A three-dimensional medical image registration method, system, and computer-readable storage medium

Abstract

This invention provides a three-dimensional medical image registration method, system, and computer-readable storage medium. The three-dimensional medical image registration method includes the following steps: acquiring the image to be registered and performing standardized preprocessing on the image; defining a new measure in three-dimensional space, analogous to the Beltrami coefficient in complex space, and constructing a registration model based on the new measure; discretizing the registration model and optimizing the discretized registration model using the Gauss-Newton iterative method to obtain the optimal transformation model; constructing a floating image in the image to be registered based on the optimal transformation model, and fusing the deformed floating image with the target image in the image to be registered for display. By adopting the above technical solution, accurate registration of three-dimensional medical images is achieved, and medical images from different modalities or times are fused, improving the accuracy of information utilization.

Description

Technical Field

[0001] This invention relates to the field of medical image processing, and more particularly to a three-dimensional medical image registration method, system, and computer-readable storage medium. Background Technology

[0002] Image registration is an important field in image processing. Registration refers to the geometric alignment of two or more images, ensuring that every point in the floating image has a unique corresponding point in the target image. The goal is to find the spatial transformation relationships between different images, thereby restoring the geometric inconsistencies between the images to be registered as much as possible. Image registration is a crucial step in image analysis and processing, especially in the field of medical imaging, where it has significant application value in disease diagnosis, surgical guidance, and disease treatment tracking. It is a necessary prerequisite for image fusion, analysis, and target recognition. Medical image registration has many clinical applications, serving as a key technology for image-guided surgery, image fusion, organ atlas generation, and tumor and bone growth monitoring, and it is also a highly challenging problem.

[0003] With the development of medical imaging technology, different modalities of medical images can be obtained, such as ultrasound (US), CT, MRI, and PET. These different modalities have different characteristics. US imaging has advantages such as being non-invasive, non-radioactive, real-time, convenient, and low-cost, and is currently widely used for screening, diagnosis, and treatment of diseases of abdominal and superficial organs. However, it suffers from low spatial resolution, low contrast, limited penetration, a small imaging area, and susceptibility to the influence of the surgeon's technique. CT imaging is realistic, clear, has high spatial resolution, and a complete imaging area. It is effective for imaging blood vessels and bones, highlighting anatomical structures and distinguishing them from surrounding tissues. However, CT imaging involves exposure to X-rays, posing a risk of cancer. MRI provides excellent imaging of soft tissues and organs, with high image quality and resolution. However, patients with metallic foreign bodies cannot undergo MRI examinations, and MRI has disadvantages such as long scan times, artifacts caused by periodic organ movement, and high cost. PET can detect metabolic processes, but it has low resolution and long acquisition times. These medical images are irreplaceable; combining their advantages would greatly assist in diagnosis and treatment, making registration technology crucial. Registration technology can improve the efficiency of detecting treatment effects. Simultaneously, it can maximize the fusion of medical images from different modalities or time periods, improving information utilization and diagnostic accuracy.

[0004] Currently, image registration primarily relies on manual alignment. For example, when diagnosing HCC risk in patients using enhanced four-phase CT scans, it's necessary to continuously adjust the four-phase images to ensure their spatial anatomical positions correspond, thereby determining whether corresponding image features are displayed, and ultimately making a diagnosis based on these features. However, when acquiring four-phase images, the patient needs to hold their breath, and different breathing levels can cause certain degrees of distortion between the four-phase images. If only manual alignment is used, it's impossible to achieve the alignment between anatomical structures, thus affecting diagnostic accuracy. Moreover, manual alignment is a time-consuming process; therefore, computer-aided image registration is necessary.

[0005] With the application of registration technology in image analysis, more and more methods are being used in medical imaging. Due to the special nature of this field, it has stricter requirements for registration: First, the transformation generated during the registration process must be one-to-one, ensuring that anatomical points on the floating image can find unique corresponding anatomical points in the target image, thus guaranteeing the significance of the registration process. Second, the registered image and the target image should be as similar as possible; that is, after registration, the two images to be registered should be aligned as closely as possible. Then, there are some specific requirements for the transformation, such as: in four-stage registration, the transformation should be volume-preserving; for incompressible tissue registration, the transformation should satisfy incompressibility. However, in addition to these specific requirements, it must also be ensured that the transformation is fold-free. Once mesh folding occurs in the transformation, it means that the transformation is unreasonable and unacceptable. Therefore, the deformation must be fold-free. Currently, several methods can achieve this requirement. The first method is to calculate the differential homeomorphic transformation by adding a time dimension, such as LDDMM. However, this method has very high requirements for the discrete calculation format and is a very time-consuming process. Another approach is to constrain the Jacobian determinant of the transformation to be greater than zero if the transformation is differentiable. However, existing registration methods that constrain the Jacobian determinant to be greater than zero, such as the Hyperelastic model, directly constrain the Jacobian determinant of the transformation to be equal to 1. This is only suitable for certain specific applications, and may lead to incorrect matching for other applications due to overly stringent requirements.

[0006] Therefore, a novel image registration method is needed, which establishes a new registration model based on a variational model to achieve topological registration. Summary of the Invention

[0007] To overcome the above-mentioned technical defects, the present invention aims to provide a three-dimensional medical image registration method, system and computer-readable storage medium, to achieve accurate registration of three-dimensional medical images, and to fuse medical images of different modalities or times to improve the accuracy of information utilization.

[0008] This invention discloses a three-dimensional medical image registration method, comprising the following steps:

[0009] Acquire the image to be registered and perform normalization preprocessing on the image;

[0010] Analogous to the Beltrami coefficient in complex space, a new measure is defined in three-dimensional space, and a registration model is constructed based on the new measure;

[0011] The registration model is discretized, and the Gauss-Newton iteration method is used to optimize the discretized registration model to obtain the optimal transformation model.

[0012] A floating image is constructed from the image to be registered based on the optimal transformation model, and the deformed floating image is fused with the target image in the image to be registered for display.

[0013] Preferably, the steps of acquiring the image to be registered and performing normalization preprocessing on the image to be registered include:

[0014] Medical images are collected to form a set of images to be registered, and the target tissue in each image to be registered is segmented to form a segmented image.

[0015] The segmented image is subjected to grayscale normalization, normalization based on window width and window level, and digital image resampling is performed on the normalized segmented image.

[0016] The segmented images are cropped to ensure that each image to be registered has the same size.

[0017] Preferably, the steps of defining a new measure in three-dimensional space, analogous to the Beltrami coefficients in complex space, and constructing a registration model based on the new measure, include:

[0018] Analogous to the definition of the Beltrami coefficient in complex space, a new measure is defined in three-dimensional space as follows:

[0019] in The sign() function represents the Jacobian determinant, and the new measure having a modulus less than 1 is equivalent to the transformed Jacobian determinant being greater than 0.

[0020] Using the new measure as the regularization term, the following registration model is constructed:

[0021]

[0022] Where F: M represents the target image in the image to be registered. Represents the floating image in the image to be registered, y:R 3 →R 3Let Ω represent the spatial transformation, and let min represent the domain of the image to be registered. y L(y) represents minimizing the energy functional, where the first and second terms together represent the data fidelity term. This represents the normalized gradient operator. Let α1 and α2 represent the smoothing constraint parameters, and β represent the parameters of the Jacobian constraint term.

[0023] Preferably, the steps for constructing the registration model using the new measure as a regularization term include:

[0024] When the modality of the image to be registered is unimodal, the data fidelity term is selected as the sum of squared differences (SSD): SSD(y) = ∫ Ω (M°yF) 2 dx;

[0025] When the modality of the image to be registered is multimodal, the data fidelity term selects the following gradient information:

[0026] Preferably, the steps of discretizing the registration model and optimizing the discretized registration model using the Gauss-Newton iteration method to obtain the optimal transformation model include:

[0027] The integral in the registration model is approximated based on the median formula, and the derivative in the registration model is discretized based on the difference scheme to obtain the discrete energy functional.

[0028]

[0029] in Φ1(r c )=(Φ1((r c )1), …,Φ1((r c ) N )), Φ(r)=(Φ((r)1),…,Φ((r)) N )),

[0030] The gradient of the discrete energy functional is obtained as follows:

[0031] Where A and B correspond to the first-order and second-order derivative matrices, respectively, and U n The displacement field is discretized, where h is the discrete unit and r(U) is the displacement field. n ) represents N(y) with respect to U n Discrete vector form, r c (U n This is obtained by simplifying GF_TM; Represents r(U)n Regarding U n gradient vector, Indicates Φ with respect to r(U) n The gradient vector of ) Indicates Φ1 with respect to r c (U n The gradient vector of ).

[0032] Solve for the following Hessian matrix corresponding to the registration model:

[0033] in This indicates that Φ1 is related to r c (U n The diagonal matrix formed by the second derivatives of ) This indicates that Φ is related to r(U) n A diagonal matrix formed by the second derivatives of ).

[0034] Find feasible directions from the Hessian matrix to solve for the corresponding linear equations:

[0035]

[0036] Then, the required displacement is solved using the following linear iteration:

[0037] U k+1 =U k +θ k δU k

[0038] Y k+1 =X n +U k+1 Where δU represents the iteration direction, θ represents the iteration step size, k represents the k-th iteration, and X n Represents the original coordinates of the deformed image;

[0039] After iteration, the optimal transformation model corresponding to the finest scale is obtained.

[0040] This invention also discloses a three-dimensional medical image registration system, comprising:

[0041] The preprocessing module acquires the image to be registered and performs standardization preprocessing on the image;

[0042] The modeling module, analogous to the Beltrami coefficient in complex space, defines a new measure in three-dimensional space and constructs a registration model based on the new measure;

[0043] The optimization module discretizes the registration model and uses the Gauss-Newton iteration method to optimize the discretized registration model to obtain the optimal transformation model.

[0044] The fusion module constructs a floating image in the image to be registered based on the optimal transformation model, and then fuses and displays the deformed floating image with the target image in the image to be registered.

[0045] The present invention also discloses a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, performs the steps described above.

[0046] Compared with existing technologies, the above technical solution has the following advantages:

[0047] 1. By mimicking the definition of the Beltrami coefficient in complex space to achieve topology preservation, the transformation Jacobian determinant of all points can be automatically constrained to be greater than 0.

[0048] 2. By using the improved Gauss-Newton method, the optimal solution can be calculated quickly and stably;

[0049] 3. The designed normalized gradient vector field similarity measure is suitable for registration between multimodal images, improving the accuracy of registration. Attached Figure Description

[0050] Figure 1 This is a flowchart illustrating the three-dimensional medical image registration method in a preferred embodiment of the present invention;

[0051] Figure 2 A schematic diagram of four-stage CT images in accordance with a preferred embodiment of the present invention. Detailed Implementation

[0052] The advantages of the present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments.

[0053] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numerals in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this disclosure. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this disclosure as detailed in the appended claims.

[0054] The terminology used in this disclosure is for the purpose of describing particular embodiments only and is not intended to be limiting of the disclosure. The singular forms “a,” “the,” and “the” as used in this disclosure and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used herein refers to and includes any and all possible combinations of one or more of the associated listed items.

[0055] It should be understood that although the terms first, second, third, etc., may be used in this disclosure to describe various information, such information should not be limited to these terms. These terms are used only to distinguish information of the same type from one another. For example, without departing from the scope of this disclosure, first information may also be referred to as second information, and similarly, second information may also be referred to as first information. Depending on the context, the word "if" as used herein may be interpreted as "when," "when," or "in response to determination."

[0056] In the description of this invention, it should be understood that the terms "longitudinal", "lateral", "up", "down", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0057] In the description of this invention, unless otherwise specified and limited, it should be noted that the terms "installation", "connection" and "linking" should be interpreted broadly. For example, they can refer to mechanical or electrical connections, or internal connections between two components. They can be direct connections or indirect connections through an intermediate medium. Those skilled in the art can understand the specific meaning of the above terms according to the specific circumstances.

[0058] In the following description, suffixes such as "module," "part," or "unit" used to denote elements are used only for the convenience of the description of the invention and have no specific meaning in themselves. Therefore, "module" and "part" can be used interchangeably.

[0059] See Figure 1 The diagram illustrates a flowchart of a three-dimensional medical image registration method according to a preferred embodiment of the present invention. In this embodiment, the three-dimensional image registration method includes the following steps:

[0060] S100: Acquire the image to be registered and perform normalization preprocessing on the image to be registered.

[0061] The acquired image to be registered can be as follows Figure 2 As shown, these are CT images of lesions at different stages. After preprocessing, these images to be registered will have the same grayscale and size.

[0062] S200: Analogous to the Beltrami coefficients in complex space, a new measure is defined in three-dimensional space, and a registration model is constructed based on the new measure.

[0063] In a complex function space, given a function μ, then and This shows that the mapping f is direction-preserving, and therefore topologically preserving. Where μ: Ω→D, f: Ω→C, satisfying the equation:

[0064]

[0065] Here, Ω and D are subsets of the complex space, μ is called the Beltrami coefficient of f, and the corresponding equation is called the Beltrami equation. However, the Beltrami coefficient has no corresponding definition in three-dimensional space. Therefore, mimicking its definition in two-dimensional space, a measure similar to the Beltrami coefficient is redefined as a new measure, and a registration model is constructed using this new measure as the regularization term.

[0066] S300: Discretize the registration model and optimize it using the Gauss-Newton iterative method to obtain the optimal transformation model.

[0067] To determine the optimal matching effect of the registration model, the registration model is discretized in step S300 to determine the deformation displacement field between the floating image and the target image under the minimum displacement (or the finest scale).

[0068] S400: Construct a floating image in the image to be registered based on the optimal transformation model, and fuse the deformed floating image with the target image in the image to be registered for display.

[0069] With the above configuration, by using the definition of the Beltrami coefficients in complex space to preserve the topology, it is possible to automatically ensure that the transformation Jacobian determinant of all points is greater than 0.

[0070] In a preferred embodiment, step S100 includes:

[0071] S110: Collect medical images to form a set of images to be registered, and segment the target tissue in each image to be registered to form a segmented image;

[0072] For example, images to be registered can be collected from the hospital's radiology department, and the portion containing only the target tissue can be segmented from the images to reduce the area to be registered.

[0073] S120: Perform grayscale normalization on the segmented image to [0, 1]. For example, MRI and CT are normalized based on window width and window level. Then, perform digital image resampling on the normalized segmented image to make the resolution in the segmented image is isotropic. Isotropic means that the physical, chemical and other properties of an object will not change due to different directions. That is, the performance values ​​of an object measured in different directions are exactly the same, also known as homogeneity.

[0074] S130: Crop the segmented image to ensure that each image to be registered is the same size.

[0075] For example, the size of all images to be registered can be standardized to 256x256x128, 128x128x128, or 224x224x128. Furthermore, an image pyramid can be constructed from 1 to L, allowing the resolution of the images to be registered to range from coarse to fine.

[0076] Further preferred or optional, step S200 includes:

[0077] S210: Analogous to the definition of the Beltrami coefficient in complex space, a new measure is defined in three-dimensional space as follows:

[0078] in The new measure represents the Jacobian determinant, sign() represents the sign function, and the modulus of the new measure being less than 1 is equivalent to the transforming Jacobian determinant being greater than 0.

[0079] S220: Using the new measure as a regularization term, construct the following registration model:

[0080]

[0081] Where F: M represents the target image in the image to be registered. Represents the floating image in the image to be registered, y:R 3 →R 3 Let Ω represent the spatial transformation, and let min represent the domain of the image to be registered. y L(y) represents minimizing the energy functional. The first and second terms in minimizing the energy functional together represent the data fidelity term. This represents the normalized gradient operator. Let α1 and α2 represent the smoothing constraint parameters, and β represent the parameters of the Jacobian constraint term.

[0082] It is understandable that when the assumption is F: M represents a fixed image (target image). Represents a floating image (source image), y:R 3 →R 3 When Ω represents the spatial transformation, and Ω represents the domain of the image, the registration process based on the variational model is the process of optimizing the following energy functional: Optimizing the energy functional yields a left-right transformation that satisfies certain conditions. Here, S() represents the data fidelity term, a similarity measure used to estimate the distance between the floating and fixed images (the smaller the value, the better), while R() represents the regularization term, a deformation constraint term, which constrains the final transformation to satisfy certain properties. Due to the special nature of medical images, deformation has stricter requirements. For example, the transformation should be one-to-one, ensuring that each anatomical point in the floating image has exactly one corresponding anatomical location in the fixed image. Secondly, the deformed floating and fixed images should be as similar as possible, meaning the fidelity term should be as small as possible. These two requirements are also necessary in general image registration. However, medical images display anatomical tissue. During deformation, the topological structure of the involved anatomical tissue should be consistent; otherwise, incorrect matching and information fusion errors will occur. Therefore, in medical image registration, the deformed mesh cannot fold, i.e., topological structure must be preserved, thus ensuring that the new measure in step S220 has good properties, for example… Based on this property, the constraint transformation can be topologically preserved by constraining N(y) < 1.

[0083] In a further preferred embodiment, step S230 includes:

[0084] S231: When the modality of the image to be registered is unimodal, the data fidelity term is selected as the sum of squared differences SSD: SSD(y)=∫ Ω (M°yF) 2 dx;

[0085] S232: When the modality of the image to be registered is multimodal, the data fidelity term selects the following gradient information (in normalized form):

[0086]

[0087] Understandably, once the data fidelity term is selected, the registration model is constructed, which is the construction of the energy functional.

[0088] In a preferred embodiment, step S300 includes:

[0089] S310: The integral in the registration model is approximated based on the median formula, and the derivative in the registration model is discretized based on the difference scheme to obtain the discrete energy functional (taking multimodal as an example).

[0090] S320: The following corresponding gradient is obtained by solving the discrete energy functional:

[0091]

[0092] in Φ1(r c )=(Φ1((r c )1), …,Φ1((r c ) N )), Φ(r)=(Φ((r)1),…,Φ((r)) N )), Where A and B correspond to the first-order and second-order derivative matrices, respectively, and U n The displacement field is discretized, where h is the discrete unit and r(U) is the displacement field. n ) represents N(y) with respect to U n Discrete vector form, r c (U n This is obtained by simplifying GF_TM; Represents r(U) n Regarding U n The gradient vector. Indicates Φ with respect to r(U) n The gradient vector of ) Indicates Φ1 with respect to r c (U n The gradient vector of ).

[0093] S330: Solve for the following Hessian matrix corresponding to the registration model:

[0094] in This indicates that Φ1 is related to r c (U n The diagonal matrix formed by the second derivatives of ) This indicates that Φ is related to r(U) n The Hessian matrix is ​​a diagonal matrix composed of the second-order partial derivatives of a multivariable real-valued function.

[0095] S340: Solve for feasible directions using the Hessian matrix, i.e., solve for the corresponding linear equations, and perform linear iteration to find the required displacements:

[0096]

[0097] U k+1 =U k +θ k δU k

[0098] Y k+1 =Xn +U k+1 Where δU represents the iteration direction, θ represents the iteration step size, k represents the k-th iteration, and X n Represents the original coordinates of the deformed image;

[0099] After iteration, the optimal transformation model corresponding to the finest scale is obtained.

[0100] This invention also discloses a three-dimensional medical image registration system, comprising: a preprocessing module for acquiring an image to be registered and performing standardized preprocessing on the image; a modeling module for defining a new measure in three-dimensional space, analogous to the Beltrami coefficient in complex space, and constructing a registration model based on the new measure; an optimization module for discretizing the registration model and optimizing the discretized registration model using the Gauss-Newton iterative method to obtain an optimal transformation model; and a fusion module for constructing a floating image in the image to be registered based on the optimal transformation model and fusing the deformed floating image with the target image in the image to be registered for display.

[0101] The present invention also discloses a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, performs the steps described above.

[0102] It should be noted that the embodiments of the present invention have better implementability and are not intended to limit the present invention in any way. Any person skilled in the art may use the above-disclosed technical content to change or modify it into equivalent effective embodiments. However, any modifications or equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention shall still fall within the scope of the technical solution of the present invention.

Claims

1. A method of three-dimensional medical image registration, characterized by, The method comprises the following steps: acquiring the images to be registered and performing standardization preprocessing on the images to be registered; analogous to the Beltrami coefficient in complex space, a new measure is defined in three-dimensional space, and a registration model is constructed based on the new measure; discretization processing is performed on the registration model, and the registration model after the discretization processing is optimized by using the Gauss-Newton iteration method to obtain an optimal transformation model; a floating image in the images to be registered is constructed based on the optimal transformation model, and the deformed floating image is fused and displayed with a target image in the images to be registered; analogous to the Beltrami coefficient in complex space, a new measure is defined in three-dimensional space, and a registration model is constructed based on the new measure; analogous to the definition of the Beltrami coefficient in complex space, the following new measure is defined in three-dimensional space: wherein denotes the Jacobian determinant, denotes the sign function, and the modulus of the new measure being smaller than 1 is equivalent to the Jacobian determinant of the transformation being larger than 0; a registration model is constructed by taking the new measure as a regularization term: wherein denotes a target image in the image to be registered, denotes a floating image in the image to be registered, denotes a spatial transformation, denotes a definition domain of the image to be registered, denotes minimizing an energy functional, the first and second terms together representing a data fidelity term in the energy functional, , denotes a normalized gradient operator, denotes a normal gradient operator, and denotes a smoothing constraint parameter, denotes a parameter of the Jacobian constraint term.

2. The three-dimensional medical image registration method of claim 1, wherein, the images to be registered are acquired, and standardization preprocessing is performed on the images to be registered; a set of images to be registered is collected, and a target tissue in each of the images to be registered is segmented to form a segmented image; gray scale normalization processing is performed on the segmented image, normalization processing is performed based on a window width and a window level, and digital image resampling is performed on the segmented image after the normalization processing; the segmented image is cropped so that the size of each pair of images to be registered is consistent.

3. The three-dimensional medical image registration method of claim 1, wherein, a registration model is constructed by taking the new measure as a regularization term: When the modality of the images to be registered is single modality, the data fidelity term is chosen as follows: ; When the modality of the image to be registered is multi-modal, the data fidelity term selects the following gradient information: .

4. The three-dimensional medical image registration method of claim 1, wherein, discretization processing is performed on the registration model, and the registration model after the discretization processing is optimized by using the Gauss-Newton iteration method to obtain an optimal transformation model; based on the mean value formula, the integral in the registration model is approximated, and the derivative in the registration model is discretized based on a difference format to obtain a discrete energy functional; ， wherein , , , ; the following corresponding gradient of the discrete energy functional is solved: where and correspond to the first and second derivative matrices, respectively, is the discretized displacement field, is the discretization unit, denotes the gradient vector with respect to the discretized vector form, is obtained by simplifying GF_TM; denotes the gradient vector with respect to the gradient vector with respect to denotes the gradient vector with respect to the gradient vector with respect to denotes the gradient vector with respect to the gradient vector with respect to the following Hessian matrix corresponding to the registration model is solved: wherein denotes a diagonal matrix consisting of the second derivative of the second derivative of denotes a diagonal matrix consisting of the second derivative of the second derivative of a feasible direction of the Hessian matrix is solved to solve the corresponding linear equation: then, the following linear iteration is used to solve the displacement that meets the requirements: wherein denotes the iteration direction, denotes the iteration step size, denotes the iteration number, denotes the iteration number, denotes the original coordinates of the deformed image; after the iteration, the optimal transformation model corresponding to the finest scale is obtained.

5. A three-dimensional medical image registration system, characterized by, comprise: a preprocessing module that acquires the images to be registered and performs standardization preprocessing on the images to be registered; a modeling module that, analogous to the Beltrami coefficient in complex space, defines a new measure in three-dimensional space, and constructs a registration model based on the new measure; an optimization module that performs discretization processing on the registration model, and optimizes the registration model after the discretization processing by using the Gauss-Newton iteration method to obtain an optimal transformation model; a fusion module that constructs a floating image in the images to be registered based on the optimal transformation model, and fuses and displays the deformed floating image with a target image in the images to be registered; analogous to the Beltrami coefficient in complex space, a new measure is defined in three-dimensional space, and a registration model is constructed based on the new measure; analogous to the definition of the Beltrami coefficient in complex space, the following new measure is defined in three-dimensional space: wherein denotes the Jacobian determinant, denotes the sign function, and the modulus of the new measure being smaller than 1 is equivalent to the Jacobian determinant of the transformation being larger than 0; a registration model is constructed by taking the new measure as a regularization term: wherein denotes a target image in the image to be registered, denotes a floating image in the image to be registered, denotes a spatial transformation, denotes a definition domain of the image to be registered, denotes a minimization of an energy functional, the first and second terms together representing a data fidelity term, , denotes a normalized gradient operator, denotes a normal gradient operator, and denotes a smoothing constraint parameter, denotes a parameter of the Jacobian constraint term.

6. A computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program, which is executed by a processor, implements the steps of the method according to any one of claims 1 to 4.

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