A nano-CT geometric parameter self-calibration method based on projection feature matching

Abstract

This invention provides a self-calibration method for geometric parameters in nano-CT based on projection feature matching. The method includes: Step 1: Scanning a sample using a nano-CT system and reading two mirrored projection images from the scan data, then preprocessing the two projection images; Step 2: Setting a feature point extraction threshold, extracting, matching, and filtering feature points from the two projection images, and recording the coordinates of all selected high-quality matching points; Step 3: Fitting two parameters—rotation axis deflection angle and rotation axis lateral offset—based on the midpoint coordinates of all high-quality matching points in the two projection images; Step 4: Calibrating the rotation axis deflection angle and rotation axis lateral offset parameters by performing affine transformation on the projection images at all angles in the scan data, and then reconstructing three-dimensional volume data without geometric artifacts. This invention achieves better noise resistance by fitting parameters using the coordinates of high-quality matching feature points.

Description

Technical Field

[0001] This invention relates to the field of image processing technology, and in particular to a method for self-calibration of geometric parameters in nano-CT based on projection feature matching. Background Technology

[0002] Computed tomography (CT) is a technique that uses the attenuation information of X-rays after they penetrate an object to achieve three-dimensional reconstruction. It has significant advantages such as non-destructive imaging, high resolution, and fast imaging speed, and is widely used in fields such as non-destructive testing. Nano-CT technology is developed based on CT and enables high-resolution tomographic imaging of objects at the nanometer scale.

[0003] The acquisition of 3D data from a sample using a nano-CT system mainly involves several key steps: projection data acquisition, data correction, image reconstruction, and image post-processing. In practical applications, factors such as the machining and manual installation precision of CT equipment can cause the X-ray source, rotating platform, and flat panel detector to be misaligned. This mismatch between the actual spatial structural parameters of the nano-CT system and the geometric parameters of the ideal imaging model leads to geometric artifacts in the reconstructed images. These artifacts primarily manifest as blurred 3D reconstructed images or even double-edge artifacts, severely impacting image quality and spatial resolution. Therefore, calibrating the geometric parameters of the CT system is crucial for acquiring high-quality 3D reconstructed images.

[0004] To address the degradation of reconstructed image quality caused by geometric parameter mismatch in cone-beam CT systems, researchers have proposed numerous methods for calibrating the geometric parameters of CT systems. These methods can be broadly categorized into: phantom-based calibration methods, reconstructed image feature-based self-calibration methods, and projection image feature-based self-calibration methods. The phantom-based method utilizes a standard template with known geometry (the phantom) to acquire one or more projections of the phantom along the trajectory to be calibrated. The geometric parameters of the system are then solved using the relationship between the parameters of the projection trajectory and the system's imaging geometry. This method offers advantages such as high calibration accuracy and fast solution speed. However, it requires the fabrication and placement of a high-precision phantom, making it difficult to apply in nanoscale CT where the single imaging field of view is only a few millimeters. Reconstructed image feature-based self-calibration algorithms primarily use the entropy, sharpness, and high-frequency energy of the reconstructed image as evaluation functions to calibrate the geometric parameters. These methods require multiple iterative reconstructions, resulting in low calibration efficiency. Projection image feature-based methods primarily utilize the mirror properties of the projected image, constructing a cost function based on the relationship between the mirror images to calibrate the geometric parameters. However, existing methods based on projection image features, which directly use the grayscale values ​​of the projection image to calculate geometric parameters, are easily affected by noise and the cone angle of the cone beam. Summary of the Invention

[0005] To address the aforementioned shortcomings of existing geometric parameter calibration algorithms, and in order to at least partially resolve these shortcomings, this invention provides a nano-CT geometric parameter self-calibration method based on projection feature matching, starting from the mirror characteristics of paired projection images under a circular scanning trajectory.

[0006] This invention provides a method for self-calibrating geometric parameters of nano-CT based on projection feature matching, comprising:

[0007] Step 1: Scan the sample using a nano-CT system and read two mirror projection images from the scan data. Preprocess the two projection images.

[0008] Step 2: Set the feature point extraction threshold, extract, match and filter feature points from the two projected images, and record the coordinates of all the selected high-quality matching points;

[0009] Step 3: Fit two parameters, the rotation axis deflection angle and the rotation axis lateral offset, based on the midpoint coordinates of all high-quality matching points in the two projected images;

[0010] Step 4: The projection images at all angles in the scanned data are calibrated using affine transformation to determine the two parameters: rotation axis deflection angle and rotation axis horizontal line offset. Then, the three-dimensional volume data without geometric artifacts is reconstructed.

[0011] Furthermore, the feature point selection process specifically includes:

[0012] In the two projected images, arbitrarily select two pairs of matching points, and denote them as matching point pairs. and matching point pairs And calculate the midpoint S of one of the matching point pairs in the same coordinate system. mid The coordinates; where, and This represents the feature points extracted from one of the projected images. and This represents feature points extracted from another projected image;

[0013] feature points and midpoint S mid Construct the first characteristic triangle, and place the characteristic points and midpoint S mid Forming the second characteristic triangle;

[0014] If the first characteristic triangle and the second characteristic triangle are congruent, then it is considered that... and These are the selected high-quality matching points.

[0015] Furthermore, the process of determining the congruence of characteristic triangles includes:

[0016] Calculate the distance between any two vertices of the first characteristic triangle. and Calculate the distance between any two vertices of the second characteristic triangle. and

[0017] If formula (2) is satisfied, then the first characteristic triangle and the second characteristic triangle are congruent:

[0018]

[0019] Furthermore, the process of determining the congruence of characteristic triangles includes:

[0020] Calculate the distance between any two vertices of the first characteristic triangle. and Calculate the distance between any two vertices of the second characteristic triangle. and

[0021] Randomly select two sets of distance values ​​from the three sets of distance values ​​in the first characteristic triangle, denoted as D1. main and D2 main Select two matching distance values ​​from the second feature triangle and denote them as D1. mirror and D2 mirror Calculate the F value according to formula (3):

[0022]

[0023] Set a threshold λ for the F value and construct the criterion function p. ij :

[0024]

[0025] Construct a voting function based on the criterion function Set the voting ratio t such that the point set S, which is the midpoint of all feature point pairs after filtering, is... mid for:

[0026]

[0027] Where N represents the number of feature points.

[0028] Furthermore, step 3 specifically includes:

[0029] The midpoint coordinates of all high-quality matching points are fitted with a straight line using the random sampling consistency method. The fitted straight line is the rotation axis. The angle between the rotation axis and the vertical centerline of the projected image is the rotation axis deflection angle. The distance between the intersection of the rotation axis and the horizontal centerline of the projected image and the horizontal coordinate of the center of the projected image is the horizontal offset of the rotation axis.

[0030] The beneficial effects of this invention are:

[0031] This invention provides a self-calibration method for nano-CT geometric parameters based on projection feature matching. It utilizes the mirror characteristics of nano-CT projection images under a circular scan trajectory and the stationary rotation axis. Using only projection data acquired in a single scan, feature points are extracted, matched, and selected based on the congruence of characteristic triangles in the mirrored projection image. Finally, the rotation axis position is fitted, thereby calibrating the rotation axis deflection angle and lateral offset. This method eliminates the need for fabricating and placing a high-precision calibration phantom, improves X-ray utilization with a single scan, and avoids repeated reconstruction; only a single reconstruction of the calibrated projection data is required to calibrate the geometric parameters of the nano-CT system. Compared to other methods that directly calculate parameters using projection values, this method, by fitting parameters through high-quality matching feature point coordinates, exhibits better noise resistance. Attached Figure Description

[0032] Figure 1 A flowchart illustrating a method for self-calibrating geometric parameters of nano-CT based on projection feature matching, provided in an embodiment of the present invention;

[0033] Figure 2 This is a schematic diagram illustrating feature point selection based on congruent feature triangles, provided in an embodiment of the present invention.

[0034] Figure 3 This is a diagram showing the geometric structure of a nano-CT imaging system.

[0035] Figure 4 Comparison of Shepp-Logan phantom reconstruction results with and without geometric artifacts: (a) Reconstructed image without artifacts; (b) Reconstructed image with artifacts.

[0036] Figure 5 Image slices reconstructed before and after ant data correction provided for embodiments of the present invention: (a) an image slice without geometric parameter calibration; (b) a reconstructed slice after geometric parameter calibration using the method of the present invention;

[0037] Figure 6 for Figure 5 The pixel value corresponds to the position of the red line. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the embodiments of this invention will be clearly described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0039] Example 1

[0040] like Figure 1 As shown, this embodiment of the invention provides a method for self-calibration of geometric parameters in nano-CT based on projection feature matching, including the following steps:

[0041] S101: Use a nano-CT system to scan the sample and read two mirror projection images from the scan data, and preprocess the two projection images;

[0042] Specifically, a mirrored projection image refers to a projection image with a scanning interval of 180 degrees under a circular scanning trajectory; preprocessing methods include, but are not limited to, image grayscale value normalization, filtering and noise reduction, histogram equalization, etc.

[0043] S102: Set the feature point extraction threshold, extract, match and filter feature points from the two projected images, and record the coordinates of all the selected high-quality matching points;

[0044] Specifically, the feature point selection process includes:

[0045] In the two projected images, arbitrarily select two pairs of matching points, and denote them as matching point pairs. and matching point pairs And calculate the midpoint S of one of the matching point pairs in the same coordinate system. mid The coordinates; where, and This represents the feature points extracted from one of the projected images. and This represents feature points extracted from another projected image;

[0046] feature points and midpoint S mid Construct the first characteristic triangle, and place the characteristic points and midpoint S mid Forming the second characteristic triangle;

[0047] If the first characteristic triangle and the second characteristic triangle are congruent, then it is considered that... and These are the selected high-quality matching points.

[0048] S103: Fit two parameters, rotation axis deflection angle and rotation axis lateral offset, based on the midpoint coordinates of all high-quality matching points in the two projected images;

[0049] Specifically, a straight-line fitting method is first used to fit the midpoint coordinates of all high-quality matching points, and the fitted straight line is the rotation axis. Further, the angle between the rotation axis and the vertical central axis of the projected image is the rotation axis deflection angle, and the distance between the intersection of the rotation axis and the horizontal central axis of the projected image and the horizontal coordinate of the center of the projected image is the horizontal offset of the rotation axis.

[0050] S104: The projection images at all angles in the scanned data are calibrated using affine transformation to determine the two parameters of rotation axis deflection angle and rotation axis horizontal line offset, and then the three-dimensional volume data without geometric artifacts is reconstructed.

[0051] The method provided in this invention creatively uses a projection feature matching approach to accurately calculate the rotation axis deflection angle and lateral offset of a nano-CT system. This method only requires the projection data of the object being scanned, solving the problems of designing high-precision calibration templates and calibrating phantoms for nano-CT systems, and the need for additional scanning of the calibration phantoms. It minimizes the interference of human factors on the calibration results during phantom placement and other processes, while effectively improving data acquisition efficiency and X-ray utilization. Furthermore, the feature extraction process does not depend on the absolute values ​​of the grayscale values ​​of the acquired images, thus exhibiting a certain degree of noise resistance. Further, the method based on congruent feature triangles effectively filters out potentially mismatched feature point pairs that may occur during feature matching. Experimental results demonstrate that this invention has high accuracy and wide applicability.

[0052] Example 2

[0053] Based on the above embodiment 1, one method of determining the congruence of characteristic triangles includes:

[0054] Calculate the distance between any two vertices of the first characteristic triangle. and Calculate the distance between any two vertices of the second characteristic triangle. and

[0055] Specifically, with For example, the calculation formula is shown in formula (1).

[0056]

[0057] If formula (2) is satisfied, then the first characteristic triangle and the second characteristic triangle are congruent:

[0058]

[0059] Example 3

[0060] Based on the above embodiment 1, another process for determining the congruence of characteristic triangles includes:

[0061] Calculate the distance between any two vertices of the first characteristic triangle. and Calculate the distance between any two vertices of the second characteristic triangle. and

[0062] Randomly select two sets of distance values ​​from the three sets of distance values ​​in the first characteristic triangle, denoted as D1. main and D2 main Select two matching distance values ​​from the second feature triangle and denote them as D1. mirror and D2 mirror Calculate the F value according to formula (3):

[0063]

[0064] Set a threshold λ for the F value and construct the criterion function p. ij :

[0065]

[0066] Construct a voting function based on the criterion function Set the voting ratio t such that the point set S, which is the midpoint of all feature point pairs after filtering, is... mid for:

[0067]

[0068] Where N represents the number of feature points.

[0069] This invention relates to a self-calibration method for geometric parameters in nano-CT based on projection feature matching. The method utilizes a nano-CT system to scan samples and acquire projection data. Leveraging the mirror properties of paired projection images differing by 180° along a circular scanning trajectory, and combining the advantages of feature-based image registration algorithms in feature matching, feature points are extracted and matched from the paired projection images. Then, feature point pairs are filtered based on the congruence of characteristic triangles. Finally, the straight line containing the rotation axis is fitted using random sampling consistency, and two parameters that significantly affect the nano-CT system—the rotation axis deflection angle and the lateral offset of the rotation axis—are determined. Finally, rotation and translation corrections are applied to the projection data at all angles, and three-dimensional volume data without geometric artifacts is obtained through reconstruction.

[0070] Example 4

[0071] Based on the above embodiments, the technical solutions provided by the embodiments of the present invention will be described in further detail, specifically including the following steps:

[0072] S401: Select and read a series of projection data according to the shape characteristics of the sample to be tested, and perform projection image gray value normalization, median filtering for noise reduction, and histogram equalization on the projection data.

[0073] S402: Set the feature point extraction threshold, extract feature points of the projected image using the SURF (Speeded Up Robust Feature) algorithm, and match feature point pairs. For matched feature point pairs, filter them by feature triangle congruence.

[0074] Specifically, based on the mirror properties of paired projected images, the triangles formed by three corresponding feature points on the projected image should be congruent; therefore, high-quality matching points can be obtained by screening the triangles formed by two pairs of feature points and the midpoint of one of the pairs being congruent.

[0075] The first feature point filtering method: In conjunction with Example 2, in this embodiment of the invention, matching point pairs are selected. Midpoint in the same coordinate system For example, the following six sets of distance values ​​are calculated according to the above formula (1):

[0076] Then, determine whether the following formula holds true according to formula (2). If it holds true, the four corresponding feature points are high-quality matching points; otherwise, follow the above process to screen other feature point pairs:

[0077]

[0078] Specifically, such as Figure 2 As shown, by feature points and midpoint The first characteristic triangle formed by the characteristic points and midpoint S mid If the resulting second characteristic triangles are congruent, then... and For the selected high-quality matching points, record their coordinates;

[0079] And from feature points and midpoint The first characteristic triangle formed by the characteristic points and midpoint If the resulting second characteristic triangles are not congruent, then these characteristic points are filtered out.

[0080] The second feature point selection method: In practical applications, due to the influence of noise and other factors between 180° projection images, the distance value is difficult to strictly satisfy the above formula (2). Therefore, this embodiment of the invention also designs a second feature point selection method, that is, using the difference and setting a threshold to achieve the selection of feature point pairs. In conjunction with embodiment 3, this embodiment of the invention selects the first feature triangle. and Taking these two sets of distance values ​​as examples, correspondingly, the two sets of distance values ​​that match these two sets of distance values ​​in the second feature triangle are... and The screening process is as follows:

[0081] Combining formula (3), the following formula can be calculated:

[0082]

[0083] Set the threshold F λ and construct the criterion function p. ij Make

[0084]

[0085] And construct a voting function based on the criterion function. Set the voting ratio t such that the point set S, which is the midpoint of all feature point pairs after filtering, is... mid for:

[0086]

[0087] Where N represents the number of feature points.

[0088] S403: As Figure 3 The diagram shows the geometric structure of the nano-CT imaging system. Since the object in the nano-CT system rotates 360° on the stage around the rotation axis under the circular scanning trajectory, ideally, the midpoint of all correctly matched feature point pairs should be located on the rotation axis. Therefore, the straight line of the rotation axis can be fitted by the feature point set composed of the midpoints of the selected feature point pairs using the straight line fitting method, thereby solving for the rotation axis deflection angle and the lateral offset of the rotation axis.

[0089] Specifically, as one possible implementation method, a linear fitting method based on random sampling consistency is used for linear fitting.

[0090] S404: Affine transformation is used to correct the rotation axis deflection angle and lateral offset of the rotation axis of the projection data at all angles. Finally, the projection data after affine transformation is reconstructed to obtain three-dimensional volume data without geometric artifacts.

[0091] Specifically, when there is only a certain angle of deflection of the rotation axis (η≠0, Δu=0), the correspondence between the point after deflection and the point before deflection is as follows:

[0092]

[0093] When the projected image simultaneously exhibits lateral offset of the rotation axis and deflection of the rotation axis within the detector plane (η≠0, Δu≠0), the relationship between feature points on the image is as follows:

[0094]

[0095] This invention proposes a self-calibration method for nano-CT geometric parameters based on projection feature matching. It utilizes the mirror characteristics of nano-CT projection images under a circular scan trajectory and the stationary rotation axis. Using only projection data acquired in a single scan, feature points are extracted, matched, and selected based on the congruence of feature triangles in the mirrored projection image. Finally, the rotation axis position is fitted, thereby calibrating the rotation axis deflection angle and lateral offset. This method eliminates the need for fabricating and placing a high-precision calibration phantom, improves X-ray utilization with a single scan, and avoids repeated reconstruction; only a single reconstruction of the calibrated projection data is required to calibrate the geometric parameters of the nano-CT system. Compared to other methods that directly calculate parameters using projection values, this method, by fitting parameters through the coordinates of well-matched feature points, exhibits better noise resistance.

[0096] Combination Figures 4 to 6 As can be seen, the uncorrected reconstructed volume data slices exhibit double-edge geometric artifacts as shown in the simulated Shepp-Logan data. The double-edge artifacts of the corresponding layer slices in the calibrated reconstructed 3D volume data are well corrected.

[0097] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for self-calibrating geometric parameters of nano-CT based on projection feature matching, characterized in that, include: Step 1: Scan the sample using a nano-CT system and read two mirror projection images from the scan data. Preprocess the two projection images. Step 2: Set the feature point extraction threshold, extract, match, and filter feature points from the two projected images, and record the coordinates of all selected high-quality matching points; the feature point filtering process specifically includes: In the two projected images, arbitrarily select two pairs of matching points, and denote them as matching point pairs. and matching point pairs And calculate the midpoint of one of the matching point pairs in the same coordinate system. The coordinates; where, and This represents the feature points extracted from one of the projected images. and This represents feature points extracted from another projected image; feature points , and midpoint Construct the first characteristic triangle, and place the characteristic points , and midpoint Forming the second characteristic triangle; If the first characteristic triangle and the second characteristic triangle are congruent, then it is considered that... , , and These are the selected high-quality matching points; Step 3: Fit two parameters, the rotation axis deflection angle and the rotation axis lateral offset, based on the midpoint coordinates of all high-quality matching points in the two projected images; Step 4: The projection images at all angles in the scanned data are calibrated using affine transformation to determine the two parameters: rotation axis deflection angle and rotation axis horizontal line offset. Then, the three-dimensional volume data without geometric artifacts is reconstructed.

2. The self-calibration method for geometric parameters of nano-CT based on projection feature matching according to claim 1, characterized in that, The process of determining whether characteristic triangles are congruent includes: Calculate the distance between any two vertices of the first characteristic triangle. , and ; Calculate the distance between any two vertices of the second characteristic triangle , and ; If formula (2) is satisfied, then the first characteristic triangle and the second characteristic triangle are congruent: （2）。 3. The self-calibration method for geometric parameters of nano-CT based on projection feature matching according to claim 1, characterized in that, The process of determining whether characteristic triangles are congruent includes: Calculate the distance between any two vertices of the first characteristic triangle. , and ; Calculate the distance between any two vertices of the second characteristic triangle , and ; From the three sets of distance values ​​in the first characteristic triangle, arbitrarily select two sets of distance values ​​and denote them as follows: and Select two matching distance values ​​from the second feature triangle and denote them as follows: and Calculate the F value according to formula (3): （3） set up Threshold of value Constructing the criterion function : （4） Construct a voting function based on the criterion function Set voting ratio This makes the set of points formed by the midpoints of all feature point pairs after filtering. for: （5） Where N represents the number of feature points.

4. The self-calibration method for geometric parameters of nano-CT based on projection feature matching according to claim 1, characterized in that, Step 3 specifically includes: The midpoint coordinates of all high-quality matching points are fitted with a straight line using the random sampling consistency method. The fitted straight line is the rotation axis. The angle between the rotation axis and the vertical centerline of the projected image is the rotation axis deflection angle. The distance between the intersection of the rotation axis and the horizontal centerline of the projected image and the horizontal coordinate of the center of the projected image is the horizontal offset of the rotation axis.

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