CN103985109B - Feature-level medical image fusion method based on 3D (three dimension) shearlet transform - Google Patents

Abstract

The invention discloses a feature-level medical image fusion method based on 3D shearlet transform, which belongs to the technical field of medical image processing and application. The main steps of the method are as follows: 1. Perform 3D-D-CSST transformation or 3D-CSST transformation on two images DT-CSST obtains transformation coefficient images C _a , C _b ; 2. Perform image fusion on the transformation coefficients to obtain the fusion coefficient C _f ; 3. Perform DWT or DTCWT inverse transformation on the coefficient C _f after step 2 fusion, and transform the transformed The image is subjected to backward shear transformation to obtain the fused image V _f . The invention solves the problems that the fusion image quality is relatively low and the locally important but insignificant information is easy to be ignored.

Description

A feature-level medical image fusion method based on 3D shearlet transform

technical field

The invention belongs to the technical field of medical image processing and application, and specifically relates to a feature-level medical image fusion method based on 3D shearlet transform, which solves the problem that the quality of the fused image is relatively low and locally important but insignificant information is easily overlooked .

Background technique

Medical image fusion is a kind of image fusion, and many methods have been widely used in clinical diagnosis. Fusion refers to the process of extracting and merging important information about the target from source images collected by different devices such as CT and MRI into one image. The information contained in images generated by different devices or different configurations of the same device is different, some information is similar, but most of the information is complementary. For example, CT images mainly provide information on dense and hard tissues of the human body, while MRI images mainly provide information on soft tissues. The post-processing image of the information collected by the same MRI equipment at the same time, such as T2* provides the contrast information of tissue relaxation time, and the magnetometric map (QSM: Quantitative SusceptibilityMapping) provides information obtained by a variety of magnetic biomarkers (such as iron , calcium, gadolinium and other contrast agents) induced susceptibility contrast information. Generally speaking, image fusion needs to register the source images first, and the T2* and QSM images are generated based on the data of the same scan through post-processing, so the two have been fully registered.

The current research on medical image fusion mainly considers the situation of two-dimensional images, but now many types of medical equipment are generating three-dimensional images. The gray value of each point in a 3D image is not only cross-correlated with neighboring points in the same layer, but also cross-correlated with neighboring points in adjacent layers. The traditional two-dimensional fusion method will lead to the loss of third-dimensional information, so it is necessary to study fusion methods that can directly process three-dimensional images.

Fusion algorithms can be processed in the spatial or transform domain. In the air domain, the fused image is usually the weighted average of the source data. This method is simple and easy to implement, but the quality of the fused image is not high. The transform domain method follows the following steps: 1) Transform the source image into the transform domain, 2) process the image coefficients according to the fusion criterion to obtain the fused coefficients, 3) finally transform the coefficients back to the space domain, and the output is the fused image. The research focus of this type of algorithm mainly focuses on two points: the selection of transformation and the design of fusion criterion. Many multi-scale (Multi-Scale) transformations can be applied to fusion algorithms, such as DWT, DTCWT, Curvelet, Shearlet, etc.

Shearlet transform is a transformation proposed in recent years and gradually matured for the efficient representation of multi-dimensional data. In fact, many other multi-scale transforms have been proposed by scholars to address the shortcomings of wavelet transform that lacks sparse representation of directional features such as edges. However, the shearlet transform is the only transformation among all methods that has the following advantages at the same time: there is only one or a limited set of generating functions, it can represent high-dimensional data almost optimally, it can handle continuous data and discrete data uniformly, and it has compact support, etc. Wait. Shearlet transform has been widely used in image processing, such as denoising, edge detection, enhancement and so on.

Shearlet is also suitable for image fusion. The existing image fusion technology has the following defects: 1. The traditional fusion method based on wavelet transform and pyramid transform lacks the sparse representation ability of image structure direction due to multi-scale transformation, resulting in fusion The quality of the image is relatively low; 2. The image fusion based on the pixel level does not consider the structural information of the image, which will cause the locally important but insignificant information to be ignored during the image fusion. These defects can adversely affect the final medical diagnosis.

Contents of the invention

In view of the above-mentioned prior art, the purpose of the present invention is to provide a feature-level medical image fusion method based on 3D shearlet transform, which solves the problem of the fusion method based on wavelet transform and pyramid transform. The quality of the fused image is relatively low due to the representation ability; and when the image is fused, locally important but insignificant information is easily ignored, and these defects will eventually have an adverse effect on medical diagnosis.

In order to solve the above technical problems, the present invention adopts the following technical solutions:

In this paper, 3D shear wave specifically refers to 3D compactly supported shear wave (3D-D-shear wave) or 3D dual tree compactly supported shear wave (3D-DT-shear wave), and the D-shear wave transform includes Two steps: forward shear transform and DWT transform; DT-shearlet transform consists of two steps: forward shear transform and DTCWT transform.

A feature-level medical image fusion method based on 3D shearlet transform, characterized in that it comprises the following steps:

1. Prepare two 3D medical images V _a and V _b to be fused, respectively perform forward shear transformation on the three directions of the two images, and perform discrete wavelet transform DWT or dual-tree complex wavelet transform DTCWT on the transformed image, Obtain corresponding sets of transformed image coefficients C _a , C _b ;

2. Perform image fusion on the coefficients obtained by the 3D shearlet transform to obtain the fusion image coefficient C _f ;

3. Perform DWT or DTCWT inverse transformation on the fused image coefficient C _f in step 2, perform backward shear transformation on the transformed image to obtain multiple sets of fused images, and average these images to obtain the final fused image V _f .

In the present invention, the detailed steps of said step 2 include the following two steps:

2.1. For the low-frequency parts C _aL and C _bL of the images C _a and C _b obtained by the 3D shearlet transform, the low-frequency part C _fL of the fused image is obtained by using the mean value criterion;

2.2. Use feature-level fusion for the high-frequency parts C _aH and C _bH to judge the feature type of the image to be fused at the same position, and perform fusion through the maximum retained information criterion to obtain C _fH ;

In the present invention, in said step one, the forward shear transformation is first carried out to the image, and then the discrete wavelet transform DWT or the dual-tree complex wavelet transform DTCWT is carried out to the transformed image; the forward shear transformation is specifically as follows: for a group The three-dimensional data l×m×n establishes a coordinate system, the origin is (0, 0, 0), and its diagonal point is (l-1, m-1, n-1), and the shear transformation in three directions is as follows Shown: The shear transformation for the z direction refers to the following coordinate transformation of the points in the data:

The shear transformation formula for the x direction is:

The shear transformation formula for the y direction is:

Among them, (x, y, z) are coordinates before transformation, and (x', y', z') are coordinates after transformation. k _tr , {tr=a1, b1, a2, b2, a3, b3} is the maximum moving distance. If k _tr takes different values, information in different directions will be retained, so the shearlet transform will produce 3D images, where with is the number of directions of k _ai and k _bi .

In the step 2.1, feature-level fusion is adopted for the low-frequency part of the transformed image, and the fusion rules are:

Cf _L ＝(C _aL +C _aL )/2(2)

In the step 2.2, feature-level fusion is adopted for the high-frequency part of the transformed image, and the specific operation steps are as follows:

2.2.1. First calculate the structural tensors of the high-frequency parts C _aH and C _bH of the transformed image coefficients C _a and C _b , and then perform rank analysis on the structural tensors:

For each point of the high-frequency part C _aH , C _bH of the transformed image coefficients C _a , C _b , the structure tensor is a 3×3 matrix, and the rank of the matrix can be 0, 1, 2, 3, corresponding to the Features of flat, planar, linear, and point-like areas; Ω is the local area l ₁ ×m ₁ ×n ₁ , and the structure tensor of point p is expressed as

w(r) is a Gaussian template of l ₁ ×m ₁ ×n ₁ size; V _x (p), V _y (p), V _z (p) are the three directions of the image pair x, y, and z respectively The partial derivative;

Calculate the eigenvalues E _x , E _y , E _z of this 3×3 tensor matrix, and set the threshold k is the control parameter, set to 0.01, the number of non-zero eigenvalues of point p For the same position of the two pictures, record the number of non-zero eigenvalues of C _a as M _a , record the number of non-zero eigenvalues of C _b as M _b , and M _a and M _b are the approximation of the rank of the tensor matrix;

2.2.2. If M _a =M _b , then the two images have the same type of features at this position, and calculate the similarity at this position

Calculate threshold The fusion rules are:

When γ _ab ≤ α, this position is redundant information, and the weighting criterion is selected:

C _fH = ω _a C _aH + ω _b C _bH (5)

When γ _ab >α, this position is complementary information, using the MRE criterion:

2.2.3. If M _a ≠ M _b , fusion criterion:

The step 3 performs backward shear transformation on the image after DWT or DTCWT inverse transformation, as follows:

For the backward shear transformation, it refers to the inverse operation of the forward shear transformation, where the shear transformation for the z direction refers to the following coordinate transformation of the points in the data:

The shear transformation formula for the x direction is:

The shear transformation formula for the y direction is:

Among them, (x, y, z) are coordinates before transformation, (x', y', z') are coordinates after transformation, k _tr , {tr=a1,b1,a2,b2,a3,b3} The value corresponds to the value of the forward shear transformation.

Compared with the prior art, the present invention has the following beneficial effects:

1. Compared with multi-scale transformations based on traditional Wavelet and pyramid transformations that lack the ability to sparsely represent directional structural properties, compactly supported shearlet transformations have the ability to almost optimally represent anisotropic features in high-dimensional signals. Fused images retain more accurate orientation information, resulting in higher fusion quality;

2. The DT-shearlet transform introduces a dual tree structure, which reduces the fusion image distortion caused by shift variability;

3. The space domain tight support of DT-shear wave and D-shear wave, compared with the frequency domain shear wave, the fusion quality is higher;

4. The present invention uses a feature-level fusion method, which considers the internal structural characteristics of the scanned organ (including flat, planar, linear, and point-like regions), and retains the structural information and physical characteristics of the object to the greatest extent. Compared with only considering high-frequency coefficient statistics The pixel-level fusion criterion of features, the fusion image quality is higher;

5. The quality of the fused image in the present invention is measured by objective indicators (MI, QAB|F), and the quality is higher.

Description of drawings

Fig. 1 is a schematic diagram of the image fusion method of the present invention;

Fig. 2 is a schematic diagram of two-dimensional shear transformation;

FIG. 3 is a schematic diagram of three-dimensional shear transformation (shear transformation in the z-axis direction).

detailed description

The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

Taking T2* magnitude image and QSM image as an example, this experiment uses the method of the present invention to process the three-dimensional T2* magnitude image and QSM image, and finally obtains a fusion image. In the example, the size of the image is 128×128×128.

The image fusion method of this embodiment first considers how to represent the anisotropy of the three-dimensional image, and the shear transform can well represent the anisotropic characteristics of the image; secondly, considering the influence of the translational change properties brought about by the DWT transform, a dual-tree complex wavelet transform is performed DTCWT; Finally, it is considered to fuse as much information as possible into the fusion coefficient image with the low-frequency coefficients and high-frequency coefficients: for low-frequency coefficients, the mean criterion is used; for high-frequency coefficients, the feature-level fusion criterion is used for fusion.

The process is shown in Figure 1 and includes the following steps:

Step 1: Perform forward 3D-DT-shearlet transformation on two images V _a and V _b to obtain transformation coefficients C _a and C _b . The implementation process includes 3D forward shear transformation and 3D DTCWT transformation.

Forward shear transformation: establish a coordinate system for a set of three-dimensional data l×m×n, the origin is (0, 0, 0), and its diagonal point is (l-1, m-1, n-1), and its Performing shear transformation in the z-axis direction refers to transforming the x and y coordinates of points in the data

The shear transformation formula for the other two directions is:

Fig. 2 is a schematic diagram of shear transformation. For this example, l=m=n=128, select k _tr , {tr=a1,b1,a2,b2,a3,b3}=-64,0,64, will produce 27 group transformation image data;

Step 2: Fusing 27 sets of coefficient image data C _a and C _b obtained from 3D-DT-shearlet transform to obtain C _f . The execution process includes fusing low-frequency coefficients and fusing high-frequency coefficients.

The low-frequency parts C _aL and C _bL of the coefficients C _a and C _b obtained by 3D-DT-shearlet transform are fused using the mean criterion:

C _fL ＝(C _aL +C _bL )/2

2) For the high-frequency parts C _aH and C _bH , select the size of the local area Ω of point p to be l ₁ ×m ₁ ×n ₁ , here 3×3×3, and calculate the structure tensor of point p:

w(r) is a Gaussian template of l ₁ ×m ₁ ×n ₁ size; V _x (p), V _y (p), V _z (p) are the three directions of the image pair x, y, and z respectively partial derivative of .

There is correlation between voxels, and it is difficult to have flat, planar, linear, and point-like areas in the strict sense. Therefore, when extracting image structure features, the condition of non-zero eigenvalues is appropriately relaxed. When an eigenvalue of the structure tensor is less than the corresponding threshold, the eigenvalue is considered to be zero, and the number of eigenvalues greater than the threshold is considered to be the rank of the matrix. Calculate the eigenvalues E _x , E _y , E _z of this 3×3 matrix, and set the threshold k is the control parameter, which can be set to 0.01, the number of non-zero eigenvalues of point p M is approximately the rank of the tensor matrix. For the same position of the two images, M _a records the number of eigenvalues with C _aH greater than the threshold value, and M _b records the number of eigenvalues with C _bH greater than the threshold value;

If M _a =M _b , then the two images have the same type of features at this position, then calculate the similarity at this position

Calculate threshold The fusion rules are:

When γ _ab ≤ α, this position is redundant information, and the weighting criterion is selected

C _fH = ω _a C _aH + ω _b C _bH

When γ _ab >α, this position is complementary information, using the MRE criterion:

If M _a ≠ M _b , fusion criterion:

Step 3: performing backward 3D-DT-shearlet transform on the fusion coefficient image C _f to obtain the final fusion image. The execution process includes 3D forward shear transformation and 3D DTCWT transformation

For the backward shear transformation, it refers to the inverse operation of the forward shear transformation, where the shear transformation for the z direction refers to the following coordinate transformation of the points in the data:

The shear transformation formula for the x direction is:

The shear transformation formula for the y direction is:

Select l=m=n=128, select k _tr , {tr=a1, b1, a2, b2, a3, b3}=-64, 0, 64; finally average the 27 reverse-transformed 3D images to get Fused image V _f .

The above is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto, any person familiar with the technical field within the scope disclosed in the present invention, according to the technical scheme of the present invention and its Any equivalent replacement or change of the inventive concept falls within the protection scope of the present invention.

Claims (5)

1. A feature-level medical image fusion method based on 3D shearlet transform, is characterized in that, comprises the steps: 1. Prepare two 3D medical images V _a and V _b to be fused, respectively perform forward shear transformation on the three directions of the two images, and perform discrete wavelet transform DWT or dual-tree complex wavelet transform DTCWT on the transformed image, Obtain corresponding sets of transformed image coefficients C _a , C _b ; 2. Perform image fusion on the coefficients obtained by the 3D shearlet transform to obtain the fusion image coefficient C _f ; the specific steps are: 2.1. Apply the mean value criterion to the low-frequency parts C _aL and C _bL of the image coefficients C _a and C _b obtained by the 3D shearlet transform to obtain the low-frequency part C _fL of the fused image; 2.2. Fusing the high-frequency parts C _aH and C bH of the image coefficients C _a and C _b obtained by the 3D _shearlet transform to obtain the high-frequency part C _fH of the fused image; 2.3. Obtain the fused image coefficient C _f according to the low frequency part C _fL and the high frequency part C _fH ; 3. Perform DWT or DTCWT inverse transformation on the fused image coefficient C _f in step 2, perform backward shear transformation on the transformed image to obtain a fused image, and average these images to obtain a final fused image V _f . 2. the feature level medical image fusion method based on 3D shearlet transform according to claim 1, is characterized in that, in described step 1, first carry out forward shear transformation to image, then carry out to the transformed image Discrete wavelet transform DWT or dual-tree complex wavelet transform DTCWT; forward shear transform is specifically as follows: for a set of three-dimensional data l × m × n to establish a coordinate system, the origin is (0, 0, 0), and its diagonal point is (l -1, m-1, n-1), the shear transformation in three directions is as follows: The shear transformation for the z direction refers to the following coordinate transformation of the points in the data: The shear transformation formula for the x direction is: The shear transformation formula for the y direction is: Among them, (x, y, z) are coordinates before transformation, (x', y', z') are coordinates after transformation; k _tr ,{tr=a1,b1,a2,b2,a3,b3} are The maximum distance to move; if k _tr takes different values, information in different directions will be retained, so the shearlet transform will produce 3D images, where with is the number of directions of k _ai and k _bi . 3. The feature-level medical image fusion method based on 3D shearlet transform according to claim 1, characterized in that the transformed image coefficients C _a , V _b corresponding to the two 3D images V _a , V b in the step 2.2 The fusion method of the high-frequency parts C _aH and C _bH of C _b is as follows: use feature-level fusion to judge the feature type of the image to be fused at the same position, and perform fusion through the maximum retained information criterion to obtain C _fH . 4. the feature-level medical image fusion method based on 3D shearlet transform according to claim 3, is characterized in that, described adopts feature-level fusion to the high-frequency part of transformation image, and concrete operation steps are as follows: 2.2.1. First calculate the structural tensors of the high-frequency parts C _aH and C _bH of the transformed image coefficients C _a and C _b , and then perform rank analysis on the structural tensors: For each point of the high-frequency part C _aH , C _bH of the transformed image coefficients C _a , C _b , the structure tensor is a 3×3 matrix, and the rank of the matrix can be 0, 1, 2, 3, corresponding to the Features of flat, planar, linear, and point-like areas; Ω is the local area l ₁ ×m ₁ ×n ₁ , and the structure tensor of point p is expressed as $\begin{array}{c}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\\ \left[\begin{array}{ccc}\underset{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>& \underset{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>& \underset{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>\\ \underset{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>& \underset{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>& \underset{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>\\ \underset{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>& \underset{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>& \underset{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>\end{array}\right]\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$ w(r) is a Gaussian template of l ₁ ×m ₁ ×n ₁ size; V _x (p), V _y (p), V _z (p) are the three directions of the image pair x, y, and z respectively The partial derivative; Calculate the eigenvalues E _x , E _y , E _z of this 3×3 tensor matrix, and set the threshold k is the control parameter, set to 0.01, the number of non-zero eigenvalues of point p M=su _t m(E _t >T _t ?1:0), t∈{x,y,z}, for the two graphs At the same position, record the number of non-zero eigenvalues of C _a as M _a , record the number of non-zero eigenvalues of C _b as M _b , and M _a and M _b are the approximation of the rank of the tensor matrix; 2.2.2. If M _a = M _b , then the two images have the same type of features at this position, and calculate the similarity at this position ${\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\underset{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>}{\underset{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$ Calculate threshold The fusion rules are: When γ _ab ≤ α, this position is redundant information, and the weighting criterion is selected: C _fH ＝ω _a C _aH +ω _b C _bH (4) ${\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}}{{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}}{{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}}$ ${\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; \&times;</span>\underset{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; b</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; \&times;</span>\underset{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; b</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; .</span>$ When γ _ab >α, this position is complementary information, using the MRE criterion: ${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; \&Greater\; Equal;</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}\mathrm{<span\; class="notranslate">\; h</span>}}\\ {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}\mathrm{<span\; class="notranslate">\; h</span>}}\end{array}\right.<span\; class="notranslate">\; ;</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$ ${\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}\sqrt{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; C</span>}}}_{\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; \&Element;</span><span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; ;</span>$ 2.2.3. If M _a ≠ M _b , fusion criterion: ${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; \&Greater\; Equal;</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}\\ {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$ 5. the feature level medical image fusion method based on 3D shearlet transform according to claim 1, is characterized in that, described step 3 is done backward shear transformation to the image after DWT or DTCWT inverse transformation, specifically as follows: For the backward shear transformation, it refers to the inverse operation of the forward shear transformation, where the shear transformation for the z direction refers to the following coordinate transformation of the points in the data: The shear transformation formula for the x direction is: The shear transformation formula for the y direction is: Among them, (x, y, z) are coordinates before transformation, and (x', y', z') are coordinates after transformation.