JPH0634789B2 - Digital tomography system - Google Patents

Description

Description: FIELD OF THE INVENTION The present invention relates to an X-ray diagnostic apparatus, and more particularly to a method and apparatus for obtaining a plurality of tomographic images by calculation processing from projection images measured from multiple directions. The present invention relates to a method and apparatus for correcting a plurality of acquired tomographic images by a calculation process to obtain a tomographic image closer to a true tomographic image.

[Background of the Invention]

Conventionally, a linear orbit tomography apparatus or a multi-orbit tomography apparatus has been used as an apparatus for capturing a tomographic image of an object to be inspected. These devices are devices for obtaining a desired tomographic image by blurring information other than the target cross section in the scanning trajectory direction, and there is a problem that a blurred shadow other than the captured tomographic plane becomes an obstacle to interpretation. Have. In addition, in normal imaging, only one cross section can be obtained by one scanning imaging, and when it is desired to comprehensively evaluate and interpret a large number of tomographic images, it is necessary to repeat the scanning imaging for the required number of tomographic images. Exposure dose becomes a problem. Further, in the case of an inspected object that moves, there is a problem that the tomographic images taken independently are not continuous.

To solve these problems, projection images at each position during traveling are independently photographed, and a plurality of tomographic images are obtained from one of the plurality of projection images by digital processing by scanning once, and other tomographic images are obtained. Several attempts have been reported to remove obstacle shadows from the fault plane. These are shown below.

1) IEEETrans, on Biomedical Eng.Vol.BME-27, No.11, p
p640 ~ 655 (Nor. 1980), HEKNUTSSON and others “Ectomography-a
new Radiographic Reconstruction method ”2) ACTA RADIOLOGICA Vol.21, Fase.4.pp433-442, (198
0), p.EDHOLM and others, “a new radiographic method for r
eproducing a selected slice of naring thickness ”3) Proceedings of ISMII'84 pp218-211 (1984), Roclf
AJgroenhuis and others, “a Prototype Digital Tomograph
ic X-Ray System for Dental Application ”4) Proceedings of ISMII'84 pp382-387 (1984), UERu
ttimann et al., “Iteratine Restoration of Tomosynthe
tie Slices ”With these methods, it is possible to obtain a multi-layered image in which the obstruction shadows have been reduced to a certain extent by one scanning scan.
There are problems that the scanning orbit is limited to a circle and that the negative undershock is remarkable around the highly absorbing material in the tomographic image.

[Object of the Invention]

The object of the present invention is to solve the problems of the prior art.
This is to obtain a high-quality tomographic image with a small number of obstacle shadows other than the target tomographic plane by one scanning imaging. Further, the scanning orbit is to provide a technique applicable to various orbit imaging methods including a linear orbit.

[Outline of Invention]

The present invention directly backprojects multi-directional projection data obtained by measurement into a three-dimensional space to obtain a three-dimensional tomographic image by calculation, and for a three-dimensional tomographic image in which obstacle shadows are mixed. Then, a technique for greatly reducing the obstruction shadow by the three-dimensional inverse filter method in the three-dimensional Fourier space is devised by utilizing the Inbals response following the scanning trajectory obtained by using a small highly absorbing object.

[Principle of Invention]

The principle of the invention presented here will be described. FIG. 1 shows the measuring method of the object to be inspected.

The inspection object measurement space is represented by coordinates (x, y, z), and the center of the coordinates is O. The radiation source S is always directed toward the center O of the inspection object measurement space and moves on the trajectory T. The detector moves centering on O, facing the radiation source S,
The center Q of the dimensional detector, the center O of the measurement coordinates, and the radiation source S are always located on a straight line, the distances SO and OQ are kept constant or their ratios are kept constant, and the detector surface is of the measurement coordinates. Scanning is performed so as to be positioned parallel to the xy plane. The detector measures the X-ray intensity after passing through the object under inspection when the source S during scanning moves on the trajectory T in a section of Δt. Each position of the two-dimensional surface image measured by the detector is indicated by coordinates (u, v) with the origin Q as the center. Next source S
Is moved to the next position along the track T, and the same measurement is performed. In this way, while the radiation source S sequentially moves on the trajectory T,
A plurality of surface images I _j (u, v) showing the X-ray intensity after passing through the object to be inspected are measured for each radiation source position.

[Multi-section calculation method]

These surface images are exchanged according to the equation (1) using the X-ray intensity distribution surface image I _oj (u, v) when the object to be inspected is not inserted at each source position.

Use _{P j (u, v) =} l n I oj (u, v) -l n I j (u, v) ...... (1) Menzo _P j (u, v) obtained as a result is the measurement X-ray absorption coefficient f (x, in the object to be inspected along the linear beam 1 passing through the beam position (u, v) of the cone-shaped beam
y, z) is a cumulative addition value and is a projected image P of the object to be inspected.
_j (u, v).

P _j (u, v) = ∫f _j (x, y, z) dl (2) The coordinate system (x, y, z) is used to represent each measurement positional relationship. The radiation source position is x _s , y _s , z _s ) and the distances OS and Q
When the O ratio and k (u, v) the origin Q of the coordinate is expressed as _{(-kx s, -ky s, -kz} s). Therefore, the position of the projected image P _j (u, v) with respect to the coordinate system (x, y, z) is expressed as (u−kx _s , v−ky _s , −kz _s ) and the equation of the beam l is Given in. Therefore (u, v) Becomes According to this equation, the point (x, y,
The point (u, v) in the projection coordinate system can be obtained from z).

The back projection method used in the X-ray CT apparatus is obtained by uniformly adding projection data P _j (u, v) along the beam 1 used for measurement in the measurement coordinate space (x, y, z). To be When this backprojection operation is expressed by an equation, the backprojection image g
(X, y, z) is Is required as. Here, (u, v) is given by the equation (4), and a three-dimensional backprojected image can be obtained by calculating g at all positions of the coordinate point (x, y, z). Of these back-projected images, g (z, y, o) is the same as a tomographic image conventionally obtained by a linear orbit tomography device or a multi-orbit tomography device, and the tomographic plane indicated by z = 0. It is an incomplete tomographic image that includes blurred shadows other than. However, by storing each projected image separately in this way and then performing calculations of equations (4) and (5), z
It is also possible to calculate tomographic images other than = 0 by one scanning measurement, and when it is desired to comprehensively evaluate and interpret a large number of tomographic images, tomographic images with good continuity between tomographic images can be obtained in a short time with low exposure. Obtainable.

[Reduction of obstacle shadows]

Next, a method of reducing an obstacle shadow included in this back projection image will be described.

The back-projected image obtained by the method described above is a tomographic image in which obstacle shadows are mixed in the z-axis direction. That is, the tomographic image g (x, y, o) cut at the plane of z = 0 includes the shade of the tomographic image g (x, y, z ₀ ) of z = z ₀ , and conversely g (x, y). , Z ₀ ) includes a shadow of g (x, y, o). These relationships are associated with each other by the scanning trajectory T between the respective tomographic images in the z direction. These relationships can be known by setting an object to be inspected that is extremely small and has a large absorption coefficient at each tomographic position and obtaining g. That shadow component of the tomographic plane of z = z ₀ is mixed with other tomographic plane knows Contaminant components to Yotsute z = z ₀ other surfaces to put a small high absorbing object in the plane of z = z ₀ be able to. When the trajectory T is in the plane z = z _s parallel to the plane of z = 0, this mixed component has a uniform relation in the fault of z = z ₀ and does not depend on the location (x, y). . On the contrary, when the trajectory T is not in the plane of z = z _s , it is not completely uniform, but it is considered to be almost uniform unless the object to be inspected exists near the origin O and the trajectory deviates greatly from the plane. It doesn't matter. Here, this mixed component is treated as being uniform in the fault at z = z ₀ , and a small highly absorbing object is obtained by placing it on the z axis, that is, (o, o, z ₀ ).

z = z of a small highly absorbing object placed in the section of z = z ₀
Fig. 2 shows the state of the components mixed in the fault plane other than ₀ .
Accordance connexion to the source scans the track T, in the fault plane z = z downward z = z ₀ from the section of ₀ -? Z orbit従Tsuta mixed pattern is drawn. In FIG. 2, T _s is a line of intersection between the conical surface formed by the trajectory T and the origin of z = z ₀ and z = z _s , and the mixing pattern is an expanded or reduced shape of this T _s .
Its intensity is inversely proportional to the distance Δz from z = z ₀ to the mixing surface.

z = mixing pattern of the equation of _{T s} in the plane of _{z s T s (x, y} ) = 0 ...... (6) to the z = _{z m} plane to z = _{z n} surface Is Given in. Here, δ is a function that becomes 0 when T _s = 0 and when T _S ≠ 0. The constant c is a standardized constant that satisfies ∫∫uz _m nz _n (x, y) dxdy = 1 (8). When this u is used, the relationship between the back projection image g (x, y, z) and the X-ray absorption coefficient f (x, y, z) in the body under inspection corresponding to the true tomographic image is g (x, y, z). ) = ∫∫∫uz′z (x′−x, y′−y) f (x ′, y ′,
z ') dx'dydz' ... (9) is given.

In the equation (9), g can be obtained by the method described above, and u is the equation (7) when the trajectory T _s shown in the equation (6) is relatively simple and can be expressed by an equation. Obtainable. When the trajectory T _s is complicated and the mathematical expression is difficult, it can be obtained experimentally by placing a small highly absorbing object on each u fault plane. Therefore, the true tomographic image f (x, y, z) having no obstacle shadow can be obtained by the inverse operation from the equation (9).

Now, the mixing pattern shown in the equation (7) is not uniform with respect to z _n . This makes the problem of finding f by the inverse operation from equation (9) difficult. Therefore, assuming that the object to be inspected exists near the origin O, it is approximated that the mixed pattern is uniform with respect to z _s .

Equation (7) is z _n = 0 Equation (9) is given by g (x, y, z) = ∫∫∫u (x′−x, y′−y, z′−z) f (x ′,
y ', z') dx'dy'dz '... (11) Equation (11) is the type of the tatami integral. Therefore, its Fourier transform is given by Eq. (12).

here Is the three-dimensional Fourier transform of g, u, f Given as.

From equation (12) By Seeking By Is required.

here Due to the above approximation, does not completely match the distribution image f of the absorption coefficient inside the true subject, but becomes a good three-dimensional tomographic image with reduced obstruction shadows.

A method of reducing an obstacle shadow when the scanning trajectory T is a relatively simple circle will be described. In the case of a circular orbit, T and T _s completely match, and the equation is that T (x, y, z) = T _s (x, y) = x ² where R is the radius of the circular orbit. + Y ² −R ² = 0 (18) Moreover, the mixing pattern u is the parameter α. U (x, y, z) αc · δ (α ² x ² + α ² y ² −R ² ) ...
Given as (20). From this u by the formula (14) Ask for. Next, from the backprojected image g obtained by the above-described multi-section calculation method, And calculate according to equation (16) Is calculated, and the tomographic image in which the obstruction shadow is reduced by Equation (17) To get

In this way, if the scanning trajectory is a simple straight line, circle, ellipse, or spiral, u can be calculated mathematically.
Even in the case of complicated trajectories, it is possible to analyze u using a computer or to directly measure u experimentally using a small high-absorber, and reduce the obstacle shadow by using u obtained by these methods. be able to. These flow charts are shown in FIG.

As above, as the method of reducing the obstacle shadow, the method of processing by using the mixed pattern of z = 0 approximately _assuming that the mixed pattern is uniform with respect to z _n has been described. Next, a method of calculating a three-dimensional tomographic image which is a further improvement of this approximation will be described.

[Tomographic image calculation method]

Introducing a new coordinate axis α represented by the following equation instead of the z axis in the above Equation (α <1) This coordinate axis is derived from the differentiation of both sides Therefore, this α coordinate is a non-uniform coordinate, and this coordinate interval is a coordinate proportional to the square of the distance from the trajectory surface z = z _s of the radiation source. Introducing these coordinates, Because Equation (23) can be approximated by Can be written.

Mixed pattern from the but connexion α = α _n α = α _n to cross Is Given in.

The (26) equation alpha = alpha contamination pattern from _{the m-plane} to alpha = alpha _n surface is a function of the distance (alpha _{m-.alpha. n)} only between the two sides alpha _n
Does not depend on the position of. Therefore, by using this new coordinate, the obstruction shadow patterns between the tomographic images can be made substantially uniform.

The backprojection image used at this time can be obtained from the g obtained by the equation (5) by the coordinate transformation to obtain the backprojection image g along the α axis. However, the backprojection image g can be obtained directly from the projection image P _j (u, v). It is more convenient to ask. The backprojection operation at this time is (U, v) is Using the coordinate point (x, y, α) and the source position (x _s ,
y _s , z _s ).

Thus asked And true tomographic image The relationship of However Is from equation (26) And T _s (x / α, y / α) in the δ function is z = z
_This is a reduction of the trajectory of the radiation source in the _s- plane (α <1).
this Similarly to the previous method, when the trajectory T _s is relatively simple, it is possible to calculate T _s by expressing T _s using a mathematical formula and by using the formula (30). Even if the trajectory is complicated,
Since Eq. (30) is only a reduced version of the orbit T _s , the position over time (x _s , y _s , z _s ) is determined as long as T _G is determined.
Is known, the reduced orbit can be directly obtained by using Eq. (30).

Therefore Tomographic image Is the mixing pattern of obstacle shadows in Fourier space as in the previous method The reverse filter processing according to the above may be performed. Ie By Seeking By Seeking By And then Tomographic image To calculate.

Is a tomographic image with reduced obstruction shadow, but it is a tomographic image on a coordinate space that is non-uniform in the α direction. If this is inconvenient, the tomographic image on the (x, y, z) coordinates can be calculated using Eq. (21). To This tomographic image is a corrected tomographic image that takes into account the non-uniformity of the mixing pattern of obstacle shadows in the z direction, and the tomographic image obtained by the previous method It is a more complete tomographic image that is closer to the true tomographic image f. FIG. 6 shows a flow chart of processing by this method.

Example of Invention

An embodiment of the present invention will be described below with reference to FIG. In FIG. 4, the scanner 25 measures a plurality of X-ray intensities after passing through the object to be inspected from multiple directions according to the trajectory. A straight line in the orbit,
Various types such as circles, ellipses, and spirals are used, but Fig. 5 shows a linear trajectory scanner. An X-ray tube 1 for irradiating the inspection object 6 placed on the table 8 with X-rays and an image intensifier II) 23 for detecting the X-rays after passing through the inspection object are supported by the support 3
Is attached to. The support arm 3 is attached to a fixedly installed support base 5 with a support rod 4, and the support arm 3
Rotational scanning is performed around the support rod 4 by a motor 21 via a rack 19 and a pinion 20 attached to the lower end. The X-ray tube 1 is fixed to a support frame 3 and generates X-rays by a high-voltage generator 2, and the X-rays are always radiated to a measurement region of an object to be inspected during scanning. I. I. 23 is the II mounting frame 9
It is attached to the supporting arm 3 by means of a supporting rod 10. Further, the II mounting wire 9 includes support rollers 15 and 16 that move smoothly along the rail 18, connection rods 13, 14 and 17 that connect the support rollers 15 and 16, and support rods 11 and 1.
2 and the II 23 is always oriented in a fixed direction by the scanning of the supporting arm 3. The X-ray tube and II scan the object to be inspected by the rotational movement of the support frame 3, and the image showing the transmitted radiation intensity of the object to be inspected at each scanning position is detected by II. TV camera 24 for II
Is attached, whereby the X-ray image is converted into an electric signal. The output a of the scan scanner is guided to the AD 26 of FIG. 4, converted into a digital value, and then taken into the processing device 27, and the processing device 27 executes the processing flow shown in FIG. 3 or FIG. A three-dimensional tomographic image is calculated. The obtained tomographic image is displayed by the CRT 28 on the cross section designated by the observer's instruction. The processing device 27 can be configured by using a computer. At this time, a tomographic image can be obtained by executing the processing flow of FIG. 3 or FIG. 6 by a program.

Next, FIG. 7 shows an example in which a processing device for executing the processing flow shown in FIG. 6 is implemented by an electric circuit.

The image I _j showing the intensity of the radiation transmitted through the object measured at each position on the orbit is converted into a digital value and then processed by the processing device 2.
It is fetched from the input b of 7 and stored in the memory 29 on the trajectory for each source position. The memory 30 stores an image I _oj indicating the radiation intensity before the installation of the inspection object. The images stored in the memories 29 and 30 are sequentially read, logarithmically converted by the logarithmic converters 31 and 32, respectively, and the difference calculator 33 executes the calculation shown in the equation (1). The projected image P _j is calculated.

This projection image P _j is subjected to the expressions (28) and (27) by the back projection computing unit 34, and the back projection image P _j is obtained. To calculate. The details of this backprojection computing unit will be described in detail with reference to FIGS. 8 and 9. This back projection image Is calculated from the formula (30) to the formula (3) by the obstacle shadow correction calculator 35.
Corrected tomographic image by calculating equation 5) To calculate. The details of the obstacle shading correction calculator 35 will be described in detail with reference to FIG. Tomographic image obtained in this way Is converted into a video signal by the video DA 36 according to the instruction of the desired tomographic plane and displayed on the CRT 28.

Next, the back projection calculator 34 will be described with reference to FIG. Projected image P _j
Is temporarily stored in the memory 37. The clock generator 38 is composed of a digital oscillator and generates pulses at regular time intervals. This pulse is input to the counter 39 to count and output the value of x. Counter 39,
40, 41 and 42 are connected in cascade, and when the previous counter overflows, the next counter is counted up. In the counters connected in this way, the counter 39 outputs the value of x, the counter 40 outputs the value of y, the counter 41 outputs the value of α, and the counter 42 outputs the value of j. The memory 44 stores the values of x _s , y _s , (k + 1) and stores these values stored in the memory 44 according to the signal of A generated by the controller 43 connected to the clock generator 38. Count the value of 39 to 4
The reading is performed in synchronization with the operation of 2. Address generator 45
Is calculated by using the output values x _s , y _s , (k + 1) of the memory 44 and the values of x, y, α output by the counters 39 to 41, and outputs u , V.

Details of this address generator will be described later with reference to FIG.
The projected image P _j stored in the memory 37 is read by the outputs u and v of the address generator and the output j of the counter 42. The memory 46 is a memory for calculating the back projection image, and the grounds x, y, α indicated by the counters 39, 40 and 41 are input to the address line of the memory 46. First, the memory 46 is cleared, and the next (x,
The data at the address designated by y, α) is read, addition with the output P _{j of the} memory 37 is performed by the adder 47, and the result is stored at the same address. According to the counting operation of the counters 39 to 41, when P _j is cumulatively added to the coordinate points corresponding to all the addresses of x, y, α, the counter 42 outputs the value of the next j, and the projection at the next orbit position is performed. The image P _j is cumulatively added. By repeating such an operation, the backprojection computing unit 34 executes the computation of the equation (27) to obtain the backprojection image. To calculate.

The relationship between the address generator 45 and the memory 44 shown in FIG.
Shown in the figure. The circuit of FIG. 9 has the memory contents x _s , y _s ,
Using (k + 1) and the counter outputs x, y, and α, the second (2
8) is calculated and u and v are calculated. The address generator is a multiplier 48, 49, 58, 53, 54, 60 and an adder 5
0, 55, subtracters 51, 56, and registers 52, 5
The clock input of the register is connected to the controller 43, and CK1 and CK respectively.
2 and CK3 are used to temporarily store and store the intermediate result of the equation (28).

The address line of the memory 44 is connected to the controller 43, and x _s , y _s , (k
+1) are sequentially output. First, x _s is output from the memory 44, and a product operation is executed using the value of the output value α of the counter 41 and the multiplier 48. Also, the multiplier 49 is the counter 3
The product operation of the output value x of 9 and the output value α of the counter 41 is executed. The output of the multiplier 48 is input to the adder 50 to add x and calculate (αx _s + x). The subtracter 51 subtracts the output (αx) of the multiplier 49 from this (αx _s + x),
The result is stored in the register 52 by the pulse signal of CK1. Next, y _s is read from the memory 44, and the multiplier 5
3 performs the product operation with α, and the adder 55 outputs y
Is added. The multiplier 54 performs a product operation of α and y, the output of the adder 54 is subtracted by the subtractor 56, and the output value is stored in the register 57. Then from memory 44 (k + 1)
Is read out, this value is multiplied by the output value of the register 52 by the multiplier 58, and the result u is stored in the register 59 by the clock signal CK3. Similarly, the value of (k + 1) and the output of the register 57 are input to the multiplier 60 and output v
Are stored in the register 61. In this way, the address generator 45 sequentially calculates the results u and v of the equation (28) for x, y and α.

Next, the obstacle shadow correction calculator 35 will be described in detail with reference to FIG. The memory 62 stores the trajectory T. This memory 6
The second address line is connected to the dividers 63 and 64, and the outputs of the counters 39, 40, 41 are x, y, α.
The output of is connected to the input of these dividers. The divider 63 divides x and α to calculate the output x / α. The divider 64 divides y and α to calculate the output y / α. By inputting these x / α and y / α into the address line of the memory 62, T _s (x / α, y /
α) is read. The output of the memory 62 is input to the divider 65 and division with α is executed. By these operations, the equation (30) is calculated and output. To get this Is temporarily stored in the memory 66. Fast Fourier Transform (FFT) 67 stored in memory 66 The Fourier transform shown in Eq. (32) is applied to Are stored in the memory 68. In addition, FFT69 is input The Fourier transform shown in Eq. (31) is applied to Are stored in the memory 70. The divider 71 Then, the division shown in Equation (33) is executed and the result is stored in memory 7.
Store in 2. FFT 73 from memory 72 And perform the inverse Fourier transform according to Eq. (34) to obtain the result. Are stored in the memory 74. In this way, the tomographic image in which the shadow of the obstacle is corrected is calculated in the memory 74.

〔The invention's effect〕

According to the present invention, since a three-dimensional tomographic image can be constructed from the multidirectional projection data obtained by measurement, it is possible to immediately present a tomographic image of a desired tomographic plane from this three-dimensional tomographic image. Become. Further, from this three-dimensional tomographic image, it is possible to obtain a more complete tomographic image in which obstacle shadows are reduced, and it is possible to clearly display the state of each cross section of the inspection.

[Brief description of drawings]

FIG. 1 is an explanatory diagram of a measurement principle of a transmitted X-ray of a subject in a tomography apparatus, FIG.
FIG. 4 is a flow chart showing a processing procedure for obtaining a three-dimensional tomographic image from conventional measurement data, FIG. 4 is a schematic device configuration of an embodiment of the present invention, FIG. 5 is a configuration diagram of an arc type linear tomographic scanner, FIG. 6 is a flow chart showing a processing procedure for obtaining a three-dimensional tomographic image in which obstacle shadows are corrected from the measurement data according to the present invention, FIG. 7 is a block diagram showing the configuration of the processing apparatus shown in FIG. 7 is a block diagram showing the configuration of the backprojection computing unit of FIG. 7, FIG. 9 is a block diagram showing the configuration of the address generator of FIG. 8, and FIG. 10 is a configuration of the fault shadow correction computing unit of FIG. FIG. 1 ... X-ray tube, 2 ... High-voltage generator, 23 ... I. I, 2
4 ... TV camera, 26 ... AD converter, 27 ... Processing device, 29, 30 ... Memory, 31, 32 ... Logarithmic converter, 33 ... Difference calculator, 34 ... Backprojection calculator, 35 ...
… Obstacle shading correction calculator, 36 …… Video DA, 44 ……
Memory, 45 ... Address generator.

Claims (5)

[Claims] 1. A plurality of two-dimensional photographed images obtained by scanning from a plurality of directions are measured at positions in a plurality of directions on a scanning trajectory, and these two-dimensional projected images are digitized. In a device for obtaining a tomographic image of an object to be inspected by calculation processing, means for performing a backprojection operation according to a measurement position in a three-dimensional space to obtain a three-dimensional tomographic image in which blur is mixed between tomographic areas, and scanning trajectory A digital tomography apparatus comprising means for correcting blurring included in a backprojection image by a filtering process in a three-dimensional space using a response characteristic of a small highly absorbing object according to the above. 2. When performing a filtering process on a three-dimensional space, the three-dimensional coordinates are non-uniform three-dimensionally with the coordinate interval set at a coordinate interval proportional to the square of the distance from the orbit plane of the radiation source. Apparatus according to claim 1, characterized in that it is performed on coordinates. 3. A response characteristic of a small high-absorption object is obtained by actually setting a small high-absorption object in an inspection area and measuring a mixed component of a shadow of the object on another tomographic plane. The apparatus according to item 1. 4. A response characteristic of a small high-absorption object is obtained by actually setting an inspection area of the small high-absorption object and measuring a mixed component of a shadow of the small object on another tomographic plane. The apparatus according to item 2. 5. The apparatus according to claim 1, wherein the response characteristic of a small highly absorbing object is calculated from the scanning trajectory by a calculation process.