CN109949307B - Image segmentation method based on principal component analysis - Google Patents
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- 238000000513 principal component analysis Methods 0.000 title claims abstract description 19
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- 238000003709 image segmentation Methods 0.000 title claims abstract description 10
- 230000003902 lesion Effects 0.000 claims abstract description 23
- 230000011218 segmentation Effects 0.000 claims abstract description 22
- 238000012549 training Methods 0.000 claims abstract description 16
- 239000011159 matrix material Substances 0.000 claims description 78
- 238000002595 magnetic resonance imaging Methods 0.000 claims description 24
- 239000013598 vector Substances 0.000 claims description 18
- 238000012360 testing method Methods 0.000 claims description 14
- 238000011156 evaluation Methods 0.000 claims description 8
- 238000004458 analytical method Methods 0.000 claims description 5
- 230000009466 transformation Effects 0.000 claims description 5
- 238000012935 Averaging Methods 0.000 claims description 3
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- 238000003745 diagnosis Methods 0.000 abstract description 2
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- 238000003384 imaging method Methods 0.000 description 1
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Abstract
The invention relates to an image segmentation method based on principal component analysis, and belongs to the technical field of biomedicine. The invention avoids inconsistent sketching results caused by subjectivity, experience deficiency and the like of doctors. The manual segmentation of lesions not only requires specialized anatomical knowledge, but also is very energy-intensive, and the segmentation with manual participation has subjectivity and has a certain influence on the segmentation result. The model which has completed the study through the training set can effectively liberate the hands of doctors, and the focus segmented by the model can provide visual diagnosis reference for the doctors, so that the focus does not need to be marked manually, and much energy and time are saved.
Description
Technical Field
The invention relates to an image segmentation method based on principal component analysis, and belongs to the technical field of biomedicine.
Background
Image segmentation is the division of an image into meaningful parts according to some uniformity (or consistency) principle, such that each part meets some consistency requirement, and the merging of any two adjacent parts breaks the consistency. The segmentation of an image can in many cases be attributed to classification problems of the pixels of the image.
In magnetic resonance imaging images, the boundaries of the intracranial tissues are extremely complex and irregular, which poses serious challenges to conventional segmentation algorithms. The manual segmentation of lesions not only requires specialized anatomical knowledge, but also is very energy-intensive, and the segmentation with manual participation has subjectivity and has a certain influence on the segmentation result.
Disclosure of Invention
The invention provides an image segmentation method based on principal component analysis, which is used for marking focus voxels and non-focus voxels in magnetic resonance imaging and obtaining segmented images of focus voxels only.
The technical scheme of the invention is as follows: a method of image segmentation based on principal component analysis, the method comprising the steps of:
s1, downloading a magnetic resonance imaging sequence data set, selecting a three-dimensional image containing focus voxels in the magnetic resonance imaging sequence data set to perform fault, obtaining a plurality of fault images containing focus voxels, forming a data set by the plurality of fault images containing focus voxels, and taking the data set containing focus voxels as a training set;
s2, voxels in a tomographic image containing focus voxels in the training set can be divided into focus voxels and non-focus voxels, the data dimension of the voxels is reduced by utilizing principal component analysis, and the focus and non-focus in the magnetic resonance imaging sequence data are classified by utilizing the distance measure as a classification basis;
s3, reading a group of unknown data from a magnetic resonance imaging sequence data set as a test group, classifying the test group image containing focus voxels by using a constructed classification model, dividing the voxels in the image into focus and non-focus according to a distance threshold, respectively marking focus voxels and non-focus voxels by using 1 and 0 to obtain a binarized image, and removing the voxels with the value of 0 to obtain a segmented image with focus voxels;
s4, reading in 'real data' corresponding to the data of the corresponding test group, namely, segmenting a magnetic resonance imaging image of an accurate focus voxel, analyzing a segmented image obtained through a model according to segmentation performance evaluation parameters, and storing an evaluation result into an Excel table for analysis.
The step S2 specifically includes the following steps:
1) Extracting a data matrix: for the images in a training set data set, extracting gray values of all focus and non-focus voxels and forming two corresponding vectors, which are marked as x and x'; because the whole training set data set contains N pictures, a non-focus voxel data matrix G with N x M dimensions can be obtained x And a focus voxel data matrix L x The method comprises the steps of carrying out a first treatment on the surface of the Where M is the number of focus voxels, here assuming that the number of focus voxels and the number of non-focus voxels are the sameM numbers are the same;
2) Data matrix centralization: before principal component analysis, the data matrix needs to be centered, and the data matrix G x And L x Respectively calculating column mean and column variance of each matrix, subtracting corresponding column mean from each data matrix, and dividing by corresponding column variance to obtain data matrix G x And L x Is at the origin position;
3) Principal component analysis dimension reduction: assuming a is a matrix of M x N, then a=uΣv is decomposed by singular values T Will get U, sigma, V T Three matrices; wherein U is a square matrix of M, and is a matrix composed of eigenvectors of the matrix A; Σ is a diagonal matrix of m×n, the elements on the diagonal of which are called eigenvalues; v (V) T The transpose of V is a matrix of N x N whose columns can be considered as a set of basis vectors representing the vector direction of the principal component; the feature vector corresponding to the largest feature value represents the data matrix G x 、L x The maximum covariance exists in the principal component direction, namely the maximum covariance exists in the projection of a low-dimensional coordinate system, and the feature vector corresponding to the feature value with the large front I term is reserved to approximately describe the matrix;
4) Data matrix basis conversion: to transform data matrix G x 、L x So that they have a lower dimension, the first 99% of the eigenvectors obtained can be used with the data matrix G x 、L x Multiplying; because of the data matrix G x ，L x The eigenvectors of (a) are not necessarily the same, the data matrix G x ，L x Performing a secondary transformation such that they are projected onto the same basis;
5) Classifying according to the distance: after obtaining the focus and non-focus data matrix under the condition of the same base, respectively calculating the distances from the value of the new data on the base to all values in the non-focus matrix and the focus matrix, averaging the two groups of distances, and observing which group has smaller average value: if the average value of the distances from the new data to the set of non-lesion matrices is smaller, classifying it as non-lesion; and vice versa classifies it as a lesion.
The beneficial effects of the invention are as follows: the invention avoids inconsistent sketching results caused by subjectivity, experience deficiency and the like of doctors. The manual segmentation of lesions not only requires specialized anatomical knowledge, but also is very energy-intensive, and the segmentation with manual participation has subjectivity and has a certain influence on the segmentation result. The model which has completed the study through the training set can effectively liberate the hands of doctors, and the focus segmented by the model can provide visual diagnosis reference for the doctors, so that the focus does not need to be marked manually, and much energy and time are saved.
Drawings
FIG. 1 is a general flow chart of the present invention;
FIG. 2 is a PD weight map, T1 weight map and T2 weight map of a 97 th slice in a magnetic resonance imaging image of a test set selected as test images;
FIG. 3 is a binarized segmented image of a set of unknown focus-containing voxels of the magnetic resonance imaging image obtained by a model;
fig. 4 is a "true data" image corresponding to a lesion image of a test group, the exact lesion location and size having been marked on the image.
Detailed Description
Example 1: as shown in fig. 1-4, a method for image segmentation based on principal component analysis, the method steps being as follows (flow chart is shown in fig. 1):
s1, downloading a magnetic resonance imaging sequence data set, selecting a three-dimensional image containing focus voxels in the magnetic resonance imaging sequence data set to perform fault, obtaining a plurality of fault images containing focus voxels, forming a data set by the plurality of fault images containing focus voxels, and taking the data set containing focus voxels as a training set;
s2, voxels in a tomographic image containing focus voxels in the training set can be divided into focus voxels and non-focus voxels, the data dimension of the voxels is reduced by utilizing principal component analysis, and the focus and non-focus in the magnetic resonance imaging sequence data are classified by utilizing the distance measure as a classification basis;
to classify a nuclear magnetic imaging image into a lesion and a non-lesion, the main idea is to measure which of the two classes of the lesion and the non-lesion has a smaller distance from new data by using a distance measure. However, direct subtraction of the gray values of the images takes into account redundant information of the high-dimensional data, and has a negative influence on the classification effect. To address this problem, principal component analysis may be utilized to reduce the data dimension of the data, thereby reducing redundant information of the data. The step S2 specifically includes the following steps:
1) Extracting a data matrix: for the images in a training set data set, extracting gray values of all focus and non-focus voxels and forming two corresponding vectors, which are marked as x and x'; because the whole training set data set contains N pictures, a non-focus voxel data matrix G with N x M dimensions can be obtained x And a focus voxel data matrix L x The method comprises the steps of carrying out a first treatment on the surface of the Wherein M is the number of focus voxels, and the number of focus voxels is assumed to be the same as the number of non-focus voxels, and M is all the number;
2) Data matrix centralization: before principal component analysis, the data matrix needs to be centered, and the data matrix G x And L x Respectively calculating column mean and column variance of each matrix, subtracting corresponding column mean from each data matrix, and dividing by corresponding column variance to obtain data matrix G x And L x Is at the origin position;
3) Principal component analysis dimension reduction: the purpose of the principal component analysis algorithm is to transform the data from high to low dimensions and to match the transformed data as much as possible with the original data. This is done because it is considered that voxel data points are high-dimensional data, often containing redundant information. If the classification is made directly using the distance of these data points to a lesion or non-lesion, it is likely that poor results will be obtained. In principle component analysis, it is common practice to find a low-dimensional coordinate system such that the projection distance of each data point in the raw data matrix to this coordinate system is minimized. This is equivalent to the maximum covariance of the projection of the raw data matrix in the low-dimensional coordinate system. This can be achieved generally by singular value decomposition. Let A be oneM x N, then a=uΣv by singular value decomposition T Will get U, sigma, V T Three matrices; wherein U is a square matrix of M, and is a matrix composed of eigenvectors of the matrix A; Σ is a diagonal matrix of m×n, the elements on the diagonal of which are called eigenvalues; v (V) T The transpose of V is a matrix of N x N whose columns can be considered as a set of basis vectors representing the vector direction of the principal component; the feature vector (principal component direction) corresponding to the largest feature value represents the data matrix G x 、L x There is a maximum covariance in this direction, i.e. the projection in the low-dimensional coordinate system, the eigenvalues are arranged from large to small in the matrix Σ and the decrease is particularly fast, and in many cases the sum of the first 10% or even 1% of the eigenvalues accounts for more than 99% of the sum of all eigenvalues. The matrix can be approximately described with respect to eigenvectors corresponding to eigenvalues that are large for the previous I term. In this experiment, the first 99% of feature vectors were retained.
4) Data matrix basis conversion: to transform data matrix G x 、L x So that they have a lower dimension, the first 99% of the eigenvectors obtained can be used with the data matrix G x 、L x Multiplication (this is the first transformation); however, because of the data matrix G x ，L x Not necessarily identical, they may be projected onto different new bases if transformed separately. In the case where the projected bases are different, comparison of distances cannot be performed; therefore, the data matrix G is required x ，L x Performing a secondary transformation (i.e., normalizing the variance of the eigenvectors in the first transformation to 1, finding a new eigenvector, multiplying the new eigenvector by a multiplication) so that they are projected onto the same basis;
5) Classifying according to the distance: after obtaining the focus and non-focus data matrix under the condition of the same base, respectively calculating the distances from the value of the new data on the base to all values in the non-focus matrix and the focus matrix, averaging the two groups of distances, and observing which group has smaller average value: if the average value of the distances from the new data to the set of non-lesion matrices is smaller, classifying it as non-lesion; and vice versa classifies it as a lesion.
S3, reading a group of unknown data from a magnetic resonance imaging sequence data set as a test group, classifying the test group image containing focus voxels by using a constructed classification model, dividing the voxels in the image into focus and non-focus according to a distance threshold, respectively marking focus voxels and non-focus voxels by using 1 and 0 to obtain a binarized image, and removing the voxels with the value of 0 to obtain a segmented image with focus voxels;
s4, reading in 'real data' corresponding to the data of the corresponding test group, namely, segmenting a magnetic resonance imaging image of an accurate focus voxel, analyzing the segmented image obtained through the model according to segmentation performance evaluation parameters such as a Dice similarity coefficient (Dice similarity coefficient, DSC), sensitivity (Sens), specificity (Spec) and accuracy (Acc), and storing an evaluation result in an Excel table for analysis. The calculation formula of these four parameters is as follows:
wherein TP is true positive (true positive), TN is true negative (true negative), FP is false positive (false positive), and FN is false negative (false negative).
The Dice similarity coefficient is a common similarity measure, and other performance evaluation parameters frequently matched with the Dice similarity coefficient are sensitivity, specificity and accuracy. Taking 97 faults as an example, the calculated performance parameters are as follows:
DSC＝0.7746，Sens＝0.8221，Spec＝0.9987，Acc＝0.9980
among them, DSC is an index most commonly used for evaluating a lesion segmentation method, and it reflects more the segmentation result and the difference in the position of the true lesion, and its value may be from 0 to 1.DSC equal to 0 indicates that the two parts are not overlapped, and DSC equal to 1 indicates that the two parts are completely matched, and the result is better when the DSC is more than or equal to 0.7. Sens is 0.8221, which indicates that the lesion segmentation result can reach about 82%. From the calculation formulas of the parameters Spec and Acc, since TN (true negative) therein relates to a broad area of varying size, the values of Spec and Acc are prone to optimistic and have little significance as image segmentation performance parameters. Although both Spec and Acc calculated values are greater than 0.99, there is not much reference value for performance evaluation.
According to experimental results, the main component analysis has a certain feasibility when applied to focus segmentation, and although the segmentation effect of the method applied to clinical medical images is not as good as that of a simulation image, the segmentation result can reach an ideal state on the basis of adding training data and improving an algorithm.
The data of the model constructed by the invention adopts simulated human craniocerebral magnetic resonance imaging (Magnetic Resonance Imaging, MRI) sequence data from BrainWeb (http:// brainWeb. Bic. Mni. Mcgill. Ca/brainWeb /). The brain web database is a simulated brain database (Simulated brain database, SBD) established by the university of montreal neuroscience study, canada, and aims to provide a solution platform for computing biologically generated data obtained consistently in vitro. The magnetic resonance imaging modes have Proton Density (PD) weighting, T1 weighting and T2 weighting. The data containing focus images in the magnetic resonance imaging sequence data set is used as a training set to enable a model to learn, and the purpose is to find the relevance of focuses and non-focuses in the images in terms of feature vectors. The "learned" model is used to image segment the test set data in the unknown magnetic resonance imaging sequence dataset. The segmentation results of the test group are compared with corresponding "real data" (i.e., gold standard images) provided by the brain web site, and four performance parameters, namely, dice similarity coefficient (Dice similarity coefficient, DSC), sensitivity (Sens), specificity (Spec), and accuracy (Acc), are calculated to evaluate the performance of the segmentation algorithm.
While the present invention has been described in detail with reference to the drawings, the present invention is not limited to the above embodiments, and various changes can be made without departing from the spirit of the present invention within the knowledge of those skilled in the art.
Claims (1)
1. A method of image segmentation based on principal component analysis, characterized by: the method comprises the following steps:
s1, downloading a magnetic resonance imaging sequence data set, selecting a three-dimensional image containing focus voxels in the magnetic resonance imaging sequence data set to perform fault, obtaining a plurality of fault images containing focus voxels, forming a data set by the plurality of fault images containing focus voxels, and taking the data set containing focus voxels as a training set;
s2, voxels in a tomographic image containing focus voxels in the training set can be divided into focus voxels and non-focus voxels, the data dimension of the voxels is reduced by utilizing principal component analysis, and the focus and non-focus in the magnetic resonance imaging sequence data are classified by utilizing the distance measure as a classification basis;
s3, reading a group of unknown data from a magnetic resonance imaging sequence data set as a test group, classifying the test group image containing focus voxels by using a constructed classification model, dividing the voxels in the image into focus and non-focus according to a distance threshold, respectively marking focus voxels and non-focus voxels by using 1 and 0 to obtain a binarized image, and removing the voxels with the value of 0 to obtain a segmented image with focus voxels;
s4, reading in a gold standard image corresponding to the real data of the corresponding test group data, namely, a magnetic resonance imaging image of the segmented accurate focus voxels, analyzing the segmented image obtained by the model according to the segmentation performance evaluation parameters, and storing the evaluation result into an Excel table for analysis;
the step S2 specifically includes the following steps:
1) Extracting a data matrix: for the images in a training set data set, extracting gray values of all focus and non-focus voxels and forming two corresponding vectors, which are marked as x and x'; because the whole training set data set contains N pictures, a non-focus voxel data matrix G with N x M dimensions can be obtained x And a focus voxel data matrix L x The method comprises the steps of carrying out a first treatment on the surface of the Wherein M is the number of focus voxels, and the number of focus voxels is assumed to be the same as the number of non-focus voxels, and M is all the number;
2) Data matrix centralization: before principal component analysis, the data matrix needs to be centered, and the data matrix G x And L x Respectively calculating column mean and column variance of each matrix, subtracting corresponding column mean from each data matrix, and dividing by corresponding column variance to obtain data matrix G x And L x Is at the origin position;
3) Principal component analysis dimension reduction: assuming a is a matrix of M x N, then a=uΣv is decomposed by singular values T Will get U, sigma, V T Three matrices; wherein U is a square matrix of M, and is a matrix composed of eigenvectors of the matrix A; Σ is a diagonal matrix of m×n, the elements on the diagonal of which are called eigenvalues; v (V) T The transpose of V is a matrix of N x N whose columns can be considered as a set of basis vectors representing the vector direction of the principal component; the feature vector corresponding to the largest feature value represents the data matrix G x 、L x The maximum covariance exists in the principal component direction, namely the maximum covariance exists in the projection of a low-dimensional coordinate system, and the feature vector corresponding to the feature value with the large front I term is reserved to approximately describe the matrix; wherein I represents the total number of terms of the feature vector corresponding to the feature value reserved for approximating the description matrix;
4) Data matrix basis conversion: to transform data matrix G x 、L x Is such that itHaving a lower dimension, can utilize the first 99% of the feature vectors obtained and the data matrix G x 、L x Multiplying; because of the data matrix G x ，L x The eigenvectors of (a) are not necessarily the same, the data matrix G x ，L x Performing a secondary transformation such that they are projected onto the same basis;
5) Classifying according to the distance: after obtaining the focus and non-focus data matrix under the condition of the same base, respectively calculating the distances from the value of the new data on the base to all values in the non-focus matrix and the focus matrix, averaging the two groups of distances, and observing which group has smaller average value: if the average value of the distances from the new data to the set of non-lesion matrices is smaller, classifying it as non-lesion; and vice versa classifies it as a lesion.
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