A method for constructing a deformable statistical atlas based on joint registration

Abstract

The present invention discloses a method for constructing a deformable statistical atlas based on joint registration, comprising the following steps: Step 1: Perform registration of the reference template and training samples based on anatomical landmark points; Step 2: Perform registration of the reference template and training samples based on gray levels using all the gray level information in the images; Step 3: Perform joint registration of the reference template and training samples based on anatomical landmark points and gray levels; Step 4: Use the anatomical structures of the training samples represented by the reference template to construct a deformable statistical atlas through statistical shape modeling. The present invention does not require segmentation of the training CT images, which will improve the automation degree of atlas construction and is applicable to atlas construction of multiple anatomical structure parts of the body (such as the head, spine, etc.). The method for constructing a deformable statistical atlas proposed by the present invention requires less manual intervention and can generate a deformable statistical atlas of higher quality, with better shape modeling accuracy.

Description

Technical Field

[0001] The present invention belongs to the field of constructing deformable statistical atlases (DSAs), and particularly relates to a method for constructing a deformable statistical atlas based on joint registration. Background Art

[0002] In the process of constructing existing deformable statistical atlases, the image segmentation of a large number of training CT images is an extremely cumbersome process, which requires a lot of manual operation workload. If the manual operation workload in the atlas construction process can be reduced, the atlas construction speed can be accelerated. The present invention will focus on researching an atlas construction method that does not require image segmentation, while ensuring the accuracy of atlas construction while reducing the manual segmentation workload. Compared with traditional methods, the present invention will improve the automation degree of atlas construction, and the researched method is applicable to the atlas construction of multi-anatomical structure body parts (such as the head, spine, etc.).

[0003] The key to constructing a deformable statistical atlas is to accurately and efficiently calculate the anatomical shape correspondence between training sample shapes. The general strategy for calculating the shape correspondence is to register a reference shape template to the training samples, so that the point cloud of the template matches the point cloud of each training sample to obtain the point-by-point correspondence between the training samples. Therefore, the accuracy of the anatomical shape correspondence of the training samples directly affects the accuracy of the anatomical structure of the deformable statistical atlas.

[0004] So far, many methods for calculating the shape correspondence between training samples have been proposed. However, most of these methods require segmenting the sample shapes from the training images, and then selecting the shape mesh of one individual or averaging the shape meshes of all individuals as the reference shape template. According to the way of registering with the reference shape template, the existing methods for calculating the correspondence of the training individual shape meshes can be divided into three categories, namely mesh-to-mesh registration, mesh-to-3D image registration, and 3D image-to-3D image registration. The mesh-to-mesh registration method uses surface meshes to represent the reference template shape and the training sample shape, and obtains the correspondence between the reference shape template and the training sample by using the surface matching method. Although the surface matching method has high computational efficiency, anatomical structure segmentation of 3D medical images is a challenging and cumbersome task, and the segmentation accuracy directly determines the accuracy of the finally constructed deformable statistical atlas. To avoid the cumbersome work of 3D image segmentation, the method of registering a 3D image to a 3D image is used to register the voxel image of the reference template to the 3D image of the training sample, and the reference template mesh is mapped to the training sample using the spatial transformation obtained by the registration. Similarly, the method of registering a mesh to a 3D image directly matches the reference template mesh with the training image through a boundary fitting strategy. The methods of registering a 3D image to a 3D image and registering a mesh to a 3D image both omit the step of segmenting the training image, but their surface matching accuracies are mostly incomparable with the method of registering a surface to a surface.

[0005] In summary, the existing methods for calculating shape correspondence have two major limitations:

[0006] (1) Most methods for calculating shape correspondence require segmenting the training images. Medical image segmentation, especially 3D medical image segmentation, is a huge project. Usually, to ensure the accuracy of the segmentation results, the image segmentation method adopts interactive segmentation with manual participation and control or even complete manual segmentation. Since multi-anatomical structure images are more complex, the segmentation process of multi-anatomical structures is more time-consuming and laborious.

[0007] (2) Few of the existing methods for calculating shape correspondence pay attention to the correspondence of key anatomical landmark points. Anatomical landmark points are feature points that uniquely identify key anatomical positions, such as bone joints, organ centers, blood vessel bifurcations, etc. The accurate correspondence of key anatomical landmark points is crucial for the anatomical structure accuracy of the constructed deformable atlas. It should be noted that although some studies have considered the alignment of anatomical landmark points in the lungs, face, and bones, most of the existing methods for calculating shape correspondence still focus on the alignment of the overall organ surface shape and ignore the registration of key anatomical landmarks.

[0008] Therefore, there is still a need to develop a more accurate and feasible method for calculating shape correspondence to improve the construction of SSM. Summary of the Invention

[0009] Object of the Invention: In view of the problems that in the construction process of existing deformable statistical atlases, it is necessary to segment training CT images, consuming a large amount of manual operations, etc., the present invention proposes a method for calculating shape correspondence without segmenting training images. This method does not require image segmentation of training samples, but fills the shape mesh of the reference template into a voxel image, and then directly registers the voxel image of the reference template to the unsegmented images of all training samples. In order to utilize the anatomical significance of key anatomical landmark points, the registration process is jointly guided by the gray information of the image and the key anatomical landmark points. This method is inspired by the research on joint registration of gray scale and anatomical landmark points in medical image analysis and surgical planning. The present invention extends this idea to the field of deformable statistical atlas construction, aiming to calculate the anatomical structure correspondence between training samples more efficiently and accurately.

[0010] Technical Solution: The present invention proposes a method for constructing a deformable statistical atlas based on joint registration. Select the images of healthy people as training data, fill the shape mesh of the reference template for constructing the atlas into a voxel image, respectively mark anatomical landmark points at key anatomical positions on the reference template and training samples, adopt a joint registration method based on anatomical landmark points and image gray scale, register the template mesh to the original training sample images, and finally construct a DSA through a statistical shape modeling method.

[0011] In order to avoid segmenting training images and also to compensate for the low-resolution soft tissue regions in CT images, the present invention uses the general human digital model BodyParts3D as the reference template and registers it to the images of each training sample. The DSA construction method proposed by the present invention is applicable to the atlas construction of multiple anatomical structure parts of the body (such as the head, spine, etc.). The shape correspondences to be calculated for different parts are different, but the shape correspondences of each anatomical structure therein need to be calculated. The head and spine are typical multi-anatomical structures. For the head, the shape correspondences of multiple anatomical structures such as skin, muscle, skull, and brain need to be calculated, and for the spine, the shape correspondence of each vertebra needs to be calculated. That is, the methods and processing procedures for constructing DSA of different parts are the same, and the only difference between them lies in the processing objects.

[0012] Therefore, in the following content of the present invention, T e is used to represent the reference template, and S u is used to represent an individual to illustrate the entire construction process. Assume that the point cloud of the reference template is represented as T e ={t1, t2,..., t N}, and N is the number of vertices of the template point cloud. The point cloud of an individual is represented as S u ={s1, s2,..., s M}, where M is the number of vertices of the individual point cloud. The anatomical landmark points manually calibrated in the point cloud are represented as AL = {al1, al2,..., al K}, where K is the number of anatomical landmark points.

[0013] The method for constructing a deformable statistical atlas based on joint registration proposed by the present invention mainly includes four steps.

[0014] First, perform landmark-based registration (LR) on the reference template and the training samples. Manually calibrate key anatomical landmark points with anatomical significance on the reference template and the training samples. Use the position information of these anatomical structures to guide and constrain the process of point cloud contour matching, ensuring the accurate alignment of key anatomical positions between the reference template and the training samples. For head images, several anatomical landmark points important for orthodontics and orthognathic surgery can be manually calibrated in the craniofacial region, while for spinal images, 5 anatomical landmark points can be respectively calibrated at the center, the front and the tail of the spinous process, and the left and right transverse processes of each vertebra. The landmark-based registration method uses the TPS-RPM algorithm, utilizes the spatial position information of the feature points of the image, calculates the feature matching relationship between the reference template point cloud and the training sample point cloud, and realizes the registration of the reference template shape point cloud to the training sample shape point cloud through the control point bending function, obtaining the spatial transformation of the reference template point cloud registered to the training sample, that is, transforming the reference template to the deformation field F of the training sample L . Finally, obtain the anatomical structure of the training sample represented by the reference template mesh topology, where the anatomical structure of the kth training sample is represented as the point cloud S uRPMk = {s uRPMk1 , s uRPMk2 ,..., s uRPMkN}.

[0015] Second, perform intensity-based registration (IR) on the reference template and the training samples. The intensity-based registration algorithm directly uses all the gray information in the image for registration, does not require prior segmentation or feature extraction of the image, but directly acts on the voxels of the original image. The present invention selects mutual information as the similarity measure of the registration algorithm, and searches for the optimal spatial transformation between the reference template and the training samples by iteratively optimizing the mutual information measure. The registration process is generally divided into three steps:

[0016] Step 1: Take the reference template as the moving image and the training sample as the fixed image, and calculate the mutual information between the reference template and the training sample;

[0017] Step 2: According to the given spatial transformation, transform the points in the reference template into the coordinate system where the training samples are located, perform gray interpolation on the points outside the integer coordinates after transformation, and recalculate the mutual information between the reference template and the training samples after transformation;

[0018] Step 3: Through an optimization method, continuously iterate the parameters of the spatial transformation to obtain a new spatial transformation, and go back to Step 2 until the mutual information between the reference template and the training samples after transformation is maximized. At this time, the spatial transformation is the optimal spatial transformation.

[0019] In the gray-based registration of the present invention, the reference template adopts the general human digital model BodyParts3D, which is in the form of a polygonal surface mesh. Therefore, it is necessary to convert the reference template from the curved surface mesh form to a label image. For different parts of the reference template curved surface mesh, fill in the corresponding gray values to obtain a pseudo-CT (Pseudo-CT, pCT) gray image with a voxel size of 1.0 mm. The gray values are determined according to the specific modal characteristics of the experimental images. The present invention uses CT images of the human head and spine as experimental data. Therefore, the filling gray values for filling the curved surface mesh are selected according to the gray characteristics (i.e., CT values, unit: Hounsfield unit, HU) of the head and spine CT images. In CT images, the CT value of cancellous bone is 400 HU, the CT value of the skull is 1000 HU, the CT value of soft tissue is 0 HU, the CT value of air is -1000 HU, and so on. It should be noted that the method of the present invention is not limited to CT images of the head and spine and is also applicable to other imaging modalities. Only the corresponding filling gray values should be adopted according to the image modality of the specific application.

[0020] To register the reference template filled with pseudo-CT to each training sample, the above steps are adopted. Based on mutual information as the similarity measure, B-spline function as the spatial transformation method, and adaptive stochastic gradient descent method as the optimization strategy, continuously iterate until the optimal spatial transformation at the maximum mutual information is obtained, that is, the deformation field F that maps the template to the training sample I , thereby realizing the registration of the reference template to the training sample. Finally, the anatomical structure of the training sample represented by the reference template mesh topology is obtained. Among them, the anatomical structure of the kth training sample is represented as a point cloud S uINTk = {s uINTk1 , s uINTk2 ,..., s uINTkN}.

[0021] Third, perform landmark-intensity-based registration (LIR) on the reference template and training samples. This algorithm addresses the respective drawbacks of the LR-based and IR-based algorithms, achieving both global alignment between the registration objects and taking into account local anatomical structure features.

[0022] For the landmark-intensity-based registration algorithm, the core is to perform non-linear weighting on the spatial transformation based on landmark registration and the spatial transformation based on intensity registration, that is:

[0023] F C (x) = W(x) · F L (x) + (1 - W(x)) · F I (x) (1)

[0024] where x is the spatial position of any point on the registration object in three-dimensional space. F L (x) and F I (x) are the deformation fields based on landmark registration and intensity registration at the spatial position x, respectively. F C (x) is the combined deformation field at the spatial position x, represented by the displacement vector as F C (x) := [Δx, Δy, Δz].

[0025] Theoretically, when the spatial position x is close to the anatomical landmark points, the value of the weighting function W(x) should tend to 1; when the spatial position x is far from the anatomical landmark points, the value of the weighting function W(x) should be close to 0. Therefore, the combined deformation field F C (x) is close to F L (x) in the region close to the anatomical landmark points and close to F I (x) in the region far from the anatomical landmark points. The specific form of the combined deformation field at the spatial position x is completely determined by the distance between the spatial position x and the anatomical landmark points. Therefore, the distance d l (x) from the spatial position x to the anatomical landmark points is introduced to quantify the weighting function W(x), and d l (x) is specifically expressed as follows:

[0026]

[0027] where L i is the coordinate of the i th th anatomical landmark point. Therefore, the weighting function W(x) can be converted into a function W(d l (x)) with respect to d l (x), which is abbreviated as W(d l ). From W(d lAccording to the physical meaning of (), its value range should be [0, 1], and the function should have the property of monotonic decrease. In addition, the curve of the function should also be concave, so that when d l approaches infinity, the decreasing speed of W(d l ) slows down and gradually approaches 1. To sum up, in mathematical theory, W(d l ) should have the following properties:

[0028] 1) Domain: d l ≥0;

[0029] 2) Boundedness: W(0) = 1, and

[0030] 3) Monotonicity: and

[0031] 4) Concavity and convexity: and

[0032] where and are the first-order derivative and the second-order derivative of the function W(d l ) with respect to d l respectively. Theoretically, there are many functions that meet the above four properties. In order to derive the specific form of W(d l ), based on the above properties such as domain, boundedness, monotonicity and concavity and convexity, hypotheses are proposed and through mathematical theoretical derivation, the specific analytical expression of W(d l ) is obtained:

[0033]

[0034] where the parameter δ determines the attenuation speed of the weighting function. In other words, δ controls the transition speed from the spatial deformation field based on anatomical landmark registration to the spatial deformation field based on gray-level registration in Equation (1). Through a large number of experiments, it is found that when the value of δ in Equation (3) is in the range of 4 - 8 mm, similar registration results will be obtained, and better registration results will be obtained compared with other values. When the value of δ is greater than 8 mm, the role of the anatomical landmark constraint will be reduced; while when the value of δ is less than 4 mm, it will lead to non-smooth transition of the combined deformation field F C (x). Therefore, the empirical value of 6 mm is selected for the value of δ. Using the weighting function defined in Equation (3), substitute it into Equation (1) to calculate the combined deformation field F C (x), so as to realize the registration from the reference template to the training sample. Finally, the anatomical structures {s uCOM1 , s uCOM2 ,..., suCOMn}, where the anatomical structure of the k-th training sample is represented as a point cloud S uCOMk ={s uCOMk1 , s uCOMk2 ,..., s uCOMkN}.

[0035] Fourth, using the anatomical structures of the training samples represented by the reference templates, construct a deformable statistical atlas through statistical shape modeling. Based on the registration of the reference templates to the anatomical structures of the training samples, perform shape analysis on the training samples, learn the deformation patterns of the training samples in the population, obtain the anatomical differences between the training individuals, and thus construct a deformable statistical atlas. The process of constructing a deformable statistical atlas based on the statistical shape modeling method is generally divided into two steps: First, apply Generalized Procrustes Analysis (GPA) to normalize the shape meshes of the registered training individuals, and perform normalization processing on all training samples in terms of spatial position and orientation. Then use the principal component analysis (PCA) method to extract the statistical deformation components of the training samples and construct a deformable statistical atlas of the point distribution model type.

[0036] Beneficial effects: 1. A new method for calculating shape correspondence relationships, namely LIR, is proposed for constructing DSA of multi-anatomical structure organs. This method combines the advantages of the algorithms based on LR and IR, and improves the accuracy of shape correspondence relationships between individuals with multi-anatomical structure features. The method of the present invention was tested on head and spinal CT images respectively, and showed higher registration accuracy and better modeling performance than the algorithms based on LR and IR in terms of shape correspondence accuracy and the performance (generalization and specificity) of the corresponding DSA.

[0037] 2. The main advantage of the method of the present invention is to avoid the cumbersome manual segmentation of multiple anatomical structures from 3D medical images. Since completely avoiding human intervention will reduce the accuracy of shape correspondence relationships between individuals, manually calibrated anatomical landmark points are used as a guide to ensure the accuracy of anatomical structures at key anatomical landmark points. The workload of manually calibrating anatomical landmark points is much less than that of organ segmentation. Therefore, the method of the present invention can not only ensure the registration accuracy but also reduce the additional manual cost. Because the registration based solely on anatomical landmark points cannot guarantee the precise alignment of the entire organ region, the method of the present invention uses the gray information of the image to achieve the overall matching of the organ. In order to match the shape mesh of the reference template with the individual CT image, the method of the present invention fills the shape mesh of the reference template into a voxel image and then registers it to the individual CT image based on the gray information.

[0038] 3. The present invention proposes to fuse the LR and IR algorithms with each other, so as to achieve the complementary advantages of the two algorithms, taking into account both the spatial anatomical position information and the gray-scale information of the image to obtain a more accurate registration result. During the registration process, the pixels to be processed are first judged. When the pixel to be registered is close to the anatomical landmark point, the deformation field is mainly based on the LR method, while when the pixel to be registered is far from the anatomical landmark point, the deformation field is mainly based on the IR method, thus ensuring the registration effect and improving the registration accuracy. The LIR method proposed by the present invention combines the respective advantages of the two registration methods, makes full use of the gray-scale information and the spatial anatomical position information of the image, takes into account both global optimization and realizes local precise alignment through anatomical feature points. The main factor affecting the registration result is the calculation of the deformation field. Therefore, the present invention comprehensively considers the feasibility of the experiment and the accuracy of scientific calculation, and selects the exponential function as the non-linear weighting function. Brief Description of the Drawings

[0039] Figure 1 is the construction process of a deformable statistical atlas based on joint registration (taking the construction of a head deformable statistical atlas as an example); it shows the principle process of constructing a DSA based on the anatomical landmark point and gray-scale joint registration algorithm proposed by the present invention. The present invention uses a publicly available high-quality anatomical model as a reference template. First, the reference template shape mesh is filled into a voxel image, and then it is registered to each training image based on the joint registration algorithm proposed by the present invention. The deformation field generated during the registration process is applied to the reference shape template, and the registered template shape mesh is used as the training sample shape correspondence to construct the DSA.

[0040] Figure 2 are the registration results of the reference template to an individual (a) head and (b) spine based on the LR, IR, and LIR algorithms; (a) and (b) respectively show the registration results of the reference template to an individual head and spine based on the LR, IR, and LIR algorithms. Figure 2 Each row shows the registration results of a representative individual in the training set. From left to right, each column corresponds to the individual itself, the individual's registration result based on LR, the individual's registration result based on IR, and the individual's registration result based on LIR.

[0041] Figure 3The generalization of the head and spine DSAs constructed based on the LR, IR, and LIR algorithms respectively was compared in terms of (a) ALAD, (b) DSC, and (c) ASD; the generalization of the deformable atlases of the head and spine constructed based on the registration algorithms of anatomical landmarks, gray scale, and the combination of anatomical landmarks and gray scale was compared in terms of the average distance of anatomical landmarks, similarity coefficient, and average surface distance. Under the existing three accuracy measures, different anatomical structures such as the head skin, skull, and spine of individuals were tested respectively. The deformable atlas constructed based on the combination of anatomical landmarks and gray scale had better generalization than the atlases constructed by the other two methods, achieving the smallest average distance of anatomical landmarks and average surface distance and the largest similarity coefficient.

[0042] Figure 4 The specificity of the head and spine DSAs constructed based on the LR, IR, and LIR algorithms respectively was compared in terms of (a) ALAD, (b) DSC, and (c) ASD; the specificity of the deformable atlases of the head and spine constructed based on the registration algorithms of anatomical landmarks, gray scale, and the combination of anatomical landmarks and gray scale was compared in terms of the average distance of anatomical landmarks, similarity coefficient, and average surface distance. Under the existing three accuracy measures, different anatomical structures such as the head skin, skull, and spine of individuals were tested respectively. The deformable atlas constructed based on the combination of anatomical landmarks and gray scale had better specificity than the atlases constructed by the other two methods, achieving the smallest average distance of anatomical landmarks and average surface distance and the largest similarity coefficient. Detailed implementation

[0043] In the present invention, two multi - anatomical structures of head and spine CT images were selected as experimental objects, and the performance of two DSA verification algorithms for the head and spine was constructed respectively. Head and spine CT image data from four different hospitals across the country were collected. Usually, healthy people's data are used as training samples for constructing atlases. Among the acquired image data, 19 head CT images of asymptomatic individuals and 17 spine CT images of asymptomatic individuals were screened for experiments. The pixel size of the CT images was between 0.59 and 1.37 mm, and the inter - slice spacing was between 1.25 and 3.00 mm, and they were acquired with a tube voltage of 100 - 140 kV and a current of 28 - 298 mA. To avoid segmenting training images and to compensate for the low - resolution soft - tissue regions in CT images, the present invention used the general human digital model BodyParts3D as a reference template and registered it to the images of each training sample.

[0044] The present invention proposes a combined registration algorithm based on anatomical landmark points and gray scale to construct DSA of the head and spine. First, anatomically significant anatomical landmark points are manually calibrated on the reference template and training samples. For head images, 15 anatomical landmark points important for orthodontics and orthognathic surgery can be manually calibrated in the craniofacial region, while for spine images, 5 anatomical landmark points can be respectively calibrated at the center, the anterior and posterior parts of the spinous process, and the left and right transverse processes of each vertebra. Using the TPS-RPM algorithm, based on the feature matching relationship between the reference template point cloud and the training sample point cloud, the reference template shape point cloud is registered to the training sample shape point cloud through the control point bending function, and the spatial transformation of the reference template point cloud registered to the training sample is obtained, that is, the deformation field one of the reference template transformed to the training sample. Second, gray-scale-based registration is performed on the reference template and the training samples. The mutual information is selected as the similarity measure of the registration algorithm, and the optimal spatial transformation between the reference template and the training samples is found by iteratively optimizing the mutual information measure, that is, the deformation field two of the reference template transformed to the training samples. Third, based on the combined registration algorithm of anatomical landmark points and gray scale, non-linear weighting is performed on the deformation field one based on anatomical landmark point registration and the deformation field two based on gray-scale registration. The empirical value of the parameter δ of the weighting function is 6 mm, and each training sample represented by the reference template is obtained. Fourth, using the anatomical structure of the training samples represented by the reference template, a deformable statistical atlas is constructed by means of statistical shape modeling. The GPA method is used to normalize the shape meshes of the registered training individuals, and normalization processing is performed on all training samples represented by the reference templates in terms of spatial position and orientation. Then, the PCA method is used to extract the statistical deformation components of the training samples, and finally a deformable statistical atlas is constructed.

[0045] To verify the performance of the method proposed in the present invention, CT images of the head and spine of the human body with typical multiple anatomical structures are selected as experimental objects, and evaluations are carried out from three aspects: visualization effect, registration accuracy, and deformable statistical atlas modeling quality.

[0046] Two comparative algorithms based on LR and IR and the algorithm based on LIR are respectively used to register the reference templates of the human head and spine to the head and spine CT images of the training sample individuals, and the registration results are as Figure 2 shown. Figure 2 (a) and (b) respectively show the registration results of the reference template to the individual head and spine based on the LR, IR, and LIR algorithms. Figure 2 Each row shows the registration results of a representative individual in the training set. From left to right, each column corresponds to the individual itself, the registration result of the individual based on LR, the registration result of the individual based on IR, and the registration result of the individual based on LIR. From Figure 2(a) It can be clearly seen that the IR-based algorithm can achieve good overall alignment of the head shape, but serious deformations will be introduced at local positions of the head (such as the sunken nose and skewed lips in the figure, etc.). Contrary to the registration results based on IR, the LR-based algorithm can produce smoother registration results. However, the registration accuracy is lacking, and the direct problem is that there are obvious visual deviations between the LR-based registration results and the individual's shape. The algorithm proposed in the present invention combines the respective advantages of the LR-based algorithm and the IR-based algorithm, taking into account both the global registration and the local area. Finally, the LIR-based algorithm not only improves the registration results with serious deformations in the local area, but also generates globally similar facial shapes. The same registration characteristics appear in Figure 2 (b), where the IR-based algorithm will generate registration results with global alignment but local distortion, while the LR-based algorithm will generate smooth but globally deviated results. The registration results generated by the LIR-based algorithm proposed in the present invention achieve both overall alignment and accuracy of the registration results in the local area.

[0047] To quantitatively analyze the accuracy of the atlases constructed based on the LR, IR, and LIR registration algorithms respectively, the registration results of the three algorithms were quantitatively compared with the gold standard annotated by medical imaging experts. Specifically, three types of accuracy metrics, namely the anatomical landmark average distance (ALAD), the dice similarity coefficient (DSC), and the average surface distance (ASD), were used for measurement. These three quantitative metrics can comprehensively quantify the accuracy of the registration algorithm. Table 1 compares the registration accuracies of the head skin, skull, and spine for two comparison algorithms based on LR and IR and the LIR algorithm. The DSC of the head skin was calculated for the entire head region enclosed by the skin, while the DSC of the skull was calculated for the skull bones. Since the structure of the skull is much more complex than that of the head skin, the registration of the skull is more difficult and the registration result is relatively worse compared to the registration of the head skin. It can be clearly seen from Table 1 that for the three registration methods, the three accuracy metrics for skull registration are all inferior to those for head skin registration. However, the LIR-based algorithm obtained a skull ASD of 1.38 mm, which is close to the pixel resolution (1.37 mm) of the CT images in the experiment. For the spine, the LIR-based algorithm obtained a sub-pixel ASD (0.92 mm) and a relatively high similarity coefficient (84.24%). It can also be seen from Table 1 that the IR-based algorithm achieved a smaller ALAD and ASD, and a higher DSC than the LR-based algorithm. This is because the global registration strategy adopted by the IR-based algorithm utilizes the overall gray information of the target CT image to obtain a more accurate registration result. The LIR-based algorithm combines key anatomical landmark points and image gray information into the same registration framework, further improving the accuracy of the registration metrics, achieving the smallest ALAD and ASD, and the highest DSC.

[0048] Table 1 Registration accuracies of the head skin, skull, and spine for the ΛP, IP, and ΛIP algorithms (mean ± standard deviation)

[0049]

[0050] The performance of a deformable statistical atlas depends on its ability to describe the object classes being modeled. Generally, two metrics, generalization and specificity, are mainly used to evaluate its overall performance. The generalization of the atlas represents the ability to represent any instance within the modeled object class, that is, it is used to measure the ability of the atlas to represent new shapes (i.e., shapes outside the training samples). It is quantified by performing a leave-one-out (LOO) test on the training set, measuring the distance from the shape of the individual training sample left out to the closest match of the simplified model. The specificity of the atlas can only represent the legitimate instances of the modeled object class and describes the effectiveness of the model in generating shapes. This value is estimated by generating random parameter values from a normal distribution with a mean of zero and the respective standard deviations in principal component analysis, and taking the average of the best matches of the generated shapes to the training set after multiple runs. In the present invention, each time a sample in the training set (a total of n training samples) is randomly selected as the test sample, and the remaining n - 1 samples are used as the reconstructed training set. The DSA constructed from the n - 1 training sets is fitted to the test sample, and the fitting accuracies (ALAD, DSC, and ASD) are calculated. This process is repeated n times, and the average accuracy is calculated to measure the generalization of the model. The generalization of the head and spine DSA constructed based on the LR, IR, and LIR algorithms is as Figure 3 shown. In the present invention, the specificity is evaluated by generating K (K = 100) random shapes from the normal distribution i of the model parameters a (i = 1, 2,..., n), matching the generated shapes with the closest samples in the training set, and calculating the accuracy metrics (average distance of anatomical landmark points, similarity coefficient, and average surface distance). The average accuracy is calculated for all K random samples to obtain a stable measure of the model specificity. The generalization of the head and spine deformable atlases constructed based on the registration algorithms of anatomical landmark points, gray scale, and the combination of anatomical landmark points and gray scale is as Figure 4 shown.

[0051] Figure 3 and 4The generalization and specificity of the deformable atlases of the head and spine constructed by the registration algorithms based on anatomical landmarks, gray scale, and the combination of anatomical landmarks and gray scale are respectively compared in terms of the average distance of anatomical landmarks, similarity coefficient, and average surface distance. Under the existing three accuracy measures, different anatomical structures such as the head skin, skull, and spine of individuals are respectively tested. The deformable atlas constructed based on the combination of anatomical landmarks and gray scale has better generalization and specificity than the atlases constructed by the other two methods, achieving the smallest average distance of anatomical landmarks and average surface distance, as well as the largest similarity coefficient. The results here are similar to the registration results of the head skin, skull, and spine by the two comparison algorithms of the registration algorithm based on anatomical landmarks and the registration algorithm based on gray scale and the combined registration algorithm based on anatomical landmarks and gray scale in Table 1. The deformable atlas constructed by the registration algorithm based on gray scale achieves a smaller average distance of anatomical landmarks and average surface distance, as well as a higher similarity coefficient than the registration algorithm based on anatomical landmarks. The deformable atlas constructed by the combined registration algorithm based on anatomical landmarks and gray scale further improves the accuracy of the registration index, achieving the smallest average distance of anatomical landmarks and average surface distance, as well as the highest similarity coefficient. Among the three anatomical structures, since the anatomical structure of the skull is the most complex, the shape modeling of the skull is the most difficult one. The difficulty of skull modeling can be reflected from the results of the similarity coefficient. The similarity coefficient results obtained by the three methods adopted in the present invention are all less than 80%. The combined registration algorithm based on anatomical landmarks and gray scale has the best performance, and only achieves a generalization of 73.01% and a specificity of 73.98%. Although the difficulty of skull modeling is very high, the median of the average surface distance of the generalization obtained by the deformable atlas constructed by the combined registration algorithm based on anatomical landmarks and gray scale is 1.45 mm, and the median of the average surface distance of the specificity is 1.44 mm, which means that the modeling of the skull shape is basically accurate.

[0052] The present invention proposes a new method for calculating the shape correspondence relationship based on the combined registration of anatomical landmarks and gray scale, which is used to construct the deformable atlases of multi-anatomical structure organs. This method combines the advantages of the registration algorithms based on anatomical landmarks and gray scale, and improves the accuracy of the shape correspondence relationship between individuals with multi-anatomical structure characteristics. The proposed method is respectively tested on the head and spine CT images of the human body, and shows higher registration accuracy and better performance than the traditional registration algorithms based on anatomical landmarks and gray scale in terms of the shape correspondence accuracy and the performance of the corresponding deformable atlases (generalization and specificity).

[0053] The main advantage of the method proposed by the present invention is to avoid the cumbersome manual segmentation of multiple anatomical structures from 3D medical images. Since completely avoiding human intervention will reduce the accuracy of the shape correspondence between individuals, anatomical landmark points manually calibrated by medical imaging experts are used as a guide to ensure the accuracy of the anatomical structures at key anatomical landmark points. The workload of manually calibrating anatomical landmark points is much less than that of organ segmentation. Therefore, the method proposed by the present invention can not only ensure the segmentation accuracy but also reduce the additional labor cost. Because the registration based solely on anatomical landmark points cannot guarantee the precise alignment of the entire organ region, the method proposed by the present invention uses the gray information of the image to achieve the overall matching of the organ. In order to match the shape mesh of the reference template with the individual CT image, the method proposed by the present invention fills the shape mesh of the reference template into a voxel image and then registers it to the individual CT image based on the gray level. According to the literature review of related work, no registration strategy based on filling the shape mesh of the reference template has been proposed in the existing literature.

[0054] The above are only the preferred embodiments of the present invention. It should be pointed out that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and modifications can be made, and these improvements and modifications should also be regarded as the protection scope of the present invention.

Claims

1. A method for constructing a deformable statistical atlas based on joint registration, characterized in that It includes the following steps: Step 1: Perform registration of the reference template and training samples based on anatomical landmark points; Step 2: Perform registration of the reference template and training samples based on gray levels using all the gray level information in the images; Step 3: Perform joint registration of the reference template and training samples based on anatomical landmark points and gray levels; Step 4: Use the anatomical structure of the training samples represented by the reference template to construct a deformable statistical atlas through statistical shape modeling; The specific steps of Step 3 include: Step 3.1: Perform non-linear weighting on the spatial transformation based on anatomical landmark point registration and the spatial transformation based on gray level registration, i.e.: F C F(x) = W(x)·F L (x)+(1 - W(x))·F I (x) (1) where x is the spatial position of any point of the registration object in the three-dimensional space, F L (x) and F I (x) are the deformation fields based on anatomical landmark registration and intensity-based registration at the spatial position x, respectively, and F C (x) is the combined deformation field at the spatial position x, which is represented by a displacement vector as F C (x):=[Δx,Δy,Δz]; Step 3.2: Introduce the distance d between the spatial position x and the anatomical landmark point l (x) to quantify the weighting function W(x), d l (x) is specifically expressed as follows: where L i is the coordinate of the i th -th anatomical landmark point; the weighted function W(x) is converted into a function W(d l (x)) with respect to d l (x), hereinafter abbreviated as W(d l ); W(d l )Specific parsing expression: where the parameter δ determines the attenuation rate of the weighting function; Step 3.3: Use the weighting function defined in Equation (3) and substitute it into Equation (1) to calculate the combined deformation field F C (x), thereby realizing the registration from the reference template to the training samples; Step 3.4: Obtain the anatomical structure of the training samples represented by the reference template grid topology.

2. The method for constructing a deformable statistical atlas based on joint registration according to claim 1, wherein The specific steps of Step 1 include: Step 1.1: Manually mark key anatomical landmark points with anatomical significance on the reference template and training samples; Step 1.2: Use the TPS-RPM algorithm to perform registration based on anatomical landmark points: Utilize the spatial position information of the anatomical landmark points in the images to calculate the feature matching relationship between the reference template point cloud and the training sample point cloud, and through the control point bending function, register the reference template shape point cloud to the training sample shape point cloud to obtain the spatial transformation of the reference template point cloud registered to the training sample, that is, the deformation field that transforms the reference template to the training sample; finally, obtain the anatomical structure of the training samples represented by the reference template grid topology.

3. A method for constructing a deformable statistical atlas based on joint registration according to claim 2, characterized in that In Step 1.1, for head images, manually mark several anatomical landmark points that are important for orthodontics and orthognathic surgery in the craniofacial region; for spinal images, mark several anatomical landmark points at the center, anterior and posterior of the spinous process, and the left and right transverse processes of each vertebra respectively.

4. A method for constructing a deformable statistical atlas based on joint registration according to claim 1, wherein The specific steps of Step 2 include: Step 2.1: Take the reference template as the moving image and the training sample as the fixed image, and calculate the mutual information between the reference template and the training sample; Step 2.2: According to the given spatial transformation, transform the points in the reference template into the coordinate system of the training sample, perform gray level interpolation on the points outside the integer coordinates after transformation, and recalculate the mutual information between the reference template and the training sample after transformation; Step 2.3: Through an optimization method, continuously iterate the parameters of the spatial transformation to obtain a new spatial transformation, and go to Step 2.2 until the mutual information between the reference template and the training sample after transformation is maximized. At this time, the spatial transformation is the optimal spatial transformation.

5. A method for constructing a deformable statistical atlas based on joint registration according to claim 4, characterized in that, In Step 2.3, based on the mutual information as the similarity measure, the B-spline function as the spatial transformation method, and the adaptive stochastic gradient descent method as the optimization strategy, continuously iterate until the optimal spatial transformation when the maximum mutual information is obtained, that is, the deformation field that maps the template to the training sample, so as to realize the registration of the reference template to the training sample, and finally obtain the anatomical structure of the training samples represented by the reference template grid topology.

6. A method for constructing a deformable statistical atlas based on joint registration according to claim 1, characterized in that The value of δ is 4 - 8 mm.

7. A method for constructing a deformable statistical atlas based on joint registration according to claim 1, characterized in that The specific steps of Step 4 include: registering the reference template to the anatomical structure of the training samples, performing shape analysis on the training samples, learning the deformation patterns of the training samples in the population, obtaining the anatomical differences among the training individuals, and thus constructing a deformable statistical atlas; the process of constructing a deformable statistical atlas based on the statistical shape modeling method includes two steps: first, applying the generalized Procrustes analysis to normalize the shape meshes of the registered training individuals, and performing normalization processing on all training samples in terms of spatial position and orientation; then using the principal component analysis method to extract the statistical deformation components of the training samples and constructing a deformable statistical atlas of the point distribution model type.

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