable material is set as the fixed point and it is applied to the function ⁇ ⁇ representing the virtual rotational axis of the sinogram; the point is now the line across the center in the sinogram (black arrows). It is placed on the center of the image in the reconstruction (white arrow). It is also noticeable that its reconstruction image is much clearer.
  • P n is the distance to which the n-t . column has to be moved in the sinogram.
  • the translat ional error is not only either a horizontal or vertical error but also a combination of both.
  • a solution for the orthogonal translat ional error is not general enough.
  • the horizontal shift of an object is hard to detect on the projection image and thereby, hard to calculate. This leads us to a need to approach this issue using a fairly new concept and a point of view. Knowing that the errors in the real settings are complicated and often a mixture of different kinds, one should start with understanding and defining the relationship between the real space and the sinogram, which is actually a projected and reconstructed version of real space, so as to further use it to draw a general and automated method of correction.
  • the center line of a sinogram is made up of the projection of
  • the circular trajectory of a point p in the real space corresponds to a curve drawn by the sinusoidal function in the sinogram.
  • r is the distance between the rotation axis and the point p.
  • o is the RA.
  • the center O is converted to To, ⁇ in the sinogram, but not in the actual sinogram.
  • Fig. 5 shows the sinogram and its reconstruction image with which we figured P CA of each column in Fig. 3b sinogram and align them on the function T 50 _ 30 ..
  • the point p is a center-of-mass for a circular object if the object has an identical medium and acts as a fixed point to represent the same spot even when the projection angle changes.
  • step S2 we determine at least one fixed point of the object in step S2 and let the fixed point to be the virtual rotation axis such that the fixed point to be a straight line across the center of the sinogram(step S3) .
  • step S4 relative positions of the points other th an the fixed point of the object relative to the fixed point in the sinogram are calculated in step S4. Based on this calculation of the relative positions of the points, this sinogram may be transformed into a reconstructed image through the inverse Radon transform(step S5).
  • CA center of attenuation
  • the center of mass estimated by X-ray densities in projection images cannot play a role in our FP because of the followings: the X-ray absorption for the thickness of specimen is not linear and the specimen size is lager than the charged coupled device (CCD).
  • CCD charged coupled device
  • Our assumption for using MAC is that there is co-relationship between a unit voxel of real object and a unit voxel of reconstruction i mage.
  • the CA calculation requires the object part in a subset of common layers. We define a common layer that a plane envelops the same whole part of the object' s axial level in the real space and perpendicular to the RA.
  • ne value of MAC should be changed into the one expressed in length to calculate the CA, we call the modified density (MD) relating to the sum of mass attenuation coefficient in a projection set.
  • MD modified density
  • any object When an x-ray beam is shot to an object, the object absorbs certain amount of the energy and the rest of attenuated energy arrives on the detect or. Then we get the projection image.
  • any object has a center-of-mass of classical mechanics, we assumed that any object has an invariable center of MAC, and it is fixed on a certain spot, either inside or outside of the specimen, acting as a fixed point that does not change depending on the projection angle. This fixed point can be calculated from the projection images obtained from each angle of x-ray penetration. It will lie on the sinogram satisfying the T r , ⁇ function that was mentioned earlier and this is how we get an ideal sinogram pattern.
  • the calculation for CA is very similar with the one for center-of-mass of classical mechanics.
  • a virtual rectangular coordinate and unit cubes are adopted in the real space and each vertex is the whole number on the coordinate.
  • the /-th cube among the n cubes of the object has mass attenuation coefficient p/p (MAC) for the given unit cube related to voxel length on its designated location and it is represented as a,- which can be linearly calculated through a series of calculation processes. (We can use other coefficients related to X-ray transmittance. )
  • ⁇ 3 ⁇ 4 is cx , and c satisfy that an unit voxel density for the given
  • A is the total sum of ⁇ ?, ⁇ and a constant value.
  • A is defined in a subset of a whole common layer set (this will be discussed in 3D) and n is the total grid number of the object in a subset of common layers of the real space.
  • r ⁇ indicates the center of i— th grid.
  • the attenuation value of the area except for the computational domain for the object shadow should be zero in the ideal status. If it is not zero, P CA might not be able to act as the fixed point. So we need to modify the attenuation value of this area to have at least the average of zero when it is not exactly zero, ensuring the same amount of MD is added or subtracted to the p,-j area.
  • CA in the real space becomes a specific point that we know and it is projected to be P CA and expressed as the T r , ⁇ p function on the sinogram.
  • the center of projection is always the center line of the sinogram. Therefore, when P CA from each angle of x-ray beam is translated onto the center line ⁇ , ⁇ of the sinogram, it can be considered the same as the fixed point of an object is placed on the RA. In other words, we are able to get rid of all the translation errors in the 2-dimensional space by translating P CA of each projection on the T r , ⁇ p function. Since P CA of each projection is one of the projected fixed points, all fixed points can be translated on ⁇ ⁇ , ⁇ and expressed in the sinogram.
  • the center line of the sinogram does not represent a RA.
  • the center line is the virtual rotation axis representing ⁇ , ⁇ , and rearrange any fixed point on ⁇ ⁇ to make one of ideal sinograms.
  • Figs. 6a-6c show how we applied this idea to the real images which illustrates analysis of a partial image of human lower jaw including the teeth.
  • Fig. 6a shows an image of the sample and its sinogram (The object is on the lower right side of the stage).
  • the P CA s of all projections are marked black in the sinogram. They follow the circular trajectory in the real space, therefore show sinusoidal graph in the sinogram.
  • Fig. 6b shows a sinogram with artificial translation errors added to the sinogram of Fig. 6a including vertical and horizontal movement at each angle and its reconstruction image.
  • the P CA s, the black marks are all scattered.
  • Fig. 6c shows a sinogram that we aligned P CA of the sinogram of Fig. 6b on ⁇ , ⁇ and its reconstruction image.
  • the P CA s are arranged linearly on the center of the sinogram. CA is on the center of the stage and the image is ideally restored.
  • a translation error is the error that happens when the object is moved by any chance during the beam time, and the movement can be in three directions in the 3D space.
  • a compensation for this error can be done through just the way we did with the translation error in 2D space, bringing P CA s on the T r , ⁇ , ⁇ function.
  • Tr,4 > ,h (r*cos( Q- ⁇ ), ),0 ⁇ ⁇ ⁇ 180 ° , where h is a level of a common layer of a projection set.
  • the translation error in 3D is different from the one in 2D in that we should adjust the layer of FPs so that the FP is on the same layers.
  • To make our calculation easier, we will place the CAs on the RA (r 0) of the projections' center layer ( F0) and this process will be more beneficial if one considers using an optimization method to correct tilting errors. By doing this, we can compensate most of the translation errors and the CA is on the center of projection (Figs. 7a-7d) .
  • Figs. 7a-7d show an object of prolate spheroid is located on the rotating stage, which has the center of CCD as the RA, and rotates for the 360 degrees.
  • the azimuthal angle of the object is 0 degree when the ⁇ is zero.
  • the white dot and the line represent where P CA lies against each ⁇ .
  • two cleared fixed points in the projection sets at bo th angles red and orange colored circle are the first and second fixed points, respectively.
  • those fixed points are placed on different axial level of the CCD.
  • tilting errors In 3-dimensional space, it is important to consider tilting errors because a tilted image carries information from different layers and consequently induces a flawed image reconstruction. Thus, if we compensate the tilting error, it means that we make one layer to carry all the information about a single part of an object.
  • To categorize and analyze tilting errors we should further discuss about the object itself and the stage that it is placed on. We will not call the case of tilted object an error. It is because we can make a reconstruction image without any correction procedures in this case. When it is the RA that is tilted, one should make sure that the tilting error is corrected.
  • Fig. 8a shows when the object is tilted whereas Fig. 8b shows when the RA is tilted.
  • the sliced image of the specimen upon a same layer is identical in those cases.
  • their sinograms show definitely different patterns.
  • the sinograms of its top and bottom follow sinusoidal functions.
  • the RA is tilted, however, the heights are the same with the ones in the former case, while the patterns of the top and bottom go linear starting from each height.
  • a vertical tilt the polar angle increases when the azimuthal angle is either 90 or 270 degrees.
  • the polar angle increases when an azimuthal angle is either 0 or 180 degrees in a parallel tilt.
  • the azimuthal angle increases counter clockwise against the beam.
  • the ideal RA which stands upright without any tilting error is assumed to be the reference for the polar angle.
  • Fig. 9a shows a projection image of the cylinder that is leaned in parallel with the beam and its depth of the shadow is changed, meaning the information of the image is changed.
  • the shadow is darker than before; the information of the image is changed and the restoration with the projection is not easy in this case.
  • Fig. 9c shows the projection image of the same cylinder tilted vertically in Fig. 9c. It is shown that the depth of shadow remains unchanged, even though the object is tilted; the projection information is not changed. In this case, it is possible to restore with the projection image.
  • the priority is to know by which angle the RA is tilted.
  • the whole projected images will be corrected accordingly to the tilted angle using the center line of whole projection , ⁇ , ⁇ , ⁇ ,, as a fiducial line.
  • the line segment of P CA stands for the trajectory of CA, and the RA is perpendicular to it. If this RA and the vertical line makes a certain angle, it is the angle by which we will rotate the projection set to meet the ideal one which doesn' t have the tilt error.
  • trajectory in the projection is clockwise or counter clockwise depends on whether the azimuthal angle of RA is 0 degree or 180 degrees. This method can be also applied to the mixed error of vertical and parallel tilts.
  • Fig. 10 shows a trajectory of a fixed point when there were several errors during beam time.
  • the CA we suggested in this disclosure will function as the fixed point that is one of the intrinsic factors of an object. It works as an invariable point inside (sometimes outside) of an object which does not change even when the object is moved, or the RA is tilted. Nonetheless, we have to calculate this CA from the projected image so as to utilize it, which results in one limitation that the intensity variation of the beam reaching each cell of the CCD in the formula for P CA should be linearly proportionate to the length of the specimen. That is, the attenuation value of each cell which consists of the image from the projection should have some linear relationship with the length of the specimen or at least should be changeable to have linear relationship.
  • Figs. 11a- lib show the cases when the x-ray density of projection is changed during the beam time.
  • Fig. lib shows the sinogram and its reconstruction image when the CA was applied to the projection with changed x-ray density.
  • the CA in our study is expected to significantly contribute to a better image reconstruction in x-ray tomography and to be utilized as a versatile tool.
  • the specimen is mixed up with materials having greatly diverse ACs to the extent where it is out of linearity, it is hard to compensate the unlinear area and this may result in errors.
  • it is not beneficial to use the CA in those cases when the specimen is projected with impermeable materials like metal to make it distinguished. It is better to project the specimen itself without any other distinguishing material when anyone wants to use CA in image reconstruction.
  • the ring artifact due to the CCD defect could be another hurdle in CA application. We need to correct the ring artifact beforehand; the correction itself can also raise some changes in reconstruction errors.
  • a computer program may be stored/distributed on a suitable medium such as an optical storage medium or a solid-state medium supplied together with or as part of other hardware, but may also be distributed in other forms, such as via the Internet or other wired or wireless telecommunication systems.
  • a suitable medium such as an optical storage medium or a solid-state medium supplied together with or as part of other hardware, but may also be distributed in other forms, such as via the Internet or other wired or wireless telecommunication systems.

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  • General Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
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  • Apparatus For Radiation Diagnosis (AREA)
  • Analysing Materials By The Use Of Radiation (AREA)

Abstract

Étant donné que la tomographie par rayons X est désormais largement adoptée dans de nombreuses domaines différents, il devient plus crucial de trouver une procédure robuste de manipulation de données tomographiques pour obtenir des images reconstituées de qualité. Bien qu'il existe déjà plusieurs techniques, il paraît utile de disposer d'un procédé plus automatisé pour éliminer les erreurs éventuelles qui gênent la reconstitution d'images plus nettes. La présente invention concerne une variante de procédé et un nouvel algorithme utilisant le sinogramme et le point invariant (FP). Un nouvel concept physique de centre d'atténuation (CA) a également été introduit pour déterminer comment ce point invariant est appliqué à la reconstitution d'images avec des erreurs qui ont en outre été catégorisées.
PCT/KR2017/000506 2016-04-29 2017-01-13 Procédé de reconstitution d'images en tomodensitométrie Ceased WO2017188559A1 (fr)

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CN110910491A (zh) * 2019-11-27 2020-03-24 广西科技大学 一种三维人体建模优化方法及系统
CN111968728A (zh) * 2019-05-20 2020-11-20 杭州依图医疗技术有限公司 一种图像的处理方法和处理设备
KR20240172854A (ko) 2023-06-02 2024-12-10 전경택 양자 알고리즘을 이용한 ct 이미지 생성방법

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CN111968728A (zh) * 2019-05-20 2020-11-20 杭州依图医疗技术有限公司 一种图像的处理方法和处理设备
CN111968728B (zh) * 2019-05-20 2024-03-08 杭州依图医疗技术有限公司 一种图像的处理方法和处理设备
CN110910491A (zh) * 2019-11-27 2020-03-24 广西科技大学 一种三维人体建模优化方法及系统
KR20240172854A (ko) 2023-06-02 2024-12-10 전경택 양자 알고리즘을 이용한 ct 이미지 생성방법

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