CN106023194B - Amygdaloid nucleus spectral clustering dividing method based on tranquillization state function connects - Google Patents

Amygdaloid nucleus spectral clustering dividing method based on tranquillization state function connects Download PDF

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CN106023194B
CN106023194B CN201610330265.7A CN201610330265A CN106023194B CN 106023194 B CN106023194 B CN 106023194B CN 201610330265 A CN201610330265 A CN 201610330265A CN 106023194 B CN106023194 B CN 106023194B
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CN106023194A (en
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林盘
窦顺阳
王刚
王雪丽
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Xian Jiaotong University
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Abstract

A kind of amygdaloid nucleus spectral clustering dividing method based on tranquillization state functional imaging, it is a kind of method that automatic high-efficiency rate is carried out to the brain area according to the similitude of amygdaloid nucleus voxel of object function based on spectral clustering, first tranquillization state MR data is pre-processed, amygdaloid nucleus brain area is extracted again, then the full brain function connection of amygdaloid nucleus voxel of object calculates and finally divides to function connects matrix spectral clustering, automatic segmentation algorithm proposed by the present invention and amygdaloid nucleus Clinical anatomic result obtain significantly consistency, and relatively satisfactory result is also obtained in terms of stability and anti-noise jamming, relative to traditional manual dividing method, it is simpler, it is convenient, efficiently, the high various advantages of repeatability.

Description

Amygdaloid nucleus spectral clustering dividing method based on tranquillization state function connects
Technical field
The invention belongs to field of image processings, and in particular to a kind of amygdaloid nucleus spectral clustering based on tranquillization state function connects point Segmentation method, more particularly to almond nucleon is carried out based on the full brain connection mode similitude of each voxel of amygdaloid nucleus using spectral clustering The method of brain area automatic segmentation.
Background technique
FMRI is one of research cerebration, the main non-invasive methods of brain function, has millimetre-sized spatial resolution. The it is proposed and development of BOLD-fMRI method have breakthrough progress to the research of brain cognitive function, it has become Neuscience Explore the important tool of human brain neuromechanism.Refer to as fMRI-and is based on Blood oxygen level dependence (blood oxygen level- Dependent, BOLD) magnetic resonance imaging, it by measurement the ingredients such as the brain blood flow as caused by nervous activity and brain blood oxygen become Change and caused by magnetic resonance signal variation to react cerebration.
Amygdaloid nucleus are the brain areas of core the most in human emotion's memory network, it sentences in the generation and expression of mood, society Important role is played in the cognitive activities such as disconnected and facial recognition.The exception of amygdaloid nucleus structure and function can cause autism, The mental diseases such as depression, parkinsonism, it has become the hot spot of Neuropathological Study, but at present both at home and abroad, amygdaloid nucleus The Study on thinning of internal structure and function is relatively fewer, and how quick exact automatic, which divides amygdaloid nucleus brain area, has shown It obtains particularly important.Human brain is the five-star part of central nervous system, it is made of 14,000,000,000 nerve cells with height Systematical organ, and the cell group activity with identity function have great consistency, equally, inside amygdaloid nucleus, Nucleus with the same function rolls into a ball its function also and can embody consistency in a way.Research shows that brain when tranquillization state Low-frequency fluctuation BOLD signal (0.01~0.1Hz) in Different brain region is relevant, motor area, vision, language area, auditory sensation area The correlation of low frequency amplitude fluctuation is proved that these relevant low-frequency fluctuations constitute tranquillization state function connects network in succession, and Tranquillization state function connects network between different crowd is consistent.In amygdaloid nucleus, nucleus group with the same function is quiet Breath state function also has the similitude of height.Based on such theoretical basis present invention by tranquillization state functional imaging according to specific The similitude of the function connects mode of each full brain of voxel is split amygdaloid nucleus brain area with spectral clustering in brain area, and trial is deeply ground Study carefully the function inside amygdaloid nucleus, fully understands the mechanism of action of amygdaloid nucleus to provide strategy for the prevention and treatment of clinically related disease.
Currently, amygdaloid nucleus are split mainly by there is the clinician on certain medical anatomy basis according to amygdaloid nucleus brain area The feature of nucleus unity structure manually divides amygdaloid nucleus brain area.On the one hand such dividing method has very researcher High medical anatomy context request, another aspect inefficiency, time-consuming, is unfavorable for promoting.
Summary of the invention
The inefficiency of brain area division is carried out manually based on structure feature is rolled into a ball according to amygdaloid nucleus nucleus and time-consuming, by The status that subjective factor is affected, it is an object of the invention to propose that a kind of almond nuclear spectrum based on tranquillization state function connects is poly- Class dividing method can be stablized, efficiently and accurately carry out automatic segmentation to human brain almond core region.
In order to achieve the above object, the technical solution of the present invention is as follows:
Amygdaloid nucleus spectral clustering dividing method based on tranquillization state function connects, the specific steps are as follows:
(1), tranquillization state magnetic resonance data acquisition is carried out to subject, and the data of acquisition is pre-processed, pretreatment is Refer to the signal-to-noise ratio for improving Brain mapping picture, and while retaining image data details, makes to be tested image and standard form carries out Affine registration transformation;
(2), subject amygdaloid nucleus brain area is extracted, pretreated tranquillization state functional MRI is registrated to MNI standard Cortex and infracortical grey matter are divided into 90 using AAL (automated anatomical labeling) template by space Brain area, left and right amygdaloid nucleus respectively correspond as No. 41 brain areas and No. 42 brain areas, and amygdaloid nucleus ROI is equally registrated to the space MNI, thus Extract subject amygdaloid nucleus brain area;
(3), it by calculating the full brain connection mode of each voxel in amygdaloid nucleus, and then obtains complete between every two voxel Brain connection mode similarity matrix extracts the time series signal of each voxel of amygdaloid nucleus;To the tranquillization state of other 88 brain areas Signal is extracted by the way of voxel signal averagings all in brain area;Secondly, by calculating the voxel letter inside each amygdaloid nucleus Related coefficient number between the signal of other 88 brain areas, obtains the full brain connection matrix M of amygdaloid nucleus voxel, wherein element (i, j) indicates i-th of amygdaloid nucleus voxel to the function connects intensity of j-th of brain area, and every a line of the matrix describes an apricot Benevolence nucleome element is in the connection mode under tranquillization state between complete other brain areas of brain, and for value closer to 1, correlation is bigger;Then it calculates Related coefficient between every two rows connection mode can measure similarity of two voxels on full brain function connection mode, note For similarity matrix N, wherein each i-th of voxel of element representation amygdaloid nucleus is to j-th of voxel on full brain function connection mode Similarity;
(4), cluster segmentation is carried out to full brain connection mode similarity matrix N obtained in step 3 with spectral clustering, realized The sub-district regional partition of amygdaloid nucleus.
Step (4) specifically:
(1) sample point x is enabled1,x2,…,xnThe function connects vector for indicating the every row of N being arbitrarily clustered, enables sijIndicate structure It makes the connection weight between two vertex of figure, the weight between vertex is defined with Gauss similarity function, wherein parameter σ is known as ruler Parameter is spent, wherein sijIt is defined as
sij=exp (- | | xi-xj||2/2σ2)
Then the similarity matrix of sample is S=(sij) (i, j=1,2 ..., n);
(2) it inputs: similarity matrix S ∈ Rn×n, cluster classification number k;The similarity join figure for establishing sample, enables W weigh for it Value matrix;
(3) non-standardization Laplacian Matrix L is calculated, each column element of W is added up to obtain N number of number, they are put On the diagonal, all it is zero elsewhere, forms the matrix of a N*N, is denoted as D, and enable L=D-W;First k for calculating L is minimum Characteristic value corresponding to feature vector v1,v2,…vk
(4) V ∈ R is enabledn×kFor v1,v2,…vkThe matrix composed by being arranged by column;
(5) y is enabled for i=1,2 ..., ni∈RkFor the i-th column of matrix V;
(6) space R will be belonged to using k mean algorithmkData yi(i=1,2 ..., n) is polymerized to k class, as C1,…Ck, Just the cluster for completing each pixel of amygdaloid nucleus realizes the sub-district regional partition of amygdaloid nucleus.
The innovation of the invention consists in that: with the comparison of amygdaloid nucleus anatomical atlas it can be found that proposed by the present invention be based on tranquillization state The amygdaloid nucleus spectral clustering automatic segmentation algorithm and amygdaloid nucleus Clinical anatomic result of function connects obtain significantly consistency, separately One side quantitative assessment segmentation result shows anatomical atlas of the present invention and physiology map have 70% or more similarity, and Also relatively satisfactory as a result, relative to traditional manual dividing method, simpler, side is obtained in terms of stability and anti-noise jamming Just, efficient, the high various advantages of repeatability.
Detailed description of the invention
Fig. 1 is flow chart of the invention.
Fig. 2 is tranquillization state function image pretreatment process figure.
Fig. 3 is head segmentation front and back comparison diagram.
Fig. 4 is the dynamic correction result of head.
Fig. 5 is the front and back comparison of function picture registration, and left side is function picture before being registrated, and centre is MNI152 standard form, right side For function picture after registration, reduce by the difference between registration image and template.
Fig. 6 is amygdaloid nucleus physiology anatomical atlas and method proposed by the present invention to amygdaloid nucleus segmentation result comparison diagram.
Fig. 7 is spectral clustering segmentation amygdaloid nucleus result and juiche map Duplication statistical chart.
Fig. 8 is that amygdaloid nucleus segmentation result and brain map spatial simlanty compare on the left of 30 subjects.
Fig. 9 is that amygdaloid nucleus segmentation result and brain map spatial simlanty compare on the right side of 30 subjects.
Figure 10 is amygdaloid nucleus segmentation result stability contrast under different signal-to-noise ratio.
Specific embodiment
The invention will now be described in detail with reference to the accompanying drawings.
The present invention is based on tranquillization state function connects progress amygdaloid nucleus brain area dividing method principle is as shown in Figure 1.
(1), the original tranquillization state MR data of acquisition is pre-processed first, due to each in magnetic resonance scan sequences The influence of the noise of kind various kinds, for individual itself there are the difference on scale and position, it is right before analyzing data to be highly desirable Data do certain pretreatment.In the data acquisition of entire experiment, main noise information source includes: (1) physical header It is dynamic;(2) interlayer sweep time difference in image;(3) inhomogeneities of exterior magnetic field.Brain function image preprocessing is to retain brain While function image details, the pretreatment of affine registration mapping mode is carried out using Brain mapping picture and standard form, and mention The signal-to-noise ratio of high Brain mapping picture.
The original tranquillization state MR data of acquisition is pre-processed, with fMRI data prediction, in linux system It is completed under Ubuntu14.04 based on AFNI and FSL software programming Batch file (data batch processing).Pretreatment process is shown in Fig. 2, Mainly include the following aspects:
1) structure is as head segmentation
The structure picture collected generally comprises head information, needs to carry out head segmentation, draws to eliminate skull position Influence of the artifact entered to subsequent data analysis.3drefit, 3dresample and the fast provided based on FSL software Segment realizes the segmentation of head skull and brain internal organizational structure, and segmentation result is as shown in Figure 3.
2) time unifying
Hemodynamics function shows that blood has regular hour delay to the response of stimulation, due to acquiring during a TR To full brain image, this causes each layer of image not to acquire in synchronization, but occurs in entire sweep time section, when Between correction be exactly by be similar to interpolation method to each tomographic image progress layer time-triggered protocol so that each layer in a TR period Image approximate is obtained in synchronization.
3) the dynamic correction of head
It carries out the dynamic timing of head and generally regards the brain of subject as a rigid body, therefore be tested head in fMRI experiment Movement can be similar to a kind of rigid motion, i.e. the only combination of translation transformation and rotation transformation.Select the first of single-subject Frame image is registrated remaining all image with reference picture as reference picture, by the 3dvolreg function of AFNI, knot Fruit is as shown in Figure 4.The subject is removed if head moves more than one voxel.
4) space smoothing
Space smoothing carries out Gaussian smoothing using Gaussian function, can effectively slacken random noise to the shadow of fMRI signal It rings, improves the signal-to-noise ratio of data.Three-dimensional Gaussian function is more commonly used spatial smoothing method, and full width at half maximum determines space Smooth dynamics, selecting full width at half maximum (Full Width at Half Maximum, FWHM) herein is the gaussian kernel function of 6mm Carry out data smoothing.
5) time domain bandpass filtering
Tranquillization state fMRI signal is a kind of low-frequency fluctuation, and frequency is concentrated mainly on 0.01~0.1Hz, and this low-frequency fluctuation is anti- Spontaneous nervous activity is reflected.Therefore use frequency range for the removal of the bandpass filter of 0.01~0.1Hz and breathing, heartbeat etc. Related physiological noise.
6) it goes linear
Due to the long-term work of machine cause temperature increase or subject it is inadaptable, as the accumulation of time can have line Property drift, carry out linear.
7) image segmentation
In order to remove the redundancies such as cerebrospinal fluid (Cerebro-Spinal Fluid, CSF), white matter (White Matter, WM) Signal needs to be split structure picture, the information production cerebrospinal fluid and white matter template obtained using segmentation;
8) redundancy removal
It removes white matter, cerebrospinal fluid, full brain signal and head and moves the redundant signals such as artefact.
(2), subject amygdaloid nucleus brain area is extracted in the space standard MNI.It, first will be quiet in order to which amygdaloid nucleus brain area is accurately positioned Breath state magnetic resonance image is registrated to MNI normed space;To improve registration accuracy, it is registrated using two steps: is first registrated function picture To structure picture, structure picture is secondly registrated to normed space, so that function picture is registrated to mark using obtained transformation matrix Quasi- space and by voxel resampling be 3mm × 3mm × 3mm;It is registrated template and uses MNI template, which is to cover spy by Canada Lear Neuroscience Research institute (Montreal Neurological Institute, MNI) researches and develops;Entire registration process It is realized using the linear registration tools that FMRIB is provided, registration front and back image comparison is as shown in Figure 5;AAL(automated Anatomical labeling) cortex and infracortical grey matter be divided into 90 brain areas by template, and left and right amygdaloid nucleus respectively correspond For No. 41 brain areas and No. 42 brain areas, No. 41 brain areas and No. 42 brain areas are equally registrated to the space standard MNI, it can as template Target brain area as our further progress segmentations.
3, apricot can be obtained on the basis of having obtained the position of tranquillization state functional MRI data amygdaloid nucleus by step 2 On the other hand the time series of benevolence vouching voxel calculates other 88 brains in AAL template other than left and right sides amygdaloid nucleus Area's average time sequence, then the related coefficient of each voxel of amygdaloid nucleus Yu this 88 each brain area average time sequence is acquired, obtain apricot The full brain connection matrix M of benevolence nucleome element, wherein element (i, j) indicate i-th of amygdaloid nucleus voxel to j-th of brain area function connects Intensity;Every a line of the matrix describes an amygdaloid nucleus voxel in the connection mould under tranquillization state between complete other brain areas of brain Formula, for value closer to 1, correlation is bigger;The entirely reading of tranquillization state magnetic resonance image data, the extraction and correlation of time series Calculating is based on the realization of 2.7 language of python, this algorithm scientific algorithm part mainly uses Numpy (Numeric Python) Module realizes that NumPy is the calculating packet an of basic science, it provides many advanced numerical value programming tools, such as: matrix function According to type, vector processing, and accurate operation library, aims at and carry out stringent digital processing and generate;To MR data It reads and writees, relies on NiBabel module, NiBabel provides the interface read to common medical image data format.
4, cluster segmentation is carried out to full brain connection mode matrix N obtained in step 3 with spectral clustering, specifically:
(1) sample point x is enabled1,x2,…,xnThe function connects vector for indicating the every row of N being arbitrarily clustered, enables sijIndicate structure It makes the connection weight between two vertex of figure, the weight between vertex is defined with Gauss similarity function, wherein parameter σ is known as ruler Parameter is spent, wherein sijIt is defined as
sij=exp (- | | xi-xj||2/2σ2)
Then the similarity matrix of sample is S=(sij) (i, j=1,2 ..., n);
(2) it inputs: similarity matrix S ∈ Rn×n, cluster classification number k;The similarity join figure for establishing sample, enables W weigh for it Value matrix;
(3) non-standardization Laplacian Matrix L is calculated, each column element of W is added up to obtain N number of number, they are put On the diagonal, all it is zero elsewhere, forms the matrix of a N*N, is denoted as D, and enable L=D-W;First k for calculating L is minimum Characteristic value corresponding to feature vector v1,v2,…vk
(4) V ∈ R is enabledn×kFor v1,v2,…vkThe matrix composed by being arranged by column;
(5) y is enabled for i=1,2 ..., ni∈RkFor the i-th column of matrix V;
(6) space R will be belonged to using k mean algorithmkData yi(i=1,2 ..., n) is polymerized to k class, as C1,…Ck, Just the cluster for completing each pixel of amygdaloid nucleus realizes the sub-district regional partition of amygdaloid nucleus.
The experimental result that amygdaloid nucleus dividing method with regard to proposed by the present invention based on tranquillization state function connects obtains below with Amygdaloid nucleus clinical physiological anatomical atlas compares, and certain spy is done to the stability of this method, anti-noise jamming etc. It begs for.
According to Amunts et al. in the research based on architecture cytoarchitectonic in 05 year, julich map calculates and constructs these almonds The probability template of core subprovince.Amygdaloid nucleus are divided into three sub-regions, respectively Basolateral Nucleus (the by the map Laterobasal, LB), superficial core (the superficial, SF) and medial central nucleus (the centromedial, CM), Respectively correspond blue on the left of Fig. 6, green and red brain area.LB includes secondary stratiform core, bottom inside core, Basolateral Nucleus and outside Core, CM are made of inside core and central nucleus, SF include amygdaloid nucleus pear cortex transitional areas, anterior amygdaloid area, amygdaloid nucleus-hippocampus with And veutro and rear side cortex core.Julich map shows the spatial relation of amygdaloid nucleus subregion in Fig. 6, and the right side Fig. 6 is then Connect for the present invention is based on amygdaloid nucleus voxel of object with other each brain zone functions carry out spectral clustering to amygdaloid nucleus divide as a result, two Person, which compares, can find that cluster result and map of the invention have high consistency, show the feasibility of this method.
On the other hand, for further quantitative assessment segmentation result, the present invention repeats the tranquillization state function being tested to 30 Image data carries out the segmentation of amygdaloid nucleus brain area, inquires into from two angles of accuracy and stability of algorithm to it.
Karr Pearson came proposes Pearson came linearly dependent coefficient based on the algorithm of Mark Lewis-Francis Galton, usually should Related coefficient is also referred to as " Pearson correlation coefficients ".Correlation coefficient ρ investigates the degree of correlation of two variables, and value range is -1 Between~1, wherein 1 indicates variable perfect positive correlation, and 0 indicates unrelated, and -1 indicates perfect negative correlation.
In formula: ρ (X, Y) --- the related coefficient of variable X and Y;Cov (X, Y) --- the covariance of variable X and Y;σX—— The standard variance of variable X;σY--- the standard variance of variable Y;μX--- the mean value of variable X;μY--- the mean value of variable Y.
We see size m × n × o 3-D image to be measured and reference picture B as stochastic variable, then two images it Between related coefficient be
A indicates that 3-D image to be evaluated, B indicate reference picture, A in formulai,j,kIndicate the pixel in testing image, Bi,j,kIndicate the pixel in reference picture,Indicate the mean value of image A,Indicating the mean value of image B, m indicates picturedeep, N indicates that the columns of image, o indicate picture altitude.The related coefficient of image A and image B are smaller (closer to 0), illustrate image A and The similarity of image B is smaller;Related coefficient is bigger (closer to 1), illustrates that the similarity of image A and B are bigger.It calculates of the invention Cluster group analysis result respectively amygdaloid nucleus subregion corresponding with julich map Pearson correlation coefficients as shown in fig. 7, knot Fruit both indicates that spatial distribution is more similar closer to 1, and right side CM subprovince segmentation result and map are closest to (CC=as seen from the figure 0.78), the subprovince right side SF is lower with respect to spectrogram similarity (CC=0.65).
The group analysis result of the segmentation result and the data set of each subject amygdaloid nucleus subprovince is carried out space phase by the present invention It closes, the stabilization of this paper partitioning algorithm is reflected with the variation severe degree of all subregion and the space overlap rate of group analysis result Property, Fig. 8 and Fig. 9 describe the overlapping cases of left and right side amygdaloid nucleus sub-district single-subject and group analysis result, pass through calculating The variance of right side CM space correlation coefficient is 0.0303 maximum, shows that the result stability of subprovince segmentation is weaker, and right side The variance of LB brain area space correlation coefficient is 0.0017 minimum, so the segmentation result repeatability of this brain area clustering algorithm is most Height, stability are preferably also that (variance of other brain areas is respectively var (CML)=0.0041, var (LBL)=0.0185, var (SFR)=0.0098, var (SFL)=0.0194)
On the basis of discussing the accuracy and stability of partitioning algorithm, the noise of varying strength is superimposed to almond nucleome Brain area is carried out in the time series of element again to divide to investigate the robustness of inventive algorithm.First by each body of amygdaloid nucleus or so brain area The time series of element extracts, and is respectively 10db, 30db, 50db, the Gauss white noise of 70db, 90db by calculating signal-to-noise ratio Sound is added to carries out the amygdaloid nucleus subprovince partitioning algorithm shown in FIG. 1 based on the basis of spectral clustering again in each time series, entirely Simulation process is tested to realize in 2.7 platform of python.
The cluster segmentation of 6 subprovinces of amygdaloid nucleus is as shown in Figure 10 after superimposed noise, wherein (A) figure reflects under different noises The function connects matrix calculated based on ROI voxel time series and remaining 88 brain area mean sequence of ALL template is split knot Fruit and that noise is not added in the case where each sub-district spatial simlanty situation of change, the image data of different signal-to-noise ratio as seen from the figure Achieve satisfied segmentation result, signal-to-noise ratio be greater than 70db in the case where, each sub-district all maintain almost with do not have The similitude of the result 100% of noise is added, is also able to maintain 0.7 left side in the area the low signal-to-noise ratio Xia Ge Pearson correlation coefficients of 10db It is right.
In conclusion present invention aims at propose a kind of can stablize based on tranquillization state functional mri, high Effect, accurately automation human brain amygdaloid nucleus region segmentation method, for the clinically moods related psychiatric conditions such as depression, autism It is further research and prevention and treatment provide strategy.

Claims (2)

1. the amygdaloid nucleus spectral clustering dividing method based on tranquillization state function connects, which is characterized in that specific step is as follows:
(1), the acquisition of tranquillization state magnetic resonance image data is carried out to subject, and carries out magnetic resonance image data pretreatment, magnetic resonance Pre-processing image data, in order to which amygdaloid nucleus brain area is accurately positioned, is first total to tranquillization state magnetic while retaining image detail Image registration of shaking is registrated using two steps to improve registration accuracy to MNI normed space: function picture being registrated to structure picture first, Secondly structure picture is registrated to normed space, the pre- place of affine registration mapping mode is carried out using Brain mapping picture and standard form The mode of reason, and improve the signal-to-noise ratio of Brain mapping picture;
(2), subject amygdaloid nucleus brain area is extracted, cortex and infracortical grey matter are divided by 90 brain areas using AAL template, left and right Amygdaloid nucleus respectively correspond as No. 41 brain areas and No. 42 brain areas, and amygdaloid nucleus ROI is equally registrated to the space MNI, thus extract by Try amygdaloid nucleus brain area;
(3), by calculating the full brain connection mode of each voxel in amygdaloid nucleus, and then the company of the full brain between every two voxel is obtained Pattern similarity matrix is connect, the time series signal of each voxel of amygdaloid nucleus is extracted;To the tranquillization state signal of other 88 brain areas It is extracted by the way of voxel signal averagings all in brain area;Secondly, by calculate the voxel signal inside each amygdaloid nucleus with Related coefficient between the signal of other 88 brain areas obtains the full brain connection matrix M of amygdaloid nucleus voxel, wherein element (i, j) I-th of amygdaloid nucleus voxel is indicated to the function connects intensity of j-th of brain area, every a line of the matrix describes an almond nucleome Element is in the connection mode under tranquillization state between complete other brain areas of brain, and for value closer to 1, correlation is bigger;Then every two row is calculated Related coefficient between connection mode can measure similarity of two voxels on full brain function connection mode, be denoted as similar Matrix N is spent, wherein each i-th of voxel of element representation amygdaloid nucleus is similar on full brain function connection mode to j-th of voxel Degree;
(4), cluster segmentation is carried out to full brain connection mode similarity matrix N obtained in step (3) with spectral clustering, realizes apricot The sub-district regional partition of benevolence core.
2. the amygdaloid nucleus spectral clustering dividing method according to claim 1 based on tranquillization state function connects, which is characterized in that Step (4) specifically:
(1) sample point x is enabled1,x2,…,xnThe function connects vector for indicating the every row of N being arbitrarily clustered, enables sijIndicate structural map Connection weight between two vertex defines the weight between vertex with Gauss similarity function, and wherein parameter σ is known as scale ginseng It counts, wherein sijIt is defined as
sij=exp (- | | xi-xj||2/2σ2)
Then the similarity matrix of sample is S=(sij) (i, j=1,2 ..., n),
(2) it inputs: similarity matrix S ∈ Rn×n, cluster classification number k;The similarity join figure for establishing sample, enabling W is its weight square Battle array;
(3) non-standardization Laplacian Matrix L is calculated, each column element of W is added up to obtain N number of number, they are placed on pair All it is zero elsewhere on linea angulata, forms the matrix of a N*N, is denoted as D, and enable L=D-W;Calculate the preceding k the smallest spies of L Feature vector v corresponding to value indicative1,v2,…vk
(4) V ∈ R is enabledn×kFor v1,v2,…vkThe matrix composed by being arranged by column;
(5) y is enabled for i=1,2 ..., ni∈RkFor the i-th column of matrix V;
(6) space R will be belonged to using k mean algorithmkData yi(i=1,2 ..., n) is polymerized to k class, as C1,…Ck, just complete The clusters of each pixels of amygdaloid nucleus, realizes the sub-district regional partition of amygdaloid nucleus.
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