CN114092594B - Cone beam CT system and geometric error correction method of axisymmetric appearance sample - Google Patents

Cone beam CT system and geometric error correction method of axisymmetric appearance sample Download PDF

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CN114092594B
CN114092594B CN202210076334.1A CN202210076334A CN114092594B CN 114092594 B CN114092594 B CN 114092594B CN 202210076334 A CN202210076334 A CN 202210076334A CN 114092594 B CN114092594 B CN 114092594B
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image
projection image
error
pixels
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CN114092594A (en
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王曌
刘清华
陈云斌
张小丽
李敬
任忠国
李寿涛
程云
李士根
胡栋才
石正军
罗为
李雷
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Institute of Applied Electronics of CAEP
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    • G06T11/00—2D [Two Dimensional] image generation
    • G06T11/003—Reconstruction from projections, e.g. tomography
    • G06T11/005—Specific pre-processing for tomographic reconstruction, e.g. calibration, source positioning, rebinning, scatter correction, retrospective gating
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T11/00—2D [Two Dimensional] image generation
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Abstract

The application belongs to the technical field of cone beam CT, and particularly discloses a cone beam CT system and a geometric error correction method of an axisymmetric appearance sample, which comprises the following steps: acquiring a projection image of the sample with the axisymmetric appearance, and constructing a binary image based on the acquired projection image; performing Radon transformation on the binary image, solving a rotation error of a sample form, and reversely rotating and correcting a projection image based on the rotation error; and solving a sample transverse offset error based on the symmetry of the projection image after reverse correction, and correcting the projection image based on the transverse offset error in a reverse translation mode. The method does not need to use a calibration phantom, simplifies the scanning process, saves the cost of designing and processing the calibration phantom, does not need to repeatedly reconstruct images to dynamically adjust geometric parameters, greatly improves the calculation efficiency, only has the requirement of shape axial symmetry on the sample, and has wide application range.

Description

Cone beam CT system and geometric error correction method of axisymmetric appearance sample
Technical Field
The application belongs to the technical field of cone beam CT, and particularly relates to a cone beam CT system and a geometric error correction method of an axisymmetric appearance sample.
Background
Geometric errors are inevitably introduced in the assembling and using processes of the cone beam CT system, the geometric errors change the mapping relation between the three-dimensional object and the two-dimensional projection image, and incorrect geometric mapping can cause geometric artifacts on the reconstructed image, reduce the quality of the reconstructed image and influence the measurement precision based on the reconstructed image. In general, the influence of the rotation error and the lateral offset error of the detector around the normal on the reconstructed image is the largest, and therefore, the rotation error and the lateral offset error must be calibrated and corrected.
At present, the commonly used geometric calibration methods include an off-line calibration method and an on-line calibration method. The off-line calibration method solves the geometrical parameters of the cone-beam CT system according to a set of calibration points (called calibration phantom) with known space coordinates and the relation between the projection coordinates of the calibration points. Therefore, the offline calibration method cannot separate the calibration phantom, usually the geometric calibration is completed by scanning the phantom first, and then the sample is scanned, so that the process is complicated, and the consistent placing positions of the phantom and the sample are difficult to ensure. In addition, the processing cost of the high-precision phantom is not high, the phantoms suitable for different cone beam CT systems are not uniform, and for some special cone beam CT systems (such as Micro-CT systems pursuing high resolution), the phantoms are difficult to design due to the limitation of some objective conditions (such as small visual field). On-line calibration methods usually start with the relation between geometric parameters and some quality evaluation indexes (such as sharpness and entropy) of reconstructed images, construct an objective function, and achieve the purpose of calibrating the geometric parameters by solving an objective function optimization problem. In general, the online calibration method needs to repeatedly reconstruct images to dynamically adjust geometric parameters, and the heavy computational burden limits the use of the online calibration method.
Accordingly, further developments and improvements are still needed in the art.
Disclosure of Invention
In order to solve the above problems, a cone beam CT system and a method for correcting geometric errors of an axisymmetric shape sample are proposed. The application provides the following technical scheme:
a method for correcting geometric errors of a cone beam CT system and an axisymmetric shape sample comprises the following steps:
acquiring a projection image of the sample with the axisymmetric appearance, and constructing a binary image based on the acquired projection image;
radon transformation is carried out on the binary image, and rotation error of sample form is solved
Figure 959418DEST_PATH_IMAGE001
And is based on
Figure 907783DEST_PATH_IMAGE001
Correcting the projected image by reverse rotation;
solving for sample lateral offset error based on symmetry of projection image after reverse correction
Figure 875739DEST_PATH_IMAGE002
And is based on
Figure 971871DEST_PATH_IMAGE003
The corrected projection image is translated in the reverse direction.
Further, obtaining a projection image of the sample with the axisymmetric appearance, wherein the calculation formula of the between-class variance is as follows:
Figure 683475DEST_PATH_IMAGE004
wherein
Figure 548663DEST_PATH_IMAGE005
the proportion of pixels that are the foreground,
Figure 687520DEST_PATH_IMAGE006
the proportion of pixels that are the background,
Figure 208631DEST_PATH_IMAGE007
is the average gray-scale value of the foreground,
Figure 723926DEST_PATH_IMAGE008
is the average gray-scale value of the background,
Figure 443620DEST_PATH_IMAGE009
the number of the pixels is the number of the pixels,
Figure 753379DEST_PATH_IMAGE010
segmentation thresholds for foreground (i.e. sample projection) and background,
Figure 824103DEST_PATH_IMAGE011
is gray value less than
Figure 877510DEST_PATH_IMAGE010
The number of the pixels of (a) is,
Figure 654973DEST_PATH_IMAGE012
is gray value greater than
Figure 135633DEST_PATH_IMAGE010
The number of pixels of (a);
obtaining the variance between classes through traversal calculation
Figure 693653DEST_PATH_IMAGE013
Maximum gray value
Figure 285172DEST_PATH_IMAGE010
。
Further, based on the acquired projection image
Figure 979458DEST_PATH_IMAGE014
Constructing a binary image
Figure 896598DEST_PATH_IMAGE015
The method comprises the following steps: order to
Figure 614019DEST_PATH_IMAGE014
Middle gray value greater than
Figure 9228DEST_PATH_IMAGE010
Is in
Figure 823600DEST_PATH_IMAGE015
The medium gray scale value is 1, and the gray scale value is,
Figure 646063DEST_PATH_IMAGE014
middle gray value less than
Figure 913096DEST_PATH_IMAGE010
Is in
Figure 111996DEST_PATH_IMAGE015
The middle gray value is 0, and the image is projected
Figure 718558DEST_PATH_IMAGE014
Conversion to binary image
Figure 711922DEST_PATH_IMAGE015
。
Further, the method for performing Radon transform on the binary image includes: setting the angle range of the inclination to
Figure 466251DEST_PATH_IMAGE016
Then the result of the Radon transform:
Figure 203263DEST_PATH_IMAGE017
，
wherein,
Figure 726648DEST_PATH_IMAGE018
representing a binary image
Figure 156493DEST_PATH_IMAGE019
Rotate in the opposite direction
Figure 332871DEST_PATH_IMAGE020
The angle is determined by taking the center of the image as the origin of coordinates and recording the rotated image as the origin of coordinates
Figure 607995DEST_PATH_IMAGE021
To, for
Figure 251466DEST_PATH_IMAGE021
Coordinate of any point in
Figure 586632DEST_PATH_IMAGE022
In a
Figure 315554DEST_PATH_IMAGE023
Find a point in
Figure 394368DEST_PATH_IMAGE024
Correspondingly, the method comprises the following steps:
Figure 830029DEST_PATH_IMAGE025
，
when in use
Figure 601676DEST_PATH_IMAGE026
And
Figure 552314DEST_PATH_IMAGE027
when not integer, it can be obtained by bilinear interpolation
Figure 434820DEST_PATH_IMAGE028
；
The bilinear interpolation calculation method comprises the following steps:
let two integers adjacent to x be respectively
Figure 787304DEST_PATH_IMAGE029
And
Figure 729852DEST_PATH_IMAGE030
，
Figure 105470DEST_PATH_IMAGE031
；
two integers adjacent to y are respectively
Figure 526087DEST_PATH_IMAGE032
And
Figure 998656DEST_PATH_IMAGE033
，
Figure 112106DEST_PATH_IMAGE034
；
then:
Figure 37336DEST_PATH_IMAGE035
；
order to
Figure 261644DEST_PATH_IMAGE036
Then, then
Figure 260824DEST_PATH_IMAGE037
Means that the images are summed column by
Figure 545175DEST_PATH_IMAGE038
Wherein
Figure 957702DEST_PATH_IMAGE039
；
obtaining a result set of Radon transforms
Figure 985701DEST_PATH_IMAGE040
Looking up in the setArray with the largest number of zero elements
Figure 167283DEST_PATH_IMAGE041
To obtain a rotation error
Figure 356956DEST_PATH_IMAGE042
；
Note the book
Figure 194462DEST_PATH_IMAGE043
To, for
Figure 760573DEST_PATH_IMAGE044
Solving for first order differences
Figure 62241DEST_PATH_IMAGE045
And then:
Figure 422815DEST_PATH_IMAGE046
is calculated to obtain
Figure 809934DEST_PATH_IMAGE047
Position index of the first non-zero element in the list
Figure 179736DEST_PATH_IMAGE048
And the position index of the last non-zero element
Figure 8015DEST_PATH_IMAGE049
Error in lateral offset of the detector
Figure 805069DEST_PATH_IMAGE050
Wherein
Figure 413905DEST_PATH_IMAGE051
is the index of the central column of the detector.
A computer readable storage medium having stored thereon a computer program for a method of geometric error correction of a cone beam CT system and an axisymmetric contoured sample when executed by a processor.
An electronic terminal, comprising: a processor and a memory;
the memory is configured to store a computer program and the processor is configured to execute the computer program stored by the memory to cause the terminal to perform a method for geometric error correction of a cone beam CT system and an axisymmetric topographic sample.
Has the advantages that:
1. the calibration phantom does not need to be scanned before the sample is scanned, so that the scanning process is simplified, and the cost for designing and processing the calibration phantom is saved; the method is suitable for the situation that a calibration phantom cannot be used;
2. geometric errors are directly solved by analysis from the projection images of the samples, the connection between the geometric errors and the quality of the reconstructed images is not needed to be established, the images are not needed to be reconstructed repeatedly to dynamically adjust geometric parameters, and the calculation efficiency is greatly improved;
3. the requirement on the quality of the sample is low, the method can be used only by requiring the shape axial symmetry of the sample, the homogenization of the sample is not required, and the internal structure axial symmetry of the sample is also not required, so that the sample is more in the actual cone beam CT application scene;
4. the correction method is not only suitable for the circular track cone beam CT system, but also suitable for the spiral track cone beam CT system;
5. the application range is increased, the rotation center does not need to be assumed to be fixed in the scanning process, and the method is suitable for the situation that the rotation center moves or the scanning angle range is limited (less than 180 degrees) in the scanning process.
Drawings
FIG. 1 is a flow chart of a projected image self-correction algorithm proposed by the present invention.
Detailed Description
The present application will be described in further detail with reference to the following drawings and examples. It is to be understood that the specific embodiments described herein are merely illustrative of the relevant invention and not restrictive of the invention. It should be further noted that, for the convenience of description, only the portions related to the related invention are shown in the drawings.
It should be noted that the embodiments and features of the embodiments in the present application may be combined with each other without conflict. The present application will be described in detail below with reference to the embodiments with reference to the attached drawings.
In a typical cone-beam CT system, SOD represents the distance from the source to the rotation axis, SDD represents the distance from the source to the detector, and when the shape of the sample to be scanned is axisymmetric, a Projection Image Self-correction Algorithm (PISC Algorithm) is proposed, which automatically solves the problem of the maximum influence on Image reconstruction from the Projection Image
Figure 587398DEST_PATH_IMAGE001
(rotation error of the detector around normal) and
Figure 598079DEST_PATH_IMAGE052
(lateral offset error of detector). Axisymmetric profile samples are very common in the context of CT applications. Compared with the traditional off-line calibration method, the PISC algorithm does not need to use a phantom, the scanning is convenient and fast, and the cost is saved; compared with the traditional online calibration method, the PISC algorithm does not need to iteratively optimize an objective function, and avoids the heavy calculation burden of repeatedly reconstructing images.
As shown in fig. 1, the PISC algorithm specifically includes the following three steps:
s1, obtaining a projection image of the axisymmetric appearance sample, and constructing a binary image based on the obtained projection image; and (4) performing binarization operation on each projection image by selecting a proper image threshold value, so that only morphological characteristics of the sample are reserved on the image.
S2, carrying out Radon transformation on the binary image, and solving the rotation error of the sample form
Figure 566035DEST_PATH_IMAGE001
And is based on
Figure 599850DEST_PATH_IMAGE001
Correcting the projected image by reverse rotation; on the basis of the binary image, the image is displayed,
Figure 311454DEST_PATH_IMAGE001
is embodied asThe inclination of the sample form can be solved by using a Radon transformation angle-by-angle searching method
Figure 176642DEST_PATH_IMAGE001
The principle is as follows: when the search angle is exactly
Figure 315499DEST_PATH_IMAGE001
Then, the number of zero elements in the array obtained by Radon transform is the largest, by rotating the projected image in the opposite direction
Figure 898927DEST_PATH_IMAGE001
And finishing the inclination correction of the detector.
S3, solving the sample lateral offset error based on the projection image symmetry after reverse correction
Figure 148643DEST_PATH_IMAGE052
And is based on
Figure 71600DEST_PATH_IMAGE052
Reverse translation correcting the projected image; to finish
Figure 381358DEST_PATH_IMAGE001
The corrected binary image, according to the symmetry of the sample morphology,
Figure 452082DEST_PATH_IMAGE052
embodied as the difference between the morphological center column and the image center column by translating the projected image in the opposite direction
Figure 505489DEST_PATH_IMAGE052
And finishing the transverse offset correction of the detector.
The order of implementation of the above three steps is not changeable.
The specific implementation of S1 is:
is arranged at the first
Figure 345269DEST_PATH_IMAGE053
The projection image collected under each scanning angle is
Figure 825929DEST_PATH_IMAGE054
Comprises N pixels, and the average gray value of all the pixels is
Figure 53124DEST_PATH_IMAGE055
(ii) a The segmentation thresholds for the foreground (i.e., sample projection) and background are recorded
Figure 910221DEST_PATH_IMAGE056
Statistical gray value less than
Figure 604508DEST_PATH_IMAGE056
Has a number of pixels of
Figure 256069DEST_PATH_IMAGE057
Is greater than
Figure 301385DEST_PATH_IMAGE056
Has a number of pixels of
Figure 696594DEST_PATH_IMAGE058
(ii) a Then
Figure 183071DEST_PATH_IMAGE054
The proportion of pixels in the foreground is
Figure 271112DEST_PATH_IMAGE059
The average gray scale of the foreground is
Figure 538146DEST_PATH_IMAGE060
(ii) a The proportion of pixels belonging to the background is
Figure 737046DEST_PATH_IMAGE061
The average gray level of the background is
Figure 140345DEST_PATH_IMAGE062
. Define the between-class variance as
Figure 399288DEST_PATH_IMAGE063
Is obtained by traversing method
Figure 153618DEST_PATH_IMAGE064
The maximum gray value is
Figure 828313DEST_PATH_IMAGE056
。
Construction and
Figure 351698DEST_PATH_IMAGE054
same size binary image
Figure 781542DEST_PATH_IMAGE065
，
Figure 757588DEST_PATH_IMAGE065
Pixel correspondence for medium gray value of 1
Figure 298291DEST_PATH_IMAGE054
Middle gray value greater than
Figure 941762DEST_PATH_IMAGE056
The number of pixels of (a) is,
Figure 214612DEST_PATH_IMAGE065
pixel correspondence for medium gray value of 0
Figure 943533DEST_PATH_IMAGE054
Middle gray value less than
Figure 22348DEST_PATH_IMAGE056
The pixel of (2).
The specific implementation of S2 is:
from binary images
Figure 520325DEST_PATH_IMAGE065
The inclination of the sample shape is roughly estimated and then is estimated
Figure 26393DEST_PATH_IMAGE066
Internally provided with
Figure 242611DEST_PATH_IMAGE067
Is a step pair
Figure 62799DEST_PATH_IMAGE065
And sequentially carrying out Radon transformation, namely:
Figure 415283DEST_PATH_IMAGE017
，
in the formula,
Figure 357831DEST_PATH_IMAGE068
the result of the Radon transform is represented,
Figure 795766DEST_PATH_IMAGE069
representing a binary image
Figure 216383DEST_PATH_IMAGE065
Rotate in the opposite direction
Figure 688952DEST_PATH_IMAGE070
Angle, order
Figure 474506DEST_PATH_IMAGE036
Then, then
Figure 399736DEST_PATH_IMAGE037
Indicating that the images are summed column by column, and, therefore,
Figure 624044DEST_PATH_IMAGE068
firstly, firstly
Figure 951121DEST_PATH_IMAGE065
Rotate in the opposite direction
Figure 235471DEST_PATH_IMAGE070
The result of the angle, then column-wise summation, is an array.
To the obtained set
Figure 647998DEST_PATH_IMAGE071
Find the array with the largest number of zero elements as
Figure 348101DEST_PATH_IMAGE072
The inclination angle of the sample form is the rotation error
Figure 529684DEST_PATH_IMAGE073
。
Will project an image
Figure 984936DEST_PATH_IMAGE074
Rotate in the opposite direction
Figure 884759DEST_PATH_IMAGE001
Then finish
Figure 450869DEST_PATH_IMAGE001
To correct, using
Figure 486958DEST_PATH_IMAGE075
Is expressed by
Figure 50795DEST_PATH_IMAGE001
The corrected projected image.
As described above
Figure 437914DEST_PATH_IMAGE076
The specific implementation of the method is as follows:
taking the center of the image as the origin of coordinates, and recording the rotated image as
Figure 542136DEST_PATH_IMAGE077
To, for
Figure 698311DEST_PATH_IMAGE077
Coordinate of any point in
Figure 495366DEST_PATH_IMAGE078
Can be at
Figure 104201DEST_PATH_IMAGE065
Find a point in
Figure 212447DEST_PATH_IMAGE079
Correspondingly, the method comprises the following steps:
Figure 223128DEST_PATH_IMAGE080
，
due to the fact that
Figure 191085DEST_PATH_IMAGE081
The method includes representing values of x-row and y-column elements of an image matrix, searching x and y used as indexes only by using integers, converting the rational numbers into the integers to be searched by using rotation operation, wherein the obtained x and y may be floating point numbers (namely rational numbers), and converting the rational numbers into the integers to be searched1,y1)、(x1,y2)、(x2,y1)、(x2,y2) The value of (d) is given to (x, y) in a certain proportion, so that a substitute integer closest to the original rational number is found. That is, when x and y are not integers, the values can be obtained by bilinear interpolation
Figure 287216DEST_PATH_IMAGE081
To make
Figure 733241DEST_PATH_IMAGE082
。
The bilinear interpolation is implemented as follows:
let two integers adjacent to x be respectively
Figure 864008DEST_PATH_IMAGE083
And
Figure 940549DEST_PATH_IMAGE084
，
Figure 523977DEST_PATH_IMAGE085
(ii) a Two integers adjacent to y are respectively
Figure 773693DEST_PATH_IMAGE086
And
Figure 758966DEST_PATH_IMAGE087
，
Figure 68725DEST_PATH_IMAGE088
(ii) a Then:
Figure 139449DEST_PATH_IMAGE035
，
note the book
Figure 130539DEST_PATH_IMAGE089
And then:
Figure 970319DEST_PATH_IMAGE090
。
the specific implementation of S3 is:
due to the number groups in S2
Figure 450979DEST_PATH_IMAGE091
The first and last non-zero element positions in the array are identified as the outermost positions on the symmetrical sample profile, and the first and last non-zero element positions are more stable than directly solving the first and last non-zero element positions of the array, solving the first order difference for the array, and then solving the first and last non-zero element positions for the first order difference result, because the first order difference operation has the effect of reducing irregular fluctuation between data, the first order difference operation is used
Figure 743420DEST_PATH_IMAGE092
Show that
Figure 600517DEST_PATH_IMAGE091
The result of the first order difference is obtained, order
Figure 294804DEST_PATH_IMAGE093
And
Figure 884048DEST_PATH_IMAGE094
respectively represent
Figure 929365DEST_PATH_IMAGE095
The position index of the first and last non-zero elements in the sample, the position index of the symmetry axis of the sample can be expressed as
Figure 324574DEST_PATH_IMAGE096
. Index of the center column of the probe is
Figure 873367DEST_PATH_IMAGE097
The index of the center column is a known quantity obtained from the detector. Since the axis of symmetry of the sample ideally should coincide with the central column of detectors, the detectors are laterally offset by
Figure 961408DEST_PATH_IMAGE098
。
Will be passed
Figure 166125DEST_PATH_IMAGE001
Corrected projected image
Figure 99446DEST_PATH_IMAGE099
Translation in the opposite direction
Figure 768325DEST_PATH_IMAGE100
Then finish
Figure 27268DEST_PATH_IMAGE100
To correct, using
Figure 516018DEST_PATH_IMAGE099
Is expressed by
Figure 518609DEST_PATH_IMAGE100
The corrected projected image.
The first-order difference is obtained by:
note the book
Figure 41994DEST_PATH_IMAGE101
And then:
Figure 143942DEST_PATH_IMAGE102
。
the PISC algorithm is an online calibration method essentially, so that the method does not depend on a calibration phantom, meanwhile, the principle of the PISC algorithm is that geometric errors are resolved and solved from projection images starting from morphological characteristics of a sample, an objective function solving process with heavy calculation burden is not needed, the calculation efficiency is greatly improved, the PISC algorithm respectively solves the geometric errors according to each projection image, the assumption that a rotation center is fixed in the scanning process is avoided, and the method is suitable for the condition that the rotation center moves in the scanning process.
The second embodiment of the invention provides equipment which comprises a memory and a processor, wherein the memory is used for storing programs, and the memory can be connected with the processor through a bus. The memory may be a non-volatile memory such as a hard disk drive and a flash memory, in which a software program and a device driver are stored. The software program is capable of performing various functions of the above-described methods provided by embodiments of the present invention; the device drivers may be network and interface drivers. The processor is used for executing a software program, and the software program can realize the method provided by the first embodiment of the invention when being executed.
A third embodiment of the present invention provides a computer program product including instructions, which, when the computer program product runs on a computer, causes the computer to execute the method provided in the first embodiment of the present invention.
The fourth embodiment of the present invention provides a computer-readable storage medium, where a computer program is stored on the computer-readable storage medium, and when the computer program is executed by a processor, the method provided in the first embodiment of the present invention is implemented.
Those of skill would further appreciate that the various illustrative components and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both, and that the various illustrative components and steps have been described above generally in terms of their functionality in order to clearly illustrate this interchangeability of hardware and software. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the implementation. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.
The steps of a method or algorithm described in connection with the embodiments disclosed herein may be embodied in hardware, a software module executed by a processor, or a combination of the two. A software module may reside in Random Access Memory (RAM), memory, Read Only Memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art.
The above embodiments are provided to further explain the objects, technical solutions and advantages of the present invention in detail, it should be understood that the above embodiments are merely exemplary embodiments of the present invention and are not intended to limit the scope of the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (3)

1. A method for correcting geometric errors of a cone beam CT system and an axisymmetric shape sample is characterized by comprising the following steps:
acquiring a projection image of the sample with the axisymmetric appearance, and constructing a binary image based on the acquired projection image;
performing Radon transformation on the binary image, solving a rotation error of a sample form, and reversely rotating and correcting a projection image based on the rotation error;
the method for carrying out Radon transformation on the binary image comprises the following steps: setting the angle range of the inclination to
Figure 417356DEST_PATH_IMAGE001
Then the result of the Radon transform:
Figure 787158DEST_PATH_IMAGE002
；
wherein,
Figure 490803DEST_PATH_IMAGE003
representing a binary image
Figure 287857DEST_PATH_IMAGE004
Rotate in the opposite direction
Figure 896693DEST_PATH_IMAGE005
The angle is determined by taking the center of the image as the origin of coordinates and recording the rotated image as the origin of coordinates
Figure 70186DEST_PATH_IMAGE006
To, for
Figure 80867DEST_PATH_IMAGE006
Coordinate of any point in
Figure 111140DEST_PATH_IMAGE007
In a
Figure 207272DEST_PATH_IMAGE008
Find a point in
Figure 918876DEST_PATH_IMAGE009
Correspondingly, the method comprises the following steps:
Figure 784064DEST_PATH_IMAGE010
，
when in use
Figure 922921DEST_PATH_IMAGE011
And
Figure 506349DEST_PATH_IMAGE012
when not integer, it can be obtained by bilinear interpolation
Figure 572044DEST_PATH_IMAGE013
；
The bilinear interpolation calculation method comprises the following steps:
let two integers adjacent to x be respectively
Figure 557317DEST_PATH_IMAGE014
And
Figure 867076DEST_PATH_IMAGE015
，
Figure 937800DEST_PATH_IMAGE016
；
two integers adjacent to y are respectively
Figure 991207DEST_PATH_IMAGE017
And
Figure 893304DEST_PATH_IMAGE018
，
Figure 373964DEST_PATH_IMAGE019
；
then:
Figure 666405DEST_PATH_IMAGE020
；
order to
Figure 523502DEST_PATH_IMAGE021
Then, then
Figure 217789DEST_PATH_IMAGE022
Means that the images are summed column by
Figure 682399DEST_PATH_IMAGE023
Wherein
Figure 727716DEST_PATH_IMAGE024
；
obtaining a result set of Radon transforms
Figure 122925DEST_PATH_IMAGE025
Finding the array with the largest number of zero elements in the set
Figure 671718DEST_PATH_IMAGE026
To obtain a rotation error
Figure 759760DEST_PATH_IMAGE027
；
Note the book
Figure 26793DEST_PATH_IMAGE028
To, for
Figure 288010DEST_PATH_IMAGE029
Solving for first order differences
Figure 691310DEST_PATH_IMAGE030
And then:
Figure 950253DEST_PATH_IMAGE031
is calculated to obtain
Figure 704582DEST_PATH_IMAGE032
Position index of the first non-zero element in the list
Figure 441594DEST_PATH_IMAGE033
And the position index of the last non-zero element
Figure 778028DEST_PATH_IMAGE034
Error in lateral offset of the detector
Figure 207873DEST_PATH_IMAGE035
Wherein
Figure 183919DEST_PATH_IMAGE036
indexing the position of the detector center column;
and solving the sample transverse offset error based on the symmetry of the projection image after reverse correction, and correcting the projection image based on the transverse offset error in a reverse translation mode.
2. The method of claim 1, wherein the projection images of the axisymmetric contour sample are obtained according to the equation for calculating the between-class variance:
Figure 724622DEST_PATH_IMAGE037
wherein
Figure 368093DEST_PATH_IMAGE038
the proportion of pixels that are the foreground,
Figure 765576DEST_PATH_IMAGE039
the proportion of pixels that are the background,
Figure 494498DEST_PATH_IMAGE040
is the average gray-scale value of the foreground,
Figure 573312DEST_PATH_IMAGE041
is the average gray-scale value of the background,
Figure 71289DEST_PATH_IMAGE042
the number of the pixels is the number of the pixels,
Figure 577357DEST_PATH_IMAGE043
the segmentation threshold for the foreground and background,
Figure 793575DEST_PATH_IMAGE044
is gray value less than
Figure 489130DEST_PATH_IMAGE043
The number of the pixels of (a) is,
Figure 841613DEST_PATH_IMAGE045
is gray value greater than
Figure 784162DEST_PATH_IMAGE043
The number of pixels of (a);
obtaining the variance between classes through traversal calculation
Figure 222096DEST_PATH_IMAGE046
Maximum gray value
Figure 642713DEST_PATH_IMAGE043
。
3. The cone-beam CT system and method for geometric error correction of an axisymmetric contoured sample of claim 2, wherein said correction is based on acquired projection images
Figure 177600DEST_PATH_IMAGE047
Constructing a binary image
Figure 25470DEST_PATH_IMAGE048
The method comprises the following steps: order to
Figure 950701DEST_PATH_IMAGE047
Middle gray value greater than
Figure 175009DEST_PATH_IMAGE043
Is in
Figure 502085DEST_PATH_IMAGE048
The medium gray scale value is 1, and the gray scale value is,
Figure 596555DEST_PATH_IMAGE047
middle gray value less than
Figure 9082DEST_PATH_IMAGE043
Is in
Figure 771502DEST_PATH_IMAGE048
The middle gray value is 0, and the image is projected
Figure 953084DEST_PATH_IMAGE047
Conversion to binary image
Figure 408337DEST_PATH_IMAGE048
。
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