Three-dimensional image rapid registration method based on conformal geometric algebraic unit circular ring

Abstract

The invention discloses a three-dimensional image rapid registration method based on a conformal geometric algebraic unit circular ring. The method comprises the following steps: preprocessing contour point clouds of a reference image and a floating image; obtaining an outer contour discrete point cloud set after correction of the reference image and the floating image; calculating the centroids of the point cloud sets of the two modal images, and aligning the point cloud sets of the reference image and the floating image; constructing geometric feature axes of two modals based on the unit ring, calculating the minimum value of the sum of distances from the point cloud set to the ring, and determining the normal vector of the plane where the unit ring is located according to the maximum value; and constructing a rotation operator to perform translation and rotation on the floating modal point cloud set to complete registration to the reference modal. According to the method, a new geometric invariant, namely a unit circular ring, is introduced, and the special property of the unit circular ring in a conformal geometric algebraic space is fully utilized, so that the geometric characteristics of the three-dimensional image can be more accurately captured, and the registration precision is remarkably improved; the problem that registration precision and calculation efficiency are not considered at the same time in the prior art is solved.

Description

Technical Field

[0001] The invention belongs to the field of image processing, and in particular relates to a three-dimensional image fast registration method based on a conformal geometric algebra unit ring. Background Art

[0002] 3D image registration is a key technology in the field of image processing and is widely used in many fields such as medical imaging, computer-aided design (CAD), remote sensing image analysis, and robot navigation. The purpose of image registration is to align images taken from different sources or at different times so that they have spatial consistency in the same coordinate system. Especially in 3D image registration, due to the large amount of data and high computational complexity, the efficiency and accuracy of registration have always been a hot research issue.

[0003] Traditional 3D image registration methods mainly include algorithms based on similarity measurement, such as the mutual information (MI) algorithm and algorithms based on geometric features, such as the iterative closest point (ICP) algorithm. The mutual information algorithm measures the similarity between different images by quantifying the statistical information between voxels and is widely used in multimodal image registration. Although the mutual information algorithm performs well in registration accuracy, its complex calculation process and huge amount of data result in a long registration time, which is a major bottleneck, especially in real-time medical diagnosis.

[0004] On the other hand, the ICP algorithm reduces the amount of calculation and improves the registration speed by iteratively matching geometric features. Although the ICP algorithm has good computational efficiency, its registration accuracy is usually inferior to that of methods based on statistical similarity metrics, and it is easily affected by local optimal solutions. There are certain problems with the stability and robustness of the registration results. In order to improve accuracy and efficiency, some scholars have introduced geometric algebra methods into three-dimensional image registration. Geometric Algebra (GA) provides a more intuitive mathematical tool that can effectively handle geometric transformations in images, especially when dealing with three-dimensional point clouds and surface matching, it shows great advantages.

[0005] Among them, conformal geometric algebra (CGA) is considered to be a potential way to solve the three-dimensional image registration problem due to its unique mathematical properties. CGA can perform efficient spatial transformation while maintaining the geometric shape of the image, and is a powerful tool for dealing with complex three-dimensional geometric problems. However, the existing registration methods based on CGA still have room for optimization in terms of computational efficiency and registration accuracy, especially in large-scale data processing and real-time registration applications.

[0006] In existing research, although the three-dimensional image registration methods based on geometric algebra or conformal geometric algebra have improved the registration accuracy and efficiency to a certain extent, they still have some significant shortcomings. First, the geometric invariants constructed by existing methods are usually simple or general, and fail to fully consider the complex geometric structure of three-dimensional images. Especially when dealing with three-dimensional images with complex shapes or irregular contours, the registration accuracy is often insufficient. This is because traditional geometric invariants often cannot accurately capture the special geometric features of the image and are easily affected by noise or image deformation, resulting in low registration accuracy. Secondly, although geometric algebra and conformal geometric algebra methods can reduce the amount of calculation, due to the reliance on a large number of iterative operations, the optimization process still faces the problems of slow convergence and easy to fall into local optimal solutions. Especially when dealing with large-scale data, the computational efficiency is low and the registration time is long. These problems seriously affect the registration efficiency in real-time applications, especially in medical image analysis and rapid diagnosis.

[0007] Therefore, how to improve the computing speed without losing accuracy in large-scale data processing and real-time registration applications remains a challenge to be solved. Summary of the invention

[0008] Purpose of the invention: The present invention provides a fast three-dimensional image registration method based on the conformal geometric algebra unit circle, aiming to solve the problems of insufficient registration accuracy and low computational efficiency in existing registration methods based on geometric algebra or conformal geometric algebra when processing complex three-dimensional images.

[0009] Invention content: The invention discloses a method for rapid three-dimensional image registration based on a conformal geometric algebraic unit ring, comprising the following steps:

[0010] (1) Preprocess the contour point clouds of the reference image and the floating image to ensure the consistency of the registration area;

[0011] (2) Obtaining a discrete point cloud set of the outer contours of the reference image and the floating image after correction, and obtaining a point cloud set suitable for further registration;

[0012] (3) Calculate the centroid of the point cloud sets of the two modal images and align the point cloud sets of the reference image and the floating image;

[0013] (4) Based on the unit ring, the geometric characteristic axes of the two modes are constructed, and the minimum value of the sum of the “distances” from the point cloud to the ring is calculated to determine the normal vector a of the plane where the unit ring C is located. r-min , a f-min , the maximum value of the sum of the “distance” and the normal vector a is determined r-max , a f-max ; Get the unit ring of the optimal position;

[0014] (5) A rotation operator is constructed to perform translation and then rotation on the floating mode point cloud set to complete the alignment with the reference mode.

[0015] Furthermore, the preprocessing process of step (1) is as follows:

[0016] The spatial resolution is unified, and the prominent feature points in the two modal contour data are used to intercept the effective registration area of ​​the two modal contours. The thickness of the slice layers of the two in the effective area is made proportional to each other, thus realizing spatial correction in three directions of the two modal axes.

[0017] Furthermore, the implementation process of step (2) is as follows:

[0018] In the conformal geometric algebraic space domain, the point cloud X i The expression is:

[0019]

[0020] in (x i ,y i ,z i ) is the Euclidean coordinate of the point cloud, (e1, e2, e3, e ∞ , e0) are the five basis vectors of the conformal geometric algebraic space, and these point clouds constitute the discrete point cloud set of the outer contour after the reference image and the floating image are corrected. and and There are two modes X i The vector form of n r 、n f Total number of contour point clouds after reference mode and floating mode correction respectively.

[0021] Furthermore, the implementation process of step (3) is as follows:

[0022] Point cloud set for the reference mode Every point X in r,i (x r,i ,y r,i ,z r,i ), its center of mass o r for:

[0023]

[0024] Among them, n r is the number of points in the reference modal point cloud set, X i (x i ,y i ,z i ) is the coordinate of the i-th point in the point cloud; for the floating mode point cloud set Every point X in f,j (x f,j ,y f,j ,z f,j ), its center of mass o f for:

[0025]

[0026] Among them, n f is the number of points in the floating mode point cloud set, X f,j (x f,j ,y f,j ,z f,j ) is the coordinate of the jth point in the point cloud;

[0027] Calculate the translation T used to align the point cloud sets of the reference image and the floating image to a unified coordinate system:

[0028] T=o r -o f

[0029] The point cloud set of the floating mode is translated by the translation vector T so that its centroid is aligned with the centroid of the reference mode.

[0030] Furthermore, the implementation process of step (4) is as follows:

[0031] In CGA, a torus is represented as the intersection of a sphere and a plane, and a unit sphere S is constructed with its center at the origin:

[0032]

[0033] Then construct a two-vector plane A through the origin:

[0034] A=xe1+ye2+ze3+d A e ∞

[0035] Among them, d A is the distance from the plane to the origin, and plane A passes through the origin, so d A = 0, then plane A is expressed in the total geometric algebraic space as:

[0036] A=xe1+ye2+ze3

[0037] The intersection of the sphere S and the two-vector plane A gives a ring C:

[0038] C=S^A

[0039] From the geometric position relationship of conformal space, we know that point X i The sum of the distances to the ring C where the sphere S intersects the plane A is:

[0040]

[0041] Set plane A as the unit plane, ||A|| 2 = 1 as its constraint condition, when the above formula D(c) is the minimum, the corresponding solution c min The expression is:

[0042]

[0043] By establishing the Lagrangian function under a single constraint, o min To solve, the constraints are:

[0044]

[0045] Substituting the expression for plane A into the equation, we get:

[0046]

[0047] Based on this constraint, the Lagrangian function is constructed as:

[0048]

[0049] Here we first calculate and deduce D(c) in the above L function:

[0050]

[0051] Then L(c,λ) becomes:

[0052]

[0053] Taking partial derivatives of the four unknown quantities x, y, z and λ in the above formula, we can get the following results:

[0054]

[0055] Convert the above equation into a matrix equation system:

[0056]

[0057] Let the matrix K be:

[0058]

[0059] in, From the above formula, we can see that the vector (x, y, z) TThe definition of K eigenvector is met, so the unknown quantity λ is the corresponding eigenvalue; and the eigenvector of matrix K can be substituted into equation (16) to achieve the equality of both sides of the equal sign of the four equations, so its eigenvector is the geometric characteristic axis to be solved, and the first and third vectors corresponding to the eigenvalue are the normal vector of the plane where the annulus is located when the "distance" between the point cloud and the annulus is the maximum and minimum respectively.

[0060] Furthermore, the construction of the rotation operator in step (5) is as follows:

[0061] T=T2T1

[0062]

[0063] The floating modality point cloud set is first translated and then rotated to complete the registration with the reference modality.

[0064] Beneficial effects: Compared with the prior art, the beneficial effects of the present invention are as follows: by introducing the new geometric invariant of "unit circle", the present invention makes full use of its special properties in conformal geometric algebraic space, and can more accurately capture the geometric features of three-dimensional images, thereby significantly improving the registration accuracy; at the same time, the design of the invariant optimizes the optimization process, improves the optimization speed, and avoids the problems of low computational efficiency and slow convergence in the existing methods, thereby effectively improving the overall efficiency and accuracy of the registration process; the design of the unit circle invariant can better adapt to the geometric characteristics of three-dimensional images, overcome the common local optimal problems in the prior art, and ensure the global stability and robustness of the registration process; the present invention solves the problem of incompatibility between registration accuracy and computational efficiency in the prior art, and is particularly suitable for fields such as medical image analysis that require efficient and accurate registration. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 It is the 3D reconstruction of the skull point cloud set of the preprocessed reference mode and floating mode;

[0066] Figure 2 Schematic diagram showing the distance from a point to a ring;

[0067] Figure 3 It is the contour map of the 3D reconstruction of the two modalities after registration;

[0068] Figure 4 It is a cross-sectional view in the XY direction; among them, (a) is a CT cross-sectional view; (b) is a PD cross-sectional view; (c) is a fusion effect view;

[0069] Figure 5 It is a cross-sectional view in the YZ direction; among them, (a) is a CT cross-sectional view; (b) is a PD cross-sectional view; (c) is a fusion effect view;

[0070] Figure 6It is the cross-sectional view in XZ direction; among them, (a) is the CT cross-sectional view; (b) is the PD cross-sectional view; (c) is the fusion effect view. DETAILED DESCRIPTION

[0071] The present invention will be further described below in conjunction with the accompanying drawings.

[0072] The present invention provides a three-dimensional image fast registration method based on conformal geometric algebra unit ring. First, the translation vector T is calculated by the centroid method, and the reference mode and floating mode point cloud set are translated to a unified coordinate space. Then a unit ring C is found in each mode to minimize the sum of the "distances" from the point cloud to the ring in the registration area of ​​interest. The distance measure from the point cloud to the ring is the shortest Euclidean distance from the point to the space ring. The projection l is the point cloud X i The projection of the straight line to the origin O on the plane where the ring C is located, and the distance d from the point to the ring is actually the point cloud X i The distance to the point P where the projection l intersects the ring C. Each step is explained in detail below.

[0073] Step 1: Preprocess the reference image and floating image. By unifying the spatial resolution of the images and extracting feature points, the consistency of the registration area is ensured, thereby optimizing the effect of the subsequent registration process.

[0074] First, the input reference image and floating image are processed to uniform spatial resolution. Since images of different modalities may have different spatial resolutions, they need to be converted to a uniform resolution for subsequent processing. This process can be achieved through interpolation methods such as nearest neighbor interpolation, bilinear interpolation, or cubic interpolation. The unified resolution helps ensure that the geometric features of different images can be compared at the same scale during the registration process.

[0075] In the reference image and the floating image, select points with significant geometric features (for example, the tip of the ear of the head). These feature points usually have strong geometric similarity in different modalities and are important reference points in the registration process. Using image processing techniques (such as edge detection, region growing or other shape-based feature extraction methods), these feature points can be accurately located.

[0076] Based on the extracted feature points, regions of interest (ROIs) are delineated in the reference image and the floating image. These regions usually cover the outer contour of the skull and its surrounding structures, ensuring the effectiveness and accuracy of the registration. In this way, interference from irrelevant areas can be avoided, ensuring that the registration process focuses on key areas. Especially in medical image registration, this step can significantly reduce redundant data, thereby improving the efficiency of subsequent registration steps.

[0077] For the three-dimensional image of slice data, there may be a problem of inconsistent thickness between different layers. Therefore, in the present invention, by adjusting the slice layer thickness of the reference image and the floating image, the two have the same slice layer thickness ratio in the direction of the spatial axis (i.e., the Z-axis direction), so that the image has consistency in space, ensuring that the subsequent registration operation can be carried out smoothly.

[0078] After the region of interest is determined, in order to eliminate the spatial differences caused by factors such as scanning angle and position, the reference image and the floating image are further spatially corrected. The purpose of spatial correction is to adjust the three-dimensional coordinate system of the image so that they are aligned in three spatial directions to ensure the geometric consistency between the images. In this way, more consistent input data can be provided for subsequent point cloud registration.

[0079] Through the preprocessing operation, the consistency of the reference image and the floating image in geometry and spatial distribution is ensured, providing a high-quality data foundation for point cloud registration in subsequent steps, such as Figure 1 shown.

[0080] Step 2: Obtain the discrete point cloud set of the outer contour after correction of the reference image and the floating image.

[0081] After completing the image preprocessing and spatial correction in step 1, the next step is to obtain the discrete point cloud set of the outer contour of the reference image and the floating image after correction. The purpose of this process is to extract the geometric features in the corrected image to obtain a point cloud set suitable for further registration and provide a basis for the subsequent geometric feature axis construction.

[0082] In the reference image and the floating image, the outer contours of each image need to be extracted first. The extraction of the outer contour point cloud set can be achieved through edge detection algorithms (such as the Canny operator, etc.) or image segmentation-based methods (such as threshold segmentation, etc.). The extracted point cloud set should contain the outer contour information of the image, representing the geometric shape of the image, especially the description of the head shape. Through these point cloud sets, the geometric structure differences of the two images can be further analyzed, and then registration can be performed.

[0083] The extracted outer contour is discretized, that is, the continuous contour line is converted into a discrete point cloud set. This process samples the contour and represents each key point on the contour as a discrete point in three-dimensional space. The discretization of the point cloud set helps to reduce the computational complexity and ensure the efficiency of subsequent operations.

[0084] For each modality, the point cloud is first recalibrated according to the adjustment results of spatial resolution and slice thickness in step 1. This process ensures that the outer contour point cloud sets of the reference image and the floating image are in the same spatial coordinate system and their geometric shapes are aligned in space. With the calibrated point cloud set, subsequent registration operations can be performed in a unified space, reducing the impact of spatial errors.

[0085] Calculate the total number of outer contour point cloud sets of each mode (respectively denoted as and ), providing basic data for subsequent calculations. These two values ​​represent the size of the outer contour point cloud set after the reference image and the floating image are corrected. In practical applications, if the number of point cloud sets is too large, appropriate downsampling can be performed to reduce the amount of calculation, but at the same time, it is necessary to ensure that the geometric features of the point cloud are not lost after downsampling.

[0086] In the Conformal Geometric Algebra (CGA) space domain, point cloud X i The expression is

[0087]

[0088] in, These point clouds constitute the discrete point cloud set of the outer contour after the reference image and the floating image are corrected. and where n r 、n f The total number of contour point clouds after reference mode and floating mode correction respectively. Through the above steps, the valid point cloud sets obtained will become the input of the subsequent registration process. These point cloud sets have been aligned in the same space and have the same geometric features, so they provide a reliable basis for the construction of geometric feature axes in the subsequent steps.

[0089] In this step, the outer contour point cloud sets of the reference image and the floating image are corrected to form a set of point cloud sets suitable for registration, which provides a data basis for the subsequent calculation and registration. These corrected point cloud sets can be used to construct geometric feature axes after further processing, and finally achieve high-precision registration of the two-modal images.

[0090] Step 3: Calculate the centroid of the point cloud sets of the two modal images and align the point cloud sets of the reference image and the floating image so that they can be compared in a unified space.

[0091] Point cloud set for the reference mode Every point X in r,i (x r,i ,y r,i ,z r,i), its center of mass o r It can be calculated by the following formula:

[0092]

[0093] Among them, n r is the number of points in the reference modal point cloud set, X i (x i ,y i ,z i ) is the coordinate of the i-th point in the point cloud. Through this formula, the centroid coordinates of the reference modal point cloud set are obtained.

[0094] Similarly, for the floating mode point cloud set Every point X in f,j (x f,j ,y f,j ,z f,j ), its center of mass o f It can be calculated by the following formula:

[0095]

[0096] Among them, n f is the number of points in the floating mode point cloud set, X f,j (x f,j ,y f,j ,z f,j ) is the coordinate of the jth point in the point cloud. Through this formula, the centroid coordinates of the floating modal point cloud set are obtained.

[0097] After obtaining the centroids of the two modalities, we need to calculate the translation T, which is used to align the point cloud sets of the reference image and the floating image to a unified coordinate system. The translation T can be calculated using the following formula:

[0098] T=o r -o f (4)

[0099] Here, T represents the translation vector from the floating mode to the reference mode. Through the translation vector T, the point cloud set of the floating mode can be translated so that its center of mass is aligned with the center of mass of the reference mode, thus preparing for the subsequent rotation and geometric feature axis construction.

[0100] After the translation T is calculated, it is applied to each point of the floating modal point cloud set to perform a translation transformation. After this translation transformation, the centroid of the floating modal point cloud set will be aligned with the centroid of the reference modal point cloud set, ensuring that the point cloud sets of the two modalities have the same starting position in space.

[0101] Through the above steps, the point cloud sets of the reference mode and the floating mode will be in a unified coordinate system, providing a basis for the subsequent geometric feature axis construction and rotation alignment.

[0102] Step 4: Construct the geometric feature axes of the two modes based on the unit circle, and obtain the unit circle at the optimal position; further capture the geometric features of the point cloud set and provide necessary reference for subsequent rotation operations.

[0103] In CGA, a torus can be represented as the intersection of a sphere and a plane. Then, construct a unit sphere S with its center at the origin, expressed as:

[0104]

[0105] Then construct a double vector A (plane) passing through the origin, the expression is:

[0106] A=xe1+ye2+ze3+d A e ∞ (6)

[0107] Among them, d A is the distance from the plane to the origin, and plane A passes through the origin, so d A =0, then the plane A can be expressed as:

[0108] A=xe1+ye2+ze3(7)

[0109] It can be seen that the intersection of the sphere S and the double vector plane A gives a ring C, which is as follows Figure 2 As shown, the expression of ring C is:

[0110] C=S^A(8)

[0111] From the geometric position relationship of conformal space, we know that point X i The sum of the distances to the ring C where the sphere S intersects the plane A is:

[0112]

[0113] Here plane A is set as the unit plane, ||A|| 2 =1 can be used as its constraint condition. When the above formula D(c) is the minimum, the corresponding solution c min The expression is:

[0114]

[0115] At this time, we can establish the Lagrangian function under a single constraint to solve o min Solve. The constraints are:

[0116]

[0117] Substituting the expression for plane A into the equation, we get:

[0118]

[0119] Based on this constraint, the Lagrangian function is constructed as:

[0120]

[0121] Here we first calculate and deduce D(c) in the above L function:

[0122]

[0123] Then L(c,λ) becomes:

[0124]

[0125] Taking partial derivatives of the four unknown quantities x, y, z and λ in the above formula, we can get the following results:

[0126]

[0127] Convert the above equation into a matrix equation system:

[0128]

[0129] The matrix K can be set as:

[0130]

[0131] in

[0132] From the above formula, we can see that the vector (x, y, z) T In line with the definition of K eigenvector, the unknown quantity λ is the corresponding eigenvalue. And the eigenvector of matrix K can be substituted into equation (16) to achieve the equality of both sides of the four equations, so its eigenvector is the geometric characteristic axis to be solved. Experience has shown that the first and third vectors corresponding to the eigenvalue are the normal vectors of the plane where the ring is located when the "distance" between the point cloud and the ring is the maximum and minimum respectively.

[0133] For the point cloud set of the reference mode and the floating mode, the normal vector determined by the above steps is the position of the geometric feature axis. This axis defines the main geometric features of the two images in space and provides a directional basis for the subsequent rotation transformation.

[0134] Step 5: Construct a rotation operator to realize the rotation transformation of the floating mode point cloud set relative to the reference mode point cloud set to complete the spatial registration of the two.

[0135] According to the calculation results of the unit circle in step 4, the geometric characteristic axis of the reference mode and floating mode point cloud set is obtained by minimizing the sum of the "distances" from the point cloud to the unit circle. This characteristic axis corresponds to the normal vector a of the plane where the unit circle is located. r-min and a f-min Through this normal vector, the spatial positioning and directionality of the point cloud can be accurately described.

[0136] Normal vector a of the reference mode r-min is the normal vector of the plane where the unit circle lies. The normal vector a of the floating mode f-min is the normal vector of the corresponding unit annulus plane in the floating mode.

[0137] By referring to the geometric relationship between the modal normal vector and the floating modal normal vector in CGA, the rotation operator can be expressed as T = T2T1, where:

[0138]

[0139] Through the above steps, the point cloud set of the floating mode is successfully aligned with the point cloud set of the reference mode after translation and rotation transformation, thereby completing the rapid registration of the three-dimensional image.

[0140] So far, the five steps of the entire implementation process have been elaborated in detail, covering the specific operations from image preprocessing, point cloud set acquisition, geometric feature axis construction, rotation operator design and registration. This method effectively improves the accuracy and speed of 3D image registration, and is particularly suitable for medical imaging, 3D reconstruction and other fields.

[0141] The present invention uses the "Retrospective Image Registration Evaluation Project" (RIRE) database of Vanderbilt University in the United States to evaluate the registration results. The registration images used for demonstration in the present invention are derived from the RIRE database. After the registration results are uploaded, the database compares the errors of the registration results with the "gold standard" for sensitive areas in neurosurgery and gives evaluation results. The "gold standard" is obtained by data collection from patients undergoing neurosurgery and registration through the fixed marking method. The evaluation results are reliable, highly referenceable, and consistent with clinical practice. The experiment selected cranial tissue image data of 7 patients. Each patient used 1 set of CT data and 4 sets of MR data, including PD, T1, and PD_rectified and T1_rectified images that have been corrected for geometric distortion. Taking patient code patient_002 as an example, the CT image is used as a floating modality, PD is used as a reference modality, and the three-dimensional reconstructed contours of the two modalities after registration are as follows. Figure 3 As shown in the figure, the three sections after registration are as follows Figure 4, 5 , 6. The error evaluation of the present invention was performed using the "Retrospective Image Registration Evaluation" project of Vanderbilt University, as shown in Table 1.

[0142] Table 1 Errors of the registration results of the present invention compared with the "gold standard"

[0143]

[0144] After evaluation, the registration error results are satisfactory and reach the level of clinical application. Table 2 shows the errors of the "unit ring" algorithm proposed in the present invention and three other registration methods compared with the "gold standard" provided by Vanderbilt University. These algorithms are the improved closest point iterative LMICP and the registration algorithm based on maximum mutual information. It can be seen that the algorithm of the present invention has obvious advantages over the improved ICP algorithm, and compared with the maximum mutual information algorithm, it has stronger algorithm robustness when the average error and median error are comparable.

[0145] Table 2 Comparison error

[0146]

[0147] The registration speed of the algorithms is compared below, as shown in Table 3. The algorithm was written on Matlab R2010a, and the computer configuration is: CPU: Intel Celeron B830 1.8 GHz, memory: 2.00 GB, operating system: Windows 7 32 bit.

[0148] Table 3 Comparison of registration speed

[0149]

[0150]

[0151] As can be seen from Table 3, the "unit ring" algorithm greatly improves the registration speed compared to the maximum mutual information algorithm while ensuring the registration accuracy, because the algorithm of the present invention completes the registration based on the skull contour point cloud at one time, the amount of computational data is small, and compared with the ICP algorithm, it also saves iteration time. The introduction of conformal geometric algebra reduces the complexity of the calculation to the same extent, reduces the scale of the calculation, and is an important factor in reducing the time consumption of registration.

[0152] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for rapid three-dimensional image registration based on a conformal geometric algebraic unit ring, characterized in that: The following steps are involved: (1) Preprocess the contour point clouds of the reference image and the floating image to ensure the consistency of the registration area; (2) Obtaining a discrete point cloud set of the outer contours of the reference image and the floating image after correction, and obtaining a point cloud set suitable for further registration; (3) Calculate the centroid of the point cloud sets of the two modal images and align the point cloud sets of the reference image and the floating image; (4) Based on the unit ring, the geometric characteristic axes of the two modes are constructed, and the minimum value of the sum of the "distances" from the point cloud to the ring is calculated to determine the normal vector a of the plane where the unit ring C is located. r-min , a f-min , the maximum value of the sum of "distance" determines the normal vector a r-max , a f-max ; Get the unit ring of the optimal position; (5) Construct a rotation operator to perform translation and then rotation on the floating mode point cloud set, thereby completing the alignment with the reference mode.

2. The method for rapid three-dimensional image registration based on a conformal geometric algebraic unit ring according to claim 1, characterized in that: The preprocessing process of step (1) is as follows: The spatial resolution is unified, and the prominent feature points in the two modal contour data are used to intercept the effective registration area of ​​the two modal contours. The thickness of the slice layers of the two in the effective area is made proportional to each other, thus realizing spatial correction in three directions of the two modal axes.

3. The method for rapid three-dimensional image registration based on a conformal geometric algebraic unit ring according to claim 1, characterized in that: The implementation process of step (2) is as follows: In the conformal geometric algebraic space domain, the point cloud X i The expression is: in (x i ,y i ,z i ) is the Euclidean coordinate of the point cloud, (e1, e2, e3, e ∞ , e0) are the five basis vectors of the conformal geometric algebraic space, and these point clouds constitute the discrete point cloud set of the outer contour after the reference image and the floating image are corrected. and and There are two modes X i The vector form of n r 、n f Total number of contour point clouds after reference mode and floating mode correction respectively.

4. The method for rapid three-dimensional image registration based on a conformal geometric algebraic unit ring according to claim 1, characterized in that: The implementation process of step (3) is as follows: Point cloud set for the reference mode Every point X in r,i (x r,i ,y r,i ,z r,i ), its center of mass o r for: Among them, n r is the number of points in the reference modal point cloud set, X i (x i ,y i ,z i ) is the coordinate of the i-th point in the point cloud; Point cloud collection for floating modes Every point X in f,j (x f,j ,y f,j ,z f,j ), its center of mass o f for: Among them, n f is the number of points in the floating mode point cloud set, X f,j (x f,j ,y f,j ,z f,j ) is the coordinate of the jth point in the point cloud; Calculate the translation T used to align the point cloud sets of the reference image and the floating image to a unified coordinate system: T=o r -o f The point cloud set of the floating mode is translated by the translation vector T so that its centroid is aligned with the centroid of the reference mode.

5. The method for rapid three-dimensional image registration based on a conformal geometric algebraic unit ring according to claim 1, characterized in that: The implementation process of step (4) is as follows: In CGA, a torus is represented as the intersection of a sphere and a plane, and a unit sphere S is constructed with its center at the origin: Then construct a two-vector plane A through the origin: A=xe1+ye2+ze3+d A e ∞ Among them, d A is the distance from the plane to the origin, and plane A passes through the origin, so d A = 0, then plane A is expressed in the total geometric algebraic space as: A=xe1+ye2+ze3 The intersection of the sphere S and the two-vector plane A gives a ring C: C=S∧A From the geometric position relationship of conformal space, we know that point X i The sum of the distances to the ring C where the sphere S intersects the plane A is: Set plane A as the unit plane, ||A|| 2 = 1 as its constraint condition, when the above formula D(c) is the minimum, the corresponding solution c min The expression is: By establishing the Lagrangian function under a single constraint, o min To solve, the constraints are: Substituting the expression for plane A into the equation, we get: Based on this constraint, the Lagrangian function is constructed as: Here we first calculate and deduce D(c) in the above L function: Then L(c,λ) becomes: Taking partial derivatives of the four unknown quantities x, y, z and λ in the above formula, we can get the following results: Convert the above equation into a matrix equation system: Let the matrix K be: in, From the above formula, we can see that the vector (x, y, z) T The definition of K eigenvector is met, so the unknown quantity λ is the corresponding eigenvalue; and the eigenvector of matrix K can be substituted into equation (16) to achieve the equality of both sides of the equal sign of the four equations, so its eigenvector is the geometric characteristic axis to be solved, and the first and third vectors corresponding to the eigenvalue are the normal vectors of the plane where the annulus is located when the "distance" between the point cloud and the annulus is the maximum and minimum respectively.

6. The method for rapid three-dimensional image registration based on a conformal geometric algebraic unit ring according to claim 1, characterized in that: The construction of the rotation operator in step (5) is as follows: T=T2T1 The floating modality point cloud set is translated and then rotated to complete the registration with the reference modality.

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