CN115018860A - Brain MRI (magnetic resonance imaging) registration method based on frequency domain and image domain characteristics - Google Patents

Brain MRI (magnetic resonance imaging) registration method based on frequency domain and image domain characteristics Download PDF

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CN115018860A
CN115018860A CN202210535477.4A CN202210535477A CN115018860A CN 115018860 A CN115018860 A CN 115018860A CN 202210535477 A CN202210535477 A CN 202210535477A CN 115018860 A CN115018860 A CN 115018860A
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杨铁军
白鑫昊
崔晓娟
苗建雨
张自豪
任笑真
樊超
张鑫
李磊
金军委
娄翠娟
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Henan University of Technology
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Abstract

The invention discloses a brain MRI (magnetic resonance imaging) registration method based on frequency domain and image domain characteristics, which is applied to the technical field of medical image processing and comprises the following steps: performing data preprocessing on the brain MRI dataset; randomly selecting a pair of images as a floating image and a fixed image, splicing and processing the images, and respectively utilizing wavelet transformation and a rotating window Transformer to perform feature extraction to obtain an optimal feature extraction image; decoding the optimal characteristic extraction image to obtain a registration deformation field; inputting the floating image and the registration deformation field into a space transformation network to obtain a registration image; similarity measurement is performed on the fixed image and the registered image, and boundary alignment and folding points in the registered deformation field are optimized. According to the method, the wavelet domain features and the image domain features of the image are extracted through two channels, the boundary alignment of the image anatomical region is promoted through structural similarity loss, a Jacobian inverse folding optimization regular term is added to a target function, and the registration accuracy and the registration authenticity are improved.

Description

Brain MRI (magnetic resonance imaging) registration method based on frequency domain and image domain characteristics
Technical Field
The invention relates to the technical field of medical image processing, in particular to a brain MRI (magnetic resonance imaging) registration method based on frequency domain and image domain characteristics.
Background
The brain is one of the most important organs of the human body, however, the mortality rate of the brain-related diseases is still high at present. The brain diseases have the characteristics of strong paroxysmal and high lethality rate. Magnetic Resonance Imaging (MRI) is a good noninvasive auxiliary diagnostic tool for soft tissue Imaging, and plays an important role in brain disease screening, diagnosis, treatment guidance and assessment. The information between the two images is fused with the brain magnetic resonance image after registration, more reliable information can be provided for doctors to judge the state of an illness, and the method plays an important role in the aspects of focus positioning, operation navigation, prognosis evaluation and the like. In clinical treatment, a physician typically uses a manual registration method to align two or more images of a patient at different times, angles, or even imaging principles. However, the way of manual registration is limited by the personal experience and status of the doctor, and the registration result varies from person to person. Moreover, the method consumes manpower and material resources, and wastes a large amount of medical resources. Therefore, clinical needs have prompted us to invent a fully automatic registration algorithm to replace the labor-consuming and time-consuming task performed manually. With the advent of Convolutional Neural Network (CNN) and the rapid development of computer hardware, deep learning-based medical image registration algorithms are gradually emerging and become the current focus of research. However, the brain image content is complex, so that the accuracy and the reality of the current brain image registration algorithm based on deep learning are difficult to meet the requirements of clinical application level.
Therefore, how to provide a brain MRI registration method based on frequency domain and image domain features, which can effectively improve the registration accuracy and authenticity, is a problem that needs to be solved by those skilled in the art.
Disclosure of Invention
In view of the above, the present invention provides a brain MRI registration method based on frequency domain and image domain features. Wavelet domain features and image domain features of the image are extracted through two channels, so that image features with higher distinguishing capability are obtained, and the registration accuracy of the network is improved; meanwhile, the registration accuracy of the network is improved by promoting the boundary alignment of the anatomical region of the image by using the structural similarity loss, and the reversible consistency of a deformation field is enhanced by adding a Jacobian inverse folding optimization regular term in the objective function, so that the authenticity of the registration result is improved.
In order to achieve the purpose, the invention adopts the following technical scheme:
a brain MRI registration method based on frequency domain and image domain features, comprising:
step (1): and acquiring a brain MRI data set, and performing data preprocessing on the brain MRI data set.
Step (2): randomly selecting a pair of images in the brain MRI dataset as a floating image and a fixed image, splicing and processing the images, and respectively extracting the characteristics by using wavelet transform and a rotating window Transformer to obtain an optimal characteristic extraction image.
And (3): and decoding the optimal characteristic extraction image to obtain a registration deformation field.
And (4): and inputting the floating image and the registration deformation field into a space transformation network to obtain a registration image.
And (5): similarity measurement is performed on the fixed image and the registered image, and boundary alignment and folding points in the registered deformation field are optimized.
And (6): and performing iterative training by using the registration network to obtain a network model of the optimal weight parameter.
And (7): and inputting the image to be registered to the network model with the optimal weight parameter to obtain a registration result.
Optionally, in step (1), the data preprocessing includes: skull removal processing, affine alignment, normalization, size clipping were performed using FreeScherfer.
Optionally, in step (2), a feature coding module with a dual-channel path is built, the floating image and the fixed image are spliced, and then the obtained images are input to a wavelet transform and a rotating window Transformer encoder respectively for down-sampling processing.
Optionally, in the step (2), the extracting the features by wavelet transform specifically includes:
the forward propagation network based on wavelet transform for each layer is defined as:
Figure BDA0003647914610000021
ψ s ＝UG s U T ；
Figure BDA0003647914610000022
wherein, G s Representing a signature signal; s is a scale coefficient describing different scales of the wavelet base signal; psi s Represents wavelet basis, and U represents a matrix formed by characteristic vectors of a Laplace matrix.
Figure BDA0003647914610000023
Is a diagonal matrix which represents the k layer convolution kernel for learning;
Figure BDA0003647914610000024
is represented by having f k N nodes of each channel. P is a feature vector
Figure BDA0003647914610000025
One dimension of (n) is n x p, q is a characteristic vector
Figure BDA0003647914610000026
N × q.
Optionally, in the step (2), the rotating window Transformer performs feature extraction specifically as follows:
the rotating window Transformer module is defined as follows:
Figure BDA0003647914610000027
Figure BDA0003647914610000028
Figure BDA0003647914610000029
Figure BDA00036479146100000210
where W-MSA denotes a window-based multi-headed attention module, MLP denotes a multi-layered perceptron, SM-WSA denotes a multi-headed attention module using regularization and rotation windows, x l-1 And
Figure BDA00036479146100000211
denotes the input and output characteristics of the W-MSA module and SM-WSA module, respectively, X l Representing the downsampled output characteristics and LN representing the slice normalization.
Optionally, in the step (3), a multi-scale information fusion decoding module is built, and features with strong distinguishing capability are extracted from the optimal feature map to obtain a registration deformation field.
Optionally, in the step (4), the floating image is transformed by applying tri-linear interpolation, and the floating image and the registration deformation field are input into a spatial transformation network to obtain a registration image; trilinear interpolation is defined as follows:
Figure BDA0003647914610000031
wherein, I M And
Figure BDA0003647914610000032
representing floating and registered images, respectively, x representing I M Y represents the voxels in the 8-pixel cube neighborhood x + phi (y), d e { i, j, k } represents the three dimensions of the image, phi represents the registration deformation field.
Optionally, in step (5), optimizing the boundary alignment by using a structural similarity loss in a similarity measure objective function; the folding points are optimized by using a smooth regularization term in the similarity measure objective function.
The similarity objective function is designed as:
Figure BDA0003647914610000033
wherein,
Figure BDA0003647914610000034
an objective function representing a measure of similarity is represented,
Figure BDA0003647914610000035
representing loss of structural similarity, is a fixed image I F And registering the images
Figure BDA0003647914610000036
A similarity measure between; λ represents the inverse-fold regularization term hyperparameter.
Fixed image I F And registering the images
Figure BDA0003647914610000037
The loss of structural similarity between is
Figure BDA0003647914610000038
The definition is as follows:
Figure BDA0003647914610000039
wherein, I F And
Figure BDA00036479146100000310
defined as a fixed image and a registered image, respectively;
Figure BDA00036479146100000311
representing an image I F The mean of the pixel intensities over a neighborhood of cube size n-11,
Figure BDA00036479146100000312
representing images
Figure BDA00036479146100000313
The mean of the pixel intensities over a neighborhood with cube size n-11;
Figure BDA00036479146100000314
representing a presentation image I F The variance of pixel intensity over a neighborhood with cube size n-11,
Figure BDA00036479146100000315
representing images
Figure BDA00036479146100000316
Pixel intensity variance over a neighborhood of cube size n-11;
Figure BDA00036479146100000317
is the covariance of two images in the neighborhood of cube size n-11A difference; c 1 ＝(K 1 L) 2 C 2 ＝(K 2 L) 2 Are two variables that are used to maintain the stability of the equation; l is the dynamic range of the pixel.
Smoothing regularization term
Figure BDA00036479146100000318
The definition is as follows:
Figure BDA00036479146100000319
Figure BDA00036479146100000320
Figure BDA0003647914610000041
Figure BDA0003647914610000042
wherein,
Figure BDA0003647914610000043
and
Figure BDA0003647914610000044
representing the first and second derivatives of the deformation field phi, respectively.
Optionally, in step (6), the registration network is subjected to iterative training, an Adam optimizer is used for optimization, a learning rate parameter is set to be 2e-4, the batch size is set to be 1, the training times are set to be 1000 cycles, each cycle is iterated for 100 times, and when a threshold of the training times is reached, the training is terminated.
Optionally, in the step (7), evaluating the registration result by using a coincidence degree coefficient;
the contact ratio coefficient is defined as follows:
Figure BDA0003647914610000045
m and W represent two images, respectively; the closer the degree of coincidence DSC is to 1, the more accurate the alignment of the anatomical structures of the images.
According to the technical scheme, compared with the prior art, the brain MRI registration method based on the frequency domain and image domain features, disclosed by the invention, has the advantages that the wavelet domain features and the image domain features of the images are extracted by using two channels, so that the image features with stronger distinguishing capability are obtained, and the registration accuracy of a network is improved; meanwhile, the registration accuracy of the network is improved by promoting the boundary alignment of the anatomical region of the image through the structural similarity loss, and the reversible consistency of a deformation field is enhanced by adding a Jacobi reverse folding optimization regular term in the objective function, so that the authenticity of the registration result is improved.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the provided drawings without creative efforts.
FIG. 1 is a schematic flow chart of the present invention.
Fig. 2 is a schematic structural diagram of the present invention.
FIG. 3 is a schematic diagram of a rotating window transform module according to the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention discloses a brain MRI registration method based on frequency domain and image domain characteristics, which comprises the following steps:
step (1): the method comprises the following steps of obtaining a brain MRI data set, and carrying out data preprocessing on the brain MRI data set, wherein the data preprocessing specifically comprises the following steps: skull removal processing and affine alignment to the same space using FreeScherfer; normalizing the obtained data so as to accelerate the convergence of the network; the data is clipped to the same size of 128 x 128 thereby reducing the network requirements on the computer hardware.
Step (2): the method comprises the following steps of building a feature coding module with a dual-path channel, randomly selecting a pair of images in a brain MRI data set as a floating image and a fixed image, splicing and processing the images, and respectively utilizing wavelet transformation and a rotating window Transformer to carry out feature extraction to obtain an optimal feature extraction image, wherein the method specifically comprises the following steps: building a feature coding module with a double-path channel, and respectively extracting multi-scale features of a frequency domain and an image domain in data; the encoding module splices a pair of floating images and fixed images with 16-fold dimensionality for the encoder to carry out four times of downsampling processing; after the data is input to the feature extraction network, the feature map size is down-sampled to 1/16 of the original size by the encoder of the wavelet transform and the rotating window transform, respectively.
The specific characteristic extraction of wavelet transform is as follows:
the forward propagation network based on wavelet transform for each layer is defined as:
Figure BDA0003647914610000051
ψ s ＝UG s U T ；
Figure BDA0003647914610000052
wherein G is s Representing a signature signal; s is a scale coefficient describing different scales of the wavelet base signal; psi s Representing wavelet basis, U representing LaplaceMatrix eigenvectors.
Figure BDA0003647914610000053
Is a diagonal matrix which represents the k layer convolution kernel for learning;
Figure BDA0003647914610000054
is represented by having f k N nodes of each channel. P is a feature vector
Figure BDA0003647914610000055
One dimension of (n) is n x p, q is a characteristic vector
Figure BDA0003647914610000056
N × q.
Because the wavelet transform has the characteristic of multi-scale, the signal can be decomposed into different frequency components, and therefore, the wavelet transform is used for extracting the characteristics of the image, and abundant global information can be provided for a network. Since the features after wavelet transform are sparse and the eigenvectors of the laplacian matrix are dense, the wavelet basis has higher sparsity and locality than the conventional fourier basis, and the wavelet transform has higher efficiency than the fourier transform.
In the image domain feature extraction process, a long-distance image feature downsampling module, namely a rotating window transform is built to replace a traditional convolution downsampling mode to extract long-distance feature dependence in data, and therefore global features in the data are extracted; the rotating window Transformer promotes the alignment of the network to the region of interest, and then improves the registration accuracy of the network.
The rotating window Transformer specifically comprises the following steps of:
the rotating window Transformer module is defined as follows:
Figure BDA0003647914610000057
Figure BDA0003647914610000058
Figure BDA0003647914610000059
Figure BDA0003647914610000061
where W-MSA denotes a window-based multi-headed attention module, MLP denotes a multi-layered perceptron, SM-WSA denotes a multi-headed attention module using regularization and rotation windows, x l-1 And
Figure BDA0003647914610000062
denotes the input and output characteristics of the W-MSA module and SM-WSA module, respectively, X l Representing the downsampled output characteristics and LN representing the slice normalization.
By using the two channels to extract the wavelet domain characteristics and the image domain characteristics of the image, the network can obtain richer characteristics, and the characteristic extraction capability of the network is improved.
And (3): and (4) building a multi-scale information fusion decoding module, and extracting the features with strong distinguishing capability from the optimal feature map to obtain a registration deformation field.
And (4): inputting the floating image and the registration deformation field into a space transformation network to obtain a registration image, which specifically comprises the following steps: transforming the floating image by using tri-linear interpolation, and inputting the floating image and the registration deformation field into a space transformation network to obtain a registration image; trilinear interpolation is defined as follows:
Figure BDA0003647914610000063
wherein, I M And
Figure BDA0003647914610000064
representing floating and registered images, respectively, x representing I M Body of (1)The pixel, y, represents the voxel in the 8-pixel cube neighborhood x + φ (y), d ∈ { i, j, k } represents the three dimensions of the image, φ represents the registration deformation field.
And (5): carrying out similarity measurement on the fixed image and the registered image, and optimizing boundary alignment and folding points in the registered deformation field; the method specifically comprises the following steps: the penalty of the boundary mismatch part in the image is increased by using the boundary loss in the similarity objective function, the attention of the network on the boundary is increased, the problem of boundary misalignment is focused, the attention of the boundary is increased, and the boundary alignment in the registration deformation field is optimized; the folding points are optimized by using a smooth regularization term in the similarity measure objective function.
The similarity objective function is designed as:
Figure BDA0003647914610000065
wherein,
Figure BDA0003647914610000066
an objective function representing a measure of similarity is represented,
Figure BDA0003647914610000067
representing loss of structural similarity, is a fixed image I F And registering the images
Figure BDA0003647914610000068
A similarity measure between; λ represents the inverse-fold regularization term hyperparameter.
Fixed image I F And registering the images
Figure BDA0003647914610000069
The loss of structural similarity between is
Figure BDA00036479146100000610
The definition is as follows:
Figure BDA00036479146100000611
wherein, I F And
Figure BDA00036479146100000612
defined as a fixed image and a registered image, respectively;
Figure BDA00036479146100000613
representing an image I F The mean of the pixel intensities over a neighborhood of cube size n-11,
Figure BDA00036479146100000614
representing images
Figure BDA00036479146100000615
Mean pixel intensity over a neighborhood of cube size n-11;
Figure BDA00036479146100000616
representing a presentation image I F The variance of pixel intensity over a neighborhood with cube size n-11,
Figure BDA0003647914610000071
representing images
Figure BDA0003647914610000072
Pixel intensity variance over a neighborhood with cube size n-11;
Figure BDA0003647914610000073
is the covariance of the two images on a neighborhood with a cube size n-11; c 1 ＝(K 1 L) 2 C 2 ＝(K 2 L) 2 Are two variables that are used to maintain the stability of the equation; l is the dynamic range of the pixel.
Use of
Figure BDA0003647914610000074
The smooth regular term is used for enhancing the reversible consistency of the deformation field, so that the registration node is improvedEffectiveness of the fruit, smoothing regularization term
Figure BDA0003647914610000075
The definition is as follows:
Figure BDA0003647914610000076
Figure BDA0003647914610000077
Figure BDA0003647914610000078
wherein,
Figure BDA0003647914610000079
and
Figure BDA00036479146100000710
the method respectively represents a first derivative and a second derivative of the deformation field phi, and promotes the reversible consistency of the registration network deformation field by designing an objective function with a reverse folding optimization regular term, thereby improving the authenticity of the registration result.
And (6): performing iterative training by using a registration network to obtain a network model of an optimal weight parameter, which specifically comprises the following steps: performing iterative training on the registration network, optimizing by using an Adam optimizer, setting a learning rate parameter to be 2e-4, setting the batch size to be 1, setting the training times to be 1000 cycles, performing iteration 100 times in each cycle, and terminating the training when a threshold value of the training times is reached.
And (7): inputting an image to be registered to a network model with optimal weight parameters to obtain a registration result, and evaluating the registration result by applying a contact ratio coefficient, wherein the method specifically comprises the following steps:
the contact ratio coefficient is defined as follows:
Figure BDA00036479146100000711
m and W represent two images, respectively; the closer the degree of coincidence DSC is to 1, the more accurate the alignment of the anatomical structures of the images.
The invention discloses a brain MRI registration method based on frequency domain and image domain characteristics. The method extracts the wavelet domain characteristics and the image domain characteristics of the image by using two channels, thereby obtaining the image characteristics with stronger distinguishing capability and helping to improve the registration accuracy of the network; meanwhile, the registration accuracy of the network is improved by promoting the boundary alignment of the anatomical region of the image by using the structural similarity loss, and the reversible consistency of a deformation field is enhanced by adding a Jacobian inverse folding optimization regular term in the objective function, so that the authenticity of the registration result is improved.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. The device disclosed by the embodiment corresponds to the method disclosed by the embodiment, so that the description is simple, and the relevant points can be referred to the method part for description.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (10)

1. A brain MRI registration method based on frequency domain and image domain features, comprising:
step (1): acquiring a brain MRI data set, and performing data preprocessing on the brain MRI data set;
step (2): randomly selecting a pair of images in the brain MRI dataset as a floating image and a fixed image, splicing and processing the images, and respectively extracting the characteristics by using wavelet transform and a rotating window Transformer to obtain an optimal characteristic extraction image;
and (3): decoding the optimal characteristic extraction image to obtain a registration deformation field;
and (4): inputting the floating image and the registration deformation field into a space transformation network to obtain a registration image;
and (5): performing similarity measurement on the fixed image and the registered image, and optimizing boundary alignment and folding points in the registered deformation field;
and (6): performing iterative training by using a registration network to obtain a network model of an optimal weight parameter;
and (7): and inputting the image to be registered to the network model of the optimal weight parameter to obtain a registration result.
2. The brain MRI registration method based on frequency domain and image domain features as claimed in claim 1, wherein in step (1), the data preprocessing is: skull removal processing, affine alignment, normalization, size clipping were performed using FreeScherfer.
3. The brain MRI registration method based on frequency domain and image domain features as claimed in claim 1, wherein in step (2), a feature encoding module with a dual channel path is built, the floating image and the fixed image are merged and then input to the encoders of the wavelet transform and the rotating window transform respectively for down-sampling.
4. The brain MRI registration method based on frequency domain and image domain features as claimed in claim 1, wherein in step (2), the wavelet transform is specifically characterized by:
the forward propagation network based on wavelet transform for each layer is defined as:
Figure FDA0003647914600000011
ψ s ＝UG s U T ；
Figure FDA0003647914600000012
wherein, G s Representing a signature signal; s is a scale coefficient describing different scales of the wavelet base signal; psi s Represents wavelet basis, and U represents a matrix formed by characteristic vectors of a Laplace matrix.
Figure FDA0003647914600000013
Is a diagonal matrix which represents the k layer convolution kernel for learning;
Figure FDA0003647914600000014
is represented by having f k N nodes of each channel. P is a feature vector
Figure FDA0003647914600000015
One dimension of (n) is n x p, q is a characteristic vector
Figure FDA0003647914600000016
Is n × q.
5. The brain MRI registration method based on frequency domain and image domain features as claimed in claim 1, wherein in step (2), the rotating window Transformer performs feature extraction specifically as follows:
the rotating window Transformer module is defined as follows:
Figure FDA0003647914600000021
Figure FDA0003647914600000022
Figure FDA0003647914600000023
Figure FDA0003647914600000024
where W-MSA denotes a window-based multi-headed attention module, MLP denotes a multi-layered perceptron, SM-WSA denotes a multi-headed attention module using regularization and rotation windows, x l-1 And
Figure FDA00036479146000000212
denote the input and output characteristics of the W-MSA module and SM-WSA module, respectively, X l Representing the downsampled output characteristics, LN represents the layer normalization.
6. The brain MRI registration method based on frequency domain and image domain features as claimed in claim 1, wherein in step (3), a multi-scale information fusion decoding module is built, and features with strong distinguishing capability are extracted from the optimal feature map to obtain the registration deformation field.
7. The brain MRI registration method based on frequency domain and image domain features as claimed in claim 1, wherein in step (4), the floating image is transformed by applying tri-linear interpolation, and the floating image and the registration deformation field are input into a spatial transform network to obtain a registration image; the trilinear interpolation is defined as follows:
Figure FDA0003647914600000025
wherein, I M And
Figure FDA00036479146000000216
representing floating and registered images, respectively, x representing I M Y represents the voxels in the 8-pixel cube neighborhood x + phi (y), d e { i, j, k } represents the three dimensions of the image, phi represents the registration deformation field.
8. The brain MRI registration method based on frequency domain and image domain features as claimed in claim 1, wherein in step (5), the boundary alignment is optimized by using the structural similarity loss in the similarity measure objective function; optimizing folding points by using a smooth regular term in a similarity measure target function;
the similarity objective function is designed as follows:
Figure FDA0003647914600000026
wherein,
Figure FDA0003647914600000027
an objective function representing a measure of similarity is represented,
Figure FDA0003647914600000028
representing loss of structural similarity, is a fixed image I F And registering the images
Figure FDA00036479146000000213
A similarity measure between; lambda represents the hyper-parameter of the anti-folding regularization term;
the fixed image I F And registering the images
Figure FDA00036479146000000214
The loss of structural similarity between is
Figure FDA0003647914600000029
The definition is as follows:
Figure FDA00036479146000000210
wherein, I F And
Figure FDA00036479146000000215
defined as a fixed image and a registered image, respectively;
Figure FDA00036479146000000211
representing an image I F The mean of the pixel intensities over a neighborhood of cube size n-11,
Figure FDA0003647914600000031
representing an image
Figure FDA00036479146000000312
The mean of the pixel intensities over a neighborhood with cube size n-11;
Figure FDA0003647914600000032
representing a presentation image I F The variance of pixel intensity over a neighborhood with cube size n-11,
Figure FDA0003647914600000033
representing images
Figure FDA00036479146000000313
Pixel intensity variance over a neighborhood with cube size n-11;
Figure FDA0003647914600000034
is the covariance of the two images on a neighborhood with a cube size n-11; c 1 ＝(K 1 L) 2 C 2 ＝(K 2 L) 2 Are two variables that are used to maintain the stability of the equation; l is the movement of the pixelA state range;
the smoothing regularization term
Figure FDA0003647914600000035
The definition is as follows:
Figure FDA0003647914600000036
Figure FDA0003647914600000037
Figure FDA0003647914600000038
wherein,
Figure FDA0003647914600000039
and
Figure FDA00036479146000000310
representing the first and second derivatives of the deformation field phi, respectively.
9. The brain MRI registration method based on frequency domain and image domain features as claimed in claim 1, wherein in step (6), the registration network is iteratively trained, optimized using an Adam optimizer, and the learning rate parameter is set to 2e-4, the batch size is set to 1, the number of training times is set to 1000 cycles, each cycle is iterated 100 times, and when the threshold of the number of training times is reached, the training is terminated.
10. The brain MRI registration method based on frequency domain and image domain features as claimed in claim 1, wherein in step (7), further comprising applying a coincidence degree coefficient to evaluate the registration result;
the contact ratio coefficient is defined as follows:
Figure FDA00036479146000000311
m and W represent two images, respectively; the closer the degree of coincidence DSC is to 1, the more accurate the alignment of the anatomical structures of the images.
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117853739A (en) * 2024-02-04 2024-04-09 耕宇牧星(北京)空间科技有限公司 Remote sensing image feature extraction model pre-training method and device based on feature transformation

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