JPH0767867A - Three-dimensional image reconstituting method - Google Patents

Abstract

PURPOSE:To improve the accuracy of a reconstituted image without decreasing an irradiated range with respect to an imperfect reconstituted area which expands by the irradiated range of a conical beam, in a CT device for irradiating a body to be examined with the conical beam. CONSTITUTION:An inclination phi made by a center axis M of a conical beam generated from an X-ray source and a body axis orthogonal axis of a body W to be examined is displaced to each different angle on a plane containing the body axis, respectively, and at every inclination, the conical beam is rotated relatively by 360 deg. around the body to be examined centering around the body axis, and based on plural two-dimensional projected images, a three-dimensional image of the body to be examined is reconstituted.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a three-dimensional image reconstruction method suitable for, for example, cone beam X-ray CT.

[0002]

2. Description of the Related Art In recent years, in X-ray CT, when reconstructing the internal information of the object to be inspected from a two-dimensional projection image into a three-dimensional image, it is efficient to project the object with a conical X-ray. Scanning schemes are being considered. For example, IEICE Transactions '88 / 4 Vol. J71-D No. In the document I entitled "Filtered Backprojection Method for Cone-Beam X-ray CT" published by Matsuo et al. In No. 4, as shown in FIG. 8, it is orthogonal to the z-axis which coincides with the body axis of the object to be inspected. Do xy
The central axis of the X-ray source is set on a plane, and the cone beam emitted from the X-ray source to the object to be inspected with a divergence angle α is set around the z axis to
X rotated by 60 ° and transmitted through the inspection object on the two-dimensional detector
Line intensity distribution Projection is described.

In the embodied apparatus, an X-ray source that emits a cone beam and a two-dimensional detector facing it are integrated, and the cone beam makes one revolution around the body to be inspected around the body axis of the body to be inspected. To do. Then, a cone beam is emitted at regular intervals during the one rotation. The two-dimensional detector is composed of a plurality of detectors. Here, the two-dimensional projection image measured by the two-dimensional detector is p (β, using the angular position θ of the X-ray source on the xy plane and the coordinates β, γ on the two-dimensional detector.
γ, θ). β is the coordinate in the direction perpendicular to the z axis,
γ is a coordinate in a parallel direction. p (β, γ, θ) is 2
It is defined as the line integral of the reconstructed image f (x, y, z) along the path of the cone beam from the X-ray source projected onto the two-dimensional detector to the two-dimensional detector.

The two-dimensional projection image is reconstructed into a three-dimensional image by the back projection method after the filter correction. In this case, if a scanning method in which projected images from all directions in the three-dimensional space are measured is adopted, the object to be inspected can be completely reconstructed by back-projecting after correction by the two-dimensional ρ filter. . However, in the scanning method using the cone beam, the cross section in which the cone beam is incident perpendicularly to the Z axis (hereinafter referred to as a perfect reconstruction plane) has an xy of z = 0 where the X-ray source rotates.
The two-dimensional ρ filter cannot be applied to the reconstruction area in the z-axis direction other than the plane because of the incompleteness of the two-dimensional projection image. Hereinafter, this area is also referred to as an incomplete reconstruction area.

Therefore, in the above document I, in the cone beam scanning method, a one-dimensional ρ filter that corrects only in the direction of rotation of the cone beam perpendicular to the z-axis is used, and an incomplete reconstruction region outside z = 0 is used. On the other hand, the two-dimensional projected image is cos
It is multiplied by the correction term of γ.

[0006]

However, according to the correction method described in the above-mentioned document I, the transmission path of the cone beam is inclined with respect to the z-axis as the reconstruction area is farther from the origin of z = 0. Becomes large, and as a result, as shown in FIG. 9, the reconstruction error increases as the reconstruction area becomes farther from the origin. Such an increase in reconstruction error is
For example, when non-destructively observing the sizes and positions of unnecessary cavities and cracks in industrially processed products, accuracy cannot be obtained, and there is a great risk of overlooking defective products that have problems in use.

[Technical Report] Vol. '90, No16
Reference II entitled “3D CT Image Reconstruction Experiment by Conical Beam Projection” published by Kudo et al. In No. 8 describes orthogonal scanning in which an X-ray source is moved on two circles orthogonal to each other, and 2-3.
Although he proposes helical scanning in which a spiral of rotation is moved, the scanning direction is displaced by 90 ° in orthogonal scanning, which complicates the mechanism for that. In the latter helical scanning, X-rays pass through the same cross section. There is a problem in accuracy because it is not done.

It is an object of the present invention to provide a technique for reducing the reconstruction error by reducing the inclination of the transmission path in the body axis direction of the object to be inspected due to the cone beam and reducing the correction width during reconstruction. And

[0009]

According to the present invention, an X-ray source and a two-dimensional detector are arranged so as to face each other with an object to be inspected interposed therebetween, and the X-ray source is based on a body axis orthogonal axis of the object to be inspected. The tilt angle of the cone beam from the above is respectively displaced to a plurality of values on a plane including the body axis, and the cone beam is relatively rotated around the body to be inspected about the body axis for each tilt angle by 360 °, The three-dimensional image of the inspection object is reconstructed based on each two-dimensional projection image obtained from the two-dimensional detector by the relative rotation.

In the method of reconstructing the three-dimensional image of the object to be inspected based on each of the two-dimensional projection images, the three-dimensional image of each of the two-dimensional projection images is formed with the central axis of the cone beam as a reference. The filtering process is performed after the weighting process is performed in the direction of the spread angle. In a preferred aspect, the tilt angle of the cone beam is set in a range in which the cone beam has a transmission path orthogonal to the body axis of the object to be inspected.

[0011]

The cone beam emitted from the X-ray source of the present invention is
The tilt angle with respect to the axis orthogonal to the body axis of the object to be inspected is displaced to a plurality of discrete angles, and the cone beam is relatively moved around the object to be inspected around the body axis at each position corresponding to each angle of inclination. Three
It is rotated 60 °. As a result, a two-dimensional projected image for each tilt angle is obtained from the two-dimensional detector. The present invention reconstructs a three-dimensional image from a plurality of two-dimensional projection images obtained as described above.

In the present invention, by displacing the tilt angles of the cone beams to different angles, regions where the cone beams intersect and overlap each other are generated. The two-dimensional projection image is measured by irradiating the object to be inspected in this overlapping region,
The z-axis divergence angle of the same region is also achieved by using one cone beam having the same divergence angle. Therefore, from the viewpoint of the cone beam used in the present invention, even if the divergence angle is narrowed, if the divergence angle of the overlapping region can secure the range that illuminates the region of interest, an equivalent reconstructed image can be obtained. As the divergence angle can be narrowed, the present invention reduces the incomplete reconstruction area and the correction width when multiplying the correction term, and as a result, the reconstruction error is also proportionally reduced. You can

For example, as shown in FIG. 1, the central axes M (center of the X-ray source) of the two cone beams are inclined so as to have an inclination angle of ± φ with respect to a body axis orthogonal axis (here, y axis) orthogonal to the z axis. Axis) is set, an area shown by the divergence angle β is formed in which each cone beam overlaps. If this area is considered to be the same as the divergence angle of the conventional cone beam, such an overlap area is defined. The divergence angle α of the resulting two cone beams may be smaller than the angle β, and the area of imperfect reconstruction by each cone beam will be reduced.

Further, in the reconstruction process of the present invention, weighting each two-dimensional projection image in the three-dimensional divergence angle direction centered on the body axis orthogonal axis is performed by the air due to the difference in distance in the same direction. It is possible to correct the absorption coefficient of water or the like and accurately acquire the absorption amount of the inspection object, and obtain further accuracy of the three-dimensional image after backprojection. Further, by limiting the tilt angle of the cone beam to a range in which the cone beam has a transmission path orthogonal to the body axis of the object to be inspected, the two-dimensional projection images obtained for each tilt angle form a perfect reconstruction plane. By having
It is possible to reconstruct a more accurate three-dimensional image. Figure 1
In the example, two perfect reconstruction planes occur. Furthermore, by increasing the set number of tilt angles, the perfect reconstruction plane is increased and the accuracy is further increased.

[0015]

As described above, according to the present invention, the cone beam emitted from the X-ray source is displaced so that the inclination angle with respect to the body axis orthogonal axis of the object to be inspected is a plurality of discrete angles. Since the cone beam for each tilt angle is relatively rotated 360 ° around the object to be inspected, the divergence angle of the cone beam can be substantially reduced,
The incomplete reconstruction area is reduced, the reconstruction error is reduced, and the internal information of the inspection object can be accurately measured.

[0016]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS A three-dimensional image reconstruction method of the present invention will be described below with reference to FIG.
An example applied to an industrial CT device for measuring a cylindrical object shown in FIG. In the X-ray CT apparatus shown in FIG. 1, the X-ray tube 1 is integrated with a base 2, for example,
A two-dimensional detector 3 is arranged on the base 2 so as to face the X-ray tube 1. Further, a bracket 4 is fixed to the base 2, and a motor 5 for rotating and driving a cylindrical object W as an object to be inspected around the z axis is attached to the bracket 4.
Furthermore, the base 2 has an origin O on the z-axis on the same plane as the z-axis.
A motor 6 that rotates the cylindrical object W around an R axis that passes through and is orthogonal to the z axis is attached. The motor 5,
6, a stepping motor is used, for example, and each is operated by a motor driver.

The scanning mechanism having the base 2 as a base is controlled by the main computer 9. That is, the main computer 9 has a motor controller 10 for controlling the motors 5 and 6 via the drivers 7 and 8 in a procedure described later.
Is connected to the X-ray control computer 11, and the X-ray transmission intensity distribution from the two-dimensional detector 3 is captured via the A / D converter 12. Here, the X-ray control computer 11 is a target computer that issues a command to the motor controller 10 by the main computer 9 to operate the X-ray tube 1 at the timing of step-driving the motor 5.

As shown in FIG. 2, the X-ray CT apparatus having the above-described structure first carries out step S1 to drive the motor 6 and, as shown in FIG. Tilt the coincident z-axis by φ [rad] in the negative direction (downward in the figure). This is equivalent to setting the inclination angle between the central axis M of the cone beam and the axis orthogonal to the body axis to -φ.
Next, in step S2, a cone beam is emitted from the X-ray tube 1. The rotation angle θ of this first cone beam is the initial measurement angle (for example, 0 °), and the cone beam is sequentially rotated around the cylindrical object W by the operation of advancing the rotation angle by Δθ in step S5 after steps S3 and S4. Is irradiated. The step of Δθ depends on the driving of the motor 5. Step S6 is a judgment as to whether or not one rotation has been performed. If “YES” in the step S6, the process proceeds to FIG.
As shown in (B), the body axis of the cylindrical object W is tilted by φ [rad] in the positive direction (upward in the figure). This is equivalent to setting the tilt angle of the cone beam to + φ. After that, similarly to FIG. 3, the rotation angle is sequentially advanced, and during that time, the processes corresponding to steps S2 to S5 of FIG. 3 are performed, and when it is confirmed that the cylindrical object W is rotated once in step S9, A two-dimensional projection image of the cylindrical object W at the corresponding Z-axis position is obtained.

The two-dimensional projection image is calculated in steps 3 and S4. In step S3, the X-ray transmission intensity distribution on the two-dimensional detector 3 is captured as a digital signal from the A / D converter 12, and in step S4, the cylindrical object W is determined from the X-ray irradiation intensity and the transmission intensity distribution. X-ray absorption coefficient distribution, that is, a two-dimensional projection image is calculated. Thus, in this embodiment, two two-dimensional projected images at the Z-axis position corresponding to the inclination angle of ± φ are obtained. In this case, the two-dimensional projection image is obtained for each irradiation, but it is also possible to collectively obtain the two-dimensional projection image after collecting the transmission intensity distribution after scanning for each two rotations. Is.

Next, a three-dimensional image is reconstructed from the two-dimensional projection image obtained as described above through the three-dimensional reconstruction process of this embodiment. The three-dimensional reconstruction process is as shown in FIG.
The two-dimensional projection image p (u, v, θ, φ) includes a weighting process 13 in the z-axis direction, a one-dimensional filtering process 14 around the z-axis, and a backprojection process 15. Where u, v
As shown in FIG. 7, represents the orthogonal coordinates on the two-dimensional detector 3, u is the direction orthogonal to the z-axis, and v is the direction parallel to the z-axis.

In the weighting process 13, the weighting functions w (u, v) in the u and v directions are multiplied as shown in Equation 1.

[0022]

[Mathematical formula-see original document] p '(u, v, [theta], [phi]) = P (u, v, [theta], [phi]) * w (u, v) The weighting function w (u, v) is expressed by Equation 2.

[0023]

[Equation 2]

Here, Cs is the distance from the X-ray tube 1 to the origin O, Cd is the distance from the origin O to the two-dimensional detector 3, and μ
Represents an absorption coefficient of a substance (for example, water or air) around the object to be inspected. This weighting function corrects the absorption coefficient in the three-dimensional divergence direction of the cone beam. Also, u and v are respectively

[0025]

[Equation 3] u = D (xcos θ + ysin θ)

[0026]

## EQU00004 ## v = D {zcos .phi .- (ycos .theta.-xsin .theta.) Sin .phi.}

[0027]

[Equation 5] Next, the filtering process 14 consists of the following three operations.

[0028]

[Equation 6] P ′ (ω _u , v, θ, φ) = F {p ′ (u, v, θ, φ)}

[0029]

[Equation 7] _{Q (ω u, v, θ} , φ) = P '(ω u, v, θ, φ) · F (ω u)

[0030]

[Mathematical formula-see original document] q (u, v, [theta], [phi]) = F < ^-1 > {Q ([omega] _u , v, [theta], [phi])} Equation 6 represents the Fourier transform of the projected image after weighting, and Equation 7 represents the Fourier transform. An operation for multiplying the filter function F (ω _u ) in space, Expression 8 represents an inverse Fourier transform. Here, ω _u is a spatial frequency, and F (ω _u ) is a mathematical expression 9.

[0031]

[Equation 9]

However, s is the number of pixels. The filter function F (ω _u ) of the present embodiment has a characteristic that monotonically increases in proportion to the spatial frequency and is corrected by Cs and Cd. The back-projection processing 15 performs the operation of Expression 10, and integrates the image signal q (u, v, θ, φ) around the z axis to obtain a reconstructed image f.

[0033]

[Equation 10] Here, the coefficient term cos α ′ / L ² is a correction term, and α ′
Is the sum of the divergence angle α and the tilt angle φ of the cone beam,
It represents an angle corresponding to the reconstruction area in the z-axis direction. L represents the distance from the origin O to the X-ray tube 1. The angle α'is the tilt angle φ
And the divergence angle α of the cone beam are summed. Compared with the divergence angle β of the conventional cone beam for one rotation only, the z-axis direction angle of the region where the two cone beams overlap is β
As a result, α ′ <β can be satisfied, and as shown by the dotted line in FIG. 9, the reconstruction error can be reduced to about half that of the conventional one on average.

The above reconstruction method is an example, and the weighting function,
The function F (ω _u ) or the coefficient term cos β / L ² can be arbitrarily selected according to the condition of the object to be inspected or the like. In particular,
In the present embodiment, before the filtering process 14, the weighting process 13 corrects the absorption coefficient due to the difference in the distance of the cone beam in the direction of the three-dimensional divergence angle of the cone beam as a reference, and the inspection target is inspected. Since the accurate absorption amount of the body is calculated, more accurate reconstructed image can be obtained.

As shown in FIG. 5, since each cone beam of this embodiment has a transmission path a which is orthogonal to the body axis of the cylinder, two perfect reconstruction surfaces are formed in this transmission path. It Although relatively accurate reconstruction images can be obtained in the incomplete reconstruction areas near both of these perfect reconstruction surfaces, in the present embodiment, by having two perfect reconstruction surfaces, the incomplete reconstruction areas in four neighborhoods can be obtained. There is a configuration area. On the other hand, in the conventional one-rotation type, since there is only one perfect construction surface, there are two incomplete reconstruction areas in the vicinity. Therefore, it can be said that the reconstructed image of the present embodiment is extremely accurate even by the number of incomplete reconstructed regions in the vicinity where a relatively accurate reconstructed image is obtained.

In the present invention, although the data of the reconstructed images are duplicated, the data closer to the perfect reconstruction plane is selected. Further, the present invention does not exclude the case where the tilt angle is set so as not to have a perfect reconstruction plane.

[Brief description of drawings]

FIG. 1 is an explanatory view schematically showing a reconstruction method of the present invention.

FIG. 2 is a block diagram showing an example of an apparatus adopted in the present invention.

FIG. 3 is a flowchart showing a process of obtaining a two-dimensional projection image of the present invention.

FIG. 4 is a flowchart showing a process of obtaining a two-dimensional projection image of the present invention.

5 is an explanatory diagram showing a state of tilt displacement in the device shown in FIG.

FIG. 6 is a block diagram showing a reconstruction process of the present invention.

FIG. 7 is an explanatory diagram illustrating a reconstruction process of the present invention.

FIG. 8 is an explanatory diagram showing a conventional reconstruction method.

FIG. 9 is a characteristic diagram of a reconstruction error compared between the present invention and the related art.

[Explanation of symbols]

W ... Inspected object, 1 ... X-ray source, 3 ... Two-dimensional detector, 5, 6
… Stepping motor, 9… Main computer, 11… X
Line control computer, φ ... inclination.

Claims (3)

[Claims] 1. An X-ray source and a two-dimensional detector are arranged to face each other with an object to be inspected interposed therebetween, and an inclination angle of a cone beam from the X-ray source with respect to an axis orthogonal to the body axis of the object to be inspected The cone beam is displaced to a plurality of values on a plane including the body axis, and the cone beam is relatively rotated about the body to be inspected about the body axis by 360 ° for each tilt angle, and the two-dimensional detection is performed by the relative rotation. A three-dimensional image reconstructing method, which reconstructs a three-dimensional image of the object to be inspected based on each two-dimensional projection image obtained from the instrument. 2. A method for reconstructing a three-dimensional image of the object to be inspected based on each of the two-dimensional projection images is a three-dimensional image of the cone beam with respect to the central axis of the cone beam. Processing for weighting in the divergent angle direction, filtering processing for multiplying each of the weighted images by a predetermined filter function after Fourier transform, and performing inverse Fourier transform of the result, and outputting the result. The three-dimensional image reconstruction method according to claim 1, further comprising backprojection processing for obtaining a reconstructed image by integrating about an axis. 3. The three-dimensional image reconstruction according to claim 1, wherein the inclination angle of the cone beam is set in a range in which the cone beam has a transmission path orthogonal to the body axis of the object to be inspected. Law.