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 PDFInfo
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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
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 solvedAnd is based onCorrecting the projected image by reverse rotation;
solving for sample lateral offset error based on symmetry of projection image after reverse correctionAnd is based onThe 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:whereinthe proportion of pixels that are the foreground,the proportion of pixels that are the background,is the average gray-scale value of the foreground,is the average gray-scale value of the background,the number of the pixels is the number of the pixels,segmentation thresholds for foreground (i.e. sample projection) and background,is gray value less thanThe number of the pixels of (a) is,is gray value greater thanThe number of pixels of (a);
Further, based on the acquired projection imageConstructing a binary imageThe method comprises the following steps: order toMiddle gray value greater thanIs inThe medium gray scale value is 1, and the gray scale value is,middle gray value less thanIs inThe middle gray value is 0, and the image is projectedConversion to binary image。
Further, the method for performing Radon transform on the binary image includes: setting the angle range of the inclination toThen the result of the Radon transform:
wherein,representing a binary imageRotate in the opposite directionThe angle is determined by taking the center of the image as the origin of coordinates and recording the rotated image as the origin of coordinatesTo, forCoordinate of any point inIn aFind a point inCorrespondingly, the method comprises the following steps:,
The bilinear interpolation calculation method comprises the following steps:
then:
obtaining a result set of Radon transformsLooking up in the setArray with the largest number of zero elementsTo obtain a rotation error;
is calculated to obtainPosition index of the first non-zero element in the listAnd the position index of the last non-zero elementError in lateral offset of the detectorWhereinis 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.
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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(rotation error of the detector around normal) and(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 formAnd is based onCorrecting the projected image by reverse rotation; on the basis of the binary image, the image is displayed,is embodied asThe inclination of the sample form can be solved by using a Radon transformation angle-by-angle searching methodThe principle is as follows: when the search angle is exactlyThen, the number of zero elements in the array obtained by Radon transform is the largest, by rotating the projected image in the opposite directionAnd finishing the inclination correction of the detector.
S3, solving the sample lateral offset error based on the projection image symmetry after reverse correctionAnd is based onReverse translation correcting the projected image; to finishThe corrected binary image, according to the symmetry of the sample morphology,embodied as the difference between the morphological center column and the image center column by translating the projected image in the opposite directionAnd 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 firstThe projection image collected under each scanning angle isComprises N pixels, and the average gray value of all the pixels is(ii) a The segmentation thresholds for the foreground (i.e., sample projection) and background are recordedStatistical gray value less thanHas a number of pixels ofIs greater thanHas a number of pixels of(ii) a ThenThe proportion of pixels in the foreground isThe average gray scale of the foreground is(ii) a The proportion of pixels belonging to the background isThe average gray level of the background is. Define the between-class variance asIs obtained by traversing methodThe maximum gray value is。
Construction andsame size binary image,Pixel correspondence for medium gray value of 1Middle gray value greater thanThe number of pixels of (a) is,pixel correspondence for medium gray value of 0Middle gray value less thanThe pixel of (2).
The specific implementation of S2 is:
from binary imagesThe inclination of the sample shape is roughly estimated and then is estimatedInternally provided withIs a step pairAnd sequentially carrying out Radon transformation, namely:
in the formula,the result of the Radon transform is represented,representing a binary imageRotate in the opposite directionAngle, orderThen, thenIndicating that the images are summed column by column, and, therefore,firstly, firstlyRotate in the opposite directionThe result of the angle, then column-wise summation, is an array.
To the obtained setFind the array with the largest number of zero elements asThe inclination angle of the sample form is the rotation error。
Will project an imageRotate in the opposite directionThen finishTo correct, usingIs expressed byThe corrected projected image.
taking the center of the image as the origin of coordinates, and recording the rotated image asTo, forCoordinate of any point inCan be atFind a point inCorrespondingly, the method comprises the following steps:
due to the fact thatThe 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 interpolationTo make。
The bilinear interpolation is implemented as follows:
let two integers adjacent to x be respectivelyAnd,(ii) a Two integers adjacent to y are respectivelyAnd,(ii) a Then:
the specific implementation of S3 is:
due to the number groups in S2The 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 usedShow thatThe result of the first order difference is obtained, orderAndrespectively representThe 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. Index of the center column of the probe isThe 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。
Will be passedCorrected projected imageTranslation in the opposite directionThen finishTo correct, usingIs expressed byThe corrected projected image.
The first-order difference is obtained by:
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 toThen the result of the Radon transform:
wherein,representing a binary imageRotate in the opposite directionThe angle is determined by taking the center of the image as the origin of coordinates and recording the rotated image as the origin of coordinatesTo, forCoordinate of any point inIn aFind a point inCorrespondingly, the method comprises the following steps:,
The bilinear interpolation calculation method comprises the following steps:
then:
obtaining a result set of Radon transformsFinding the array with the largest number of zero elements in the setTo obtain a rotation error;
is calculated to obtainPosition index of the first non-zero element in the listAnd the position index of the last non-zero elementError in lateral offset of the detectorWhereinindexing 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:whereinthe proportion of pixels that are the foreground,the proportion of pixels that are the background,is the average gray-scale value of the foreground,is the average gray-scale value of the background,the number of the pixels is the number of the pixels,the segmentation threshold for the foreground and background,is gray value less thanThe number of the pixels of (a) is,is gray value greater thanThe number of pixels of (a);
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 imagesConstructing a binary imageThe method comprises the following steps: order toMiddle gray value greater thanIs inThe medium gray scale value is 1, and the gray scale value is,middle gray value less thanIs inThe middle gray value is 0, and the image is projectedConversion to binary image。
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