CN100411587C - Elastic registration method of stereo MRI brain image based on machine learning - Google Patents

Abstract

The present invention relates to a stereo MRI brain image elastic registration method based on machine learning. By using the method of the machine learning, the best dimension of attribute vector, which is computed on every point in a reference picture is obtained. The obtained best attribute vector maintains maximum extent discrepancy with the attribute vectors surrounding points and maintains maximum extent similarity with the attribute vector on a corresponding point in a training sample. According to the distinctiveness and the consistency condition of the attribute vector on every point in an image, a standard for evaluating a key point is defined. Through the method the machine learning, the key point is selected automatically and hierarchically at every registration stage to prevent registration process from trapping in a local minimum point. Finally, a framework based on the machine learning and the existing registration algorithm are combined to complete the elastic registration of a stereo MRI brain image. The present invention enhances the registration precision and the robustness of a real MR image or a simulated MR image, and further lays the foundation for the feasibility and the accuracy of subsequent clinical application.

Description

Elastic registration method of stereo MRI brain image based on machine learning

Technical field

The present invention relates to a kind of elastic registration method of stereo MRI brain image based on machine learning, method by machine learning, on each point of three-dimensional brain image, learn best attribute vector, in order to represent the feature of this point exactly, and select to stratification the key point in the image, thereby improve the precision and the robustness of elastic registrating.The present invention can be for follow-up image co-registration, accurately locate clinical practices such as the formulation of focus, surgical planning and curative effect tracking lays the foundation, and relates to image elastic registrating, machine learning, fields such as stereo MRI brain (MR) image.

Background technology

Medical figure registration has very important clinical application value.The medical image that uses various similar and different imaging means to obtain is carried out registration not only can be used for medical diagnosis, can also be used for the formulation of surgical planning, the formulation of radiotherapy treatment planning, the tracking of pathological change and the each side such as evaluation of therapeutic effect.

The non-linear registration of three-dimensional brain image is the research focus of field of medical image processing in recent years.In fact so-called image registration be meant seeks between two width of cloth images mapping relations one to one, that is to say, the point corresponding to the space same position in two width of cloth images be connected.The mapping here is commonly referred to as conversion, shows as two-dimensional transform in two-dimensional space, shows as three-dimension varying in three dimensions.In the actual registration process, both can adopt simple rigid body translation, also can adopt complicated elastic deformation according to different characteristics and requirement.The present invention is primarily aimed at is elastic registrating problem between the 3-D view.

Most registration Algorithm can be divided into based on the control point with based on two big classes of pixel.Algorithm based on the control point needs the handmarking control point, for example embeds screw in skull, makes marks on skin etc.The advantage of this class algorithm is fast simple, do not need complicated optimization algorithm, and precision is higher.And shortcoming is to need manual intervention, is difficult to realize automatization, and is subjected to people's subjectivity to influence bigger.Method based on pixel can be carried out registration to two width of cloth images in full automation ground, and makes full use of the statistical information of image, therefore is many class methods of studying at present.These class methods can be subdivided into again based on pixel with based on two branches of attribute vector.The former only uses the half-tone information of image, and speed is fast, but degree of accuracy is not enough.The latter is attribute vector of definition on each point of image, can mate corresponding relation in another width of cloth image exactly by this feature.

HAMMER (abbreviation of Hierarchical Attribute Matching Mechanism for Elastic Registration) is a kind of elastic registrating algorithm based on attribute vector (D.Shen and C.Davatzikos. " HAMMER:Hierarchical attribute matching mechanism for elastic registration. " IEEE Trans on Med.Imaging, 2002, vol.21, pp.1421-1439), its feature is attribute vector of definition on each point, focus on the corresponding relation between the anatomical structure, and unlike other algorithms of the same type, only gray value is determined point correspondence between two width of cloth images as unique attribute.Like this, the registration accuracy of HAMMER and robustness will significantly be better than the algorithm based on gray value.Attribute vector among the HAMMER comprise gray value, boundary information and the various geometric invariant moment of in this neighborhood of a point, calculating that can reflect this anatomical information (Geometric Moment Invariants, GMI).Yet the weak point of HAMMER is: the neighborhood size of calculating GMI is pre-determined, and all calculates GMI in onesize neighborhood for each point in the image.In the abundant zone of boundary information, for example near the angle point of the cerebral cortex (cortical) and the ventricles of the brain (ventricle), the GMI that calculates in less neighborhood can reflect the anatomical information of these points; On the contrary, in white matter (White Matter) zone, variation of image grayscale is slow, if at this moment still calculate GMI in little neighborhood, will make that the attribute vector of these points is very approaching so that be difficult to distinguish.

Summary of the invention

The objective of the invention is at the deficiencies in the prior art, a kind of elastic registration method of stereo MRI brain image based on machine learning is provided, improve the degree of accuracy and the robustness of registration Algorithm, and then lay the foundation for the feasibility and the accuracy of follow-up clinical practice.

Be to realize this purpose, the present invention at first proposes to obtain with the method for machine learning the only spheric neighbo(u)rhood size of the last computation attribute vector of each point in the reference picture, obtains best attribute vector thus.Best attribute vector is not only wanted and is kept maximum diversity between the attribute vector of each point on every side, and and training sample in attribute vector on the corresponding point keep maximum similarity.Secondly, the present invention give chapter and verse in the image significance and the consistency condition of attribute vector on each pixel, define a standard of estimating key point, key point is selected in each stage of registration in method stratification automatically ground by machine learning, thereby has avoided registration process to be absorbed in local minizing point.At last, in the image registration stage, the present invention combines framework and the existing registration Algorithm (HAMMER) based on machine learning, finishes the stereo MRI brain image elastic registrating, improves the degree of accuracy of registration results.

Method of the present invention comprises following concrete steps:

1, the preparation of training data

The main purpose of this step is the corresponding relation of setting up between reference picture and each image.At first, gather enough stereo MRI brain images and set up training sample set, should comprise on each point in the training sample set image the attribute vector that might in image registration, use.Concentrate from training sample then and select a sample as the reference image.For each concentrated individual images of training sample, earlier itself and reference picture are carried out linear registration, and then carry out non-linear registration with existing elastic registrating algorithm, and obtain the displacement field between two width of cloth images, obtain corresponding relation between two width of cloth picture point and the point by displacement field again.Repeat said process, obtain the corresponding relation between all individual images and reference picture in the training set.

2, best attribute vector determines

According to the local message of reference picture, the present invention proposes to determine with the method for machine learning the suitable spheric neighbo(u)rhood size of each point in the reference picture, and promptly the best scale of each point calculates the best attribute vector on each point in the reference picture thus.Wherein, best attribute vector must satisfy three conditions: 1) best attribute vector must keep similarity as much as possible with the attribute vector on the corresponding point in the training sample; 2) best attribute vector and on every side the diversity between the attribute vector of each point be maximum; 3) being distributed in of the pairing best scale of best attribute vector will guarantee in the image space smoothly.At last, the present invention has constructed the energy function that reacts above-mentioned three conditions by the entropy that attribute vector distributes, and uses the optimized method that descends based on gradient to calculate the best scale on each point in the reference picture.

3, select key point

Can determine the significance and the concordance of best attribute vector to define an evaluation function M (x)=Sal (x)/Con (x) thus according to the distribution histogram of best attribute vector on each point in the reference picture.Wherein, molecule Sal (x) is a significant indexes, and denominator Con (x) is a coincident indicator.On each point, calculate the value of M (x), according to the size ordering of M (x), extract the key point in the reference picture then.

4, image registration

To the advanced line linearity registration of individual images subject to registration, make it generally be deformed to reference picture, used attribute vector during each puts according to reference picture in individual images then, calculate all properties vector of the last corresponding different spheric neighbo(u)rhoods of each point in the individual images, select the key point in the individual images and the key point in the individual images is remained unchanged in process of image registration; In each iterative process of elastic registrating, select the key point in the reference picture earlier, and in individual images, carry out similarity relatively according to the Euclidean distance between attribute vector one by one, determine its corresponding point in individual images; Last in each iterative process of elastic registrating, generate the displacement field of two width of cloth images according to the corresponding relation of key point in reference picture and the individual images, according to this displacement field individual images is out of shape, and the input of the new images after the interpolation as the next iteration process, brain image pixels all in reference picture all become key point, finish the elastic registrating of stereo MRI brain image.

Method of the present invention is no matter be at true MR image or on mimic MR image, registration results all is greatly improved.In the experiment that true MR image is carried out, near the registration accuracy of the present invention cerebral cortex is significantly improved; In the experiment that analog data is carried out, registration error of the present invention can drop to 0.66mm by original 0.95mm, and accuracy has improved about 30.5%.For specific brain structure (for example digitation of hippocamps), the result behind the registration and the registration of reference picture bring up to 93.7% from original 92.8%, and meanwhile volumetric errors drops to 1.2% from original 2.6%.

Description of drawings

Fig. 1 is the framework that the present invention is based on the elastic registrating algorithm of machine learning.

What Fig. 2 showed is the distribution situation of the best scale from the high-resolution to the low resolution.(a) expression is a section in the reference picture, (b)-(d) represents the distribution of best scale under high-resolution, intermediate-resolution and the low resolution respectively.The yardstick of the minimum that shows (e) is 4 (dark colors), and maximum yardstick is 24 (light color).The rightmost color table of Fig. 2 has been indicated the magnitude relationship of best scale.

Fig. 3 has shown 7 points that the meaning represented is arranged, and is respectively the tip of gyrus, the borderline point of the root of brain ditch, the angle point of the ventricles of the brain and corpus callosum.What (a)-(c) represent respectively is high-resolution, intermediate-resolution and low resolution.The size of circle is represented corresponding best scale among the figure, and the red solid line circle is represented the spheric neighbo(u)rhood of yardstick from 4 to 8; Green pecked line circle is represented the spheric neighbo(u)rhood of yardstick from 8 to 15; Blue long dashed circle represents that yardstick is the spheric neighbo(u)rhood more than 15.

Fig. 4 has shown the example of the superiority of an explanation best attribute vector.Red cross coordinate among Fig. 4 (a) is represented a point of reference picture midbrain ditch root, red asterisk among Fig. 4 (b) and purple round dot are all represented the root points of individual images midbrain ditch, but the former is reference picture correct corresponding point in individual images, and the latter then is not.Fig. 4 (a) and (b) in solid line circle and dashed circle represent little and big spheric neighbo(u)rhood respectively, the picture material in the neighborhood is drawn among Fig. 4 (e) and shows.Fig. 4 (c) and that (d) show is similarity figure between the attribute vector of being had a few in the attribute vector of the red cross coordinate points in the reference picture and the individual images, the darker regions among the figure in the rectangle frame represents that similarity is big, light areas represents that similarity is little.Fig. 4 (c) does not pass through the improved result of the present invention, and Fig. 4 (d) is the result after optimizing through the present invention.

Fig. 5 has shown the situation that key point increases gradually along with iterations in the registration process.Fig. 5 (a)-(d) is respectively the distribution situation of the key point of reference picture in registration starting stage, interstage and terminal stage, and Fig. 5 (e) shows is key point in the floating image.

Fig. 6 has shown registration results of the present invention and the registration results of not optimizing through machine learning.

The specific embodiment

Below in conjunction with drawings and Examples technical scheme of the present invention is further described.

Present embodiment mainly comprises training and two parts of image registration, as shown in Figure 1.In the training stage, main task is included in each point of reference picture and goes up definite best attribute vector and select key point.In the image registration stage, result who obtains in the training stage and existing medical figure registration algorithm are combined (for example HAMMER algorithm), determine the corresponding relation between two width of cloth images.Following constipation closes the HAMMER algorithm specific implementation method of the present invention is described in further detail.

The MR image that embodiment adopts is the 3-D view of T1 weighting.Whole invention implementation procedure is as follows:

1. the preparation of training data

● gather MR brain image sample, generate training set.In the present embodiment, sample space comprises the MR image of 18 Different Individual.

● select an image as the reference image, remaining individual images linearity is registrated to this reference picture.Existing linear registration Algorithm has FSL, ITK etc. (being disclosed source code).

● do elastic registrating with the individual images of HAMMER algorithm after, obtain accurate point correspondence linear registration.The HAMMER algorithm provides disclosed executable code, can be at the presenter's (Dingang Shen) of algorithm homepage https: //www.rad.upenn.edu/sbia/rsoftware.html downloads.

● to reference picture with calculate in different big or small spheric neighbo(u)rhoods through each point on the individual images behind the linear registration

S={i|i=4*j wherein, j=1,2,3 ..., 6}.The detailed step that calculates is as follows:

Suppose image be divided into white matter (White Matter, WM), grey matter (Gray Matter, GM), the ventricles of the brain (Ventricle), cerebrospinal fluid (cerebrospinal fluid, CSF) four parts.Use three-dimensional (p+q+r) the rank square of formula (1) computed image earlier:

$M_{p,q,r}=\underset{{\left(x_1\right)}^2+{\left(x_2\right)}^2+{\left(x_3\right)}^2<S^2}{\&Integral;\&Integral;\&Integral;}{x}_1^p{x}_2^q{x}_3^r{f}_{\mathrm{tissue}}(x_1,x_2,x_3){\mathrm{dx}}_1{\mathrm{dx}}_2{\mathrm{dx}}_3---\left(1\right)$

Wherein, f _TissueThe expression tissue class (WM for example, GM, VN, CSF), s represents to calculate radius.Attribute vector (GMI) on each point just can calculate with formula (2) then:

GMI ₁＝M _0，0，0

GMI ₂＝M _2，0，0+M _0，2，0+M _0，0，2

${\mathrm{GMI}}_3=M_{\mathrm{2,0,0}}{M}_{\mathrm{0,2,0}}+M_{\mathrm{2,0,0}}{M}_{\mathrm{0,0,2}}+M_{\mathrm{0,2,0}}{M}_{\mathrm{0,0,2}}-M_{1,0,1}^2-M_{\mathrm{1,1,0}}^2-M_{\mathrm{0,1,1}}^2$

${\mathrm{GMI}}_4=M_{\mathrm{2,0,0}}{M}_{\mathrm{0,2,0}}{M}_{\mathrm{0,0,2}}-M_{\mathrm{0,0,2}}{M}_{\mathrm{1,1,0}}^2+2M_{\mathrm{1,1,0}}{M}_{\mathrm{1,0,1}}{M}_{\mathrm{0,1,1}}$

(2)

$-M_{\mathrm{0,2,0}}{M}_{\mathrm{1,0,1}}^2{-M}_{\mathrm{2,0,0}}{M}_{\mathrm{0,1,1}}^2$

2. best attribute vector determines

The structure energy function, as shown in Equation (3):

$E=\underset{x}{\mathrm{\&Sigma;}}(-E_1(x,S_x)+\mathrm{\&alpha;}{E}_2(x,S_x)+\mathrm{\&beta;}{E}_3(x,S_x))---\left(3\right)$

Wherein, E ₁(x, S _x) be illustrated in the entropy of (radius is 5 spheric neighbo(u)rhood) GMI distribution histogram in the big image neighborhood, E ₂(x, S _x) be illustrated in the entropy of (radius is 2 spheric neighbo(u)rhood) GMI distribution histogram in the little image neighborhood, $E_3(x,S_x)={\mathrm{\&Sigma;}}_{y\&Element;r_x}{(S_x-S_y)}^2$ The difference of optimal scale on the expression consecutive points.Minimize this energy function, can obtain the best scale S (x) on each point.The present invention adopts Markov random field to be optimized.Preceding two (E of formula (3) ₁, E ₂) be used as likelihood energy, the 3rd (E ₃) as level and smooth energy.Consider the amount of calculation problem of 3-D view, what the present invention adopted is that suboptimization method (ICM) is optimized Markov random field.If training sample is arranged, α=1.0 then, otherwise α=0.β value in the present embodiment is 1.0.

Usually in order to increase the robustness of algorithm, many registration Algorithm have all been used the multiresolution technology.Therefore, the present invention has carried out same calculating to each resolution, has obtained the distribution of corresponding best scale.What Fig. 2 from left to right showed is the distribution situation of the best scale from the high-resolution to the low resolution.Yardstick minimum among the figure is 4, and maximum yardstick is 24.The rightmost color table of Fig. 2 has been indicated the magnitude relationship of best scale.As can be seen from the figure the distribution of best scale meets the anatomical features of MR brain image.Little yardstick all is distributed in the zone of border complexity such as cortex, and the yardstick ecto-entad increases gradually then, reaches maximum in the mild zone of greyscale transformations such as white matter.

Fig. 3 has shown 7 points that the meaning represented is arranged that the present invention selects, and is respectively the tip of gyrus, the borderline point of the root of brain ditch, the angle point of the ventricles of the brain and corpus callosum.The size of circle is represented corresponding best scale among the figure, and the red solid line circle is represented the spheric neighbo(u)rhood of yardstick from 4 to 8; Green pecked line circle is represented the spheric neighbo(u)rhood of yardstick from 8 to 15; Blue long dashed circle represents that yardstick is the spheric neighbo(u)rhood more than 15.In order to show that conveniently the image of low resolution and intermediate-resolution all is upsampled to the size of high-definition picture.

Provide a concrete example below the present invention's superiority in the present embodiment has been described.Red cross coordinate among Fig. 4 (a) is represented a point of reference picture midbrain ditch root, red asterisk among Fig. 4 (b) and purple round dot are all represented the root points of individual images midbrain ditch, but the former is reference picture correct corresponding point in individual images, and the latter then is not.Fig. 4 (a) and (b) in solid line circle and dashed circle represent little and big spheric neighbo(u)rhood respectively, the picture material in the neighborhood is drawn among Fig. 4 (e) and shows.Fig. 4 (c) and that (d) show is similarity figure between the attribute vector of being had a few in the attribute vector of the red cross coordinate points in the reference picture and the individual images, the darker regions among the figure in the rectangle frame represents that similarity is big, light areas represents that similarity is little.Fig. 4 (c) does not pass through the improved result of the present invention, and Fig. 4 (d) is the result after optimizing through the present invention.

3. selection key point

In step 2, obtain best attribute vector ${\stackrel{\&RightArrow;}{G}}_b=\left\{g_i\right\}$ After, calculate the significance value Sal (x) that each puts the best attribute vector on x according to formula (4).

$\mathrm{Sal}(s,x)=L(s,x)\&CenterDot;S_x\&CenterDot;\underset{i}{\mathrm{\&Sigma;}}\left|\right|\frac{{\&PartialD;p}_i(s,x)}{\&PartialD;s}{|}_{S_x}\left|\right|---\left(4\right)$

Wherein $L(s,x)=-\underset{i}{\mathrm{\&Sigma;}}{p}_i(s,x)\log p_i(s,x),$ p _i(s, x) being illustrated in an x is the center, s is in the neighborhood of radius, certain attribute vector GMI _iThe probability that occurs.Need to prove that the s that occurs in the formula is the best scale that is the best attribute vector correspondence that obtains in step 2.

The concordance value of best attribute vector is the E in the formula (3) ₂, only Ci Shi s is optimal radius S _bThe method of computing method is similar.

At last, on each point of reference picture, calculate M (x)=Sal (x)/Con (x), and sort according to the size of M (x).The value of M (x) is big more, represents that near the local feature this point is obvious more, and like this corresponding relation is also just easy more determines.

Fig. 5 has shown the situation that key point increases gradually along with iterations in the registration process.Fig. 5 (a)-(d) is respectively the distribution situation of the key point of reference picture in registration starting stage, interstage and terminal stage, and Fig. 5 (e) shows is key point in the floating image.Can see that in the drawings the key point of starting stage distributes more sparse, concentrate on the top of the ventricles of the brain, brain ditch root and gyrus, these exactly are exactly the most outstanding zone of local feature.The corresponding relation of the point in these zones is the easiest to be found exactly, and this initial stage in distortion determines that the general shape of displacement field is very important.Along with the increase of iterations, increasing boundary point has become key point.Arrive the last of iteration, all boundary points have all become key point, shown in Fig. 5 (d).

4. image registration

4.1 data are prepared

For an image subject to registration, at first use the algorithm (FSL) of linear registration that this image is roughly transformed to the reference picture space.Because training result of the present invention only at reference picture, therefore must all calculate all GMI that use in the reference picture space one time for individual images, promptly calculates GMI

S={i|i=4*j, j=1,2,3 ..., 6}.Secondly, also need to calculate M (x) value on each point in the individual images, and according to from big to small rank order, so as middle-levelization of process of registration the key point in the selection individual images.

4.2 elastic registrating process

Select key point { y in the individual images according to the size of M (x) value _i| 1≤i≤N _s, N _sBe the key point number of selecting, be about 15% of whole brain image pixel (not comprising background dot) number.Key point in the individual images remains unchanged in registration process.

Select the key point { x in the reference picture _i| 1≤i≤N _T, N _tBe the key point number in the reference picture.At the starting stage of registration, N _tLess, be about 15% of whole brain image pixel (not comprising background dot) number.Along with the increase of iterations, N _tIncrease gradually, during to iteration convergence, all brain image pixels can be as key point.

4.3 determine corresponding relation and generate displacement field

● determine that the key point in the individual images arrives the corresponding relation of reference picture.Promptly for the key point y in any individual image _i, in certain neighborhood, seek the key point x in the highest reference picture of similarity _j(in the present embodiment, the threshold value of similarity is 0.8).If x _jExist, then set up (x from h _j) to y _iCorresponding relation.

● for any one the key point x in the reference picture _jIf, in previous step, set up corresponding relation, then the direction that is subjected to displacement of this point is exactly along h (x _j) to y _iOtherwise, at x _jAround in the Search of Individual image and x _jThe point of similarity maximum, the direction of displacement is just pointed to point the most similar in the individual images.Notice that if more than one of similar point, the direction of displacement is the resultant direction of these power so.

● with the level and smooth displacement field of Gaussian filter.

If stopping criterion for iteration does not satisfy, come back to step 4.3.

Effect of the present invention

In the present embodiment, the present invention tests mimic MR brain image and true picture.All experiments finish on microcomputer all that (Pentium IV 3.0GHz), and uses identical parameter.

At first, the present invention has carried out registration to the MR brain image of 18 width of cloth older individuals.For contrast and experiment, the present invention has also carried out registration to 18 same width of cloth images with original HAMMER algorithm.By find that relatively registration results of the present invention is significantly improved near the cerebral cortex of complexity, as shown in Figure 6.In the red circle in the drawings, the present invention can also keep the corresponding relation of anatomical structure, but manifest error has appearred in the registration results of HAMMER algorithm.

Secondly, the present invention has also carried out the contrast experiment on simulation MR brain image.In the present embodiment, earlier with document (Z.Xue, D.Shen et al, " Statistical Representation and Simulation ofHigh-Dimensional Deformations:Application to Synthesizing Brain Deformations " .MICCAI, Palm Springs, California, USA, Oct 26～29,2005.) in algorithm reference picture has been transformed into different individual images, obtained the displacement field between reference picture and the individual images simultaneously.In this experiment, the Different Individual image is transformed to the reference picture space respectively with the present invention.Displacement field that obtains behind the registration by checking and the error between the prior known displacement field just can compare the levels of precision of registration results.Algorithm after the improvement will be significantly better than original HAMMER algorithm.Do not having under the situation of training sample, registration accuracy has improved about 12.6%; If half is used for training all analog datas, second half is used for test, and then the precision on test set can improve 30.5%.

Claims (1)

1. the elastic registration method of stereo MRI brain image based on machine learning is characterized in that comprising the steps:

1) preparation of training data: gather 18 width of cloth stereo MRI brain images and set up training sample set, each point in the training sample set image go up comprise the attribute vector that might in image registration, use, select a sample as the reference image from training sample is concentrated then; For each concentrated individual images of training sample, earlier itself and reference picture are carried out linear registration, and then carry out non-linear registration with existing elastic registrating algorithm, obtain the displacement field between two width of cloth images, obtain corresponding relation between two width of cloth picture point and the point by displacement field again, obtain the corresponding relation between all individual images and reference picture in the training set thus;

2) determining of best attribute vector: according to the local message of reference picture, determine the suitable spheric neighbo(u)rhood size of each point in the reference picture with the method for machine learning, be the best scale of each point, calculate the best attribute vector on each point in the reference picture thus; Wherein, best attribute vector must satisfy three conditions: 1) best attribute vector must keep similarity as much as possible with the attribute vector on the corresponding point in the training sample; 2) best attribute vector and on every side the diversity between the attribute vector of each point be maximum; 3) being distributed in of the pairing best scale of best attribute vector will guarantee in the image space smoothly; The entropy structure that distributes by attribute vector reacts the energy function of above-mentioned three conditions, and uses the optimization method that descends based on gradient to calculate the best scale on each point in the reference picture;

3) select key point: significance and the concordance of determining best attribute vector according to the distribution histogram of the best attribute vector on each point in the reference picture, define an evaluation function M (x)=Sal (x)/Con (x) thus, wherein, molecule Sal (x) is a significant indexes, and denominator Con (x) is a coincident indicator; On each point, calculate the value of M (x), according to the size ordering of M (x), extract the key point in the reference picture then; The value of M (x) is big more, represents that near the local feature this point is obvious more, thereby corresponding relation is also just easy more definite;

4) image registration: to the advanced line linearity registration of individual images subject to registration, make it generally be deformed to reference picture, used attribute vector during each puts according to reference picture in individual images then, calculate all properties vector of the last corresponding different spheric neighbo(u)rhoods of each point in the individual images, select the key point in the individual images and the key point in the individual images is remained unchanged in process of image registration; In each iterative process of elastic registrating, select the key point in the reference picture earlier, and in individual images, carry out similarity relatively according to the Euclidean distance between attribute vector one by one, determine its corresponding point in individual images; Last in each iterative process of elastic registrating, generate the displacement field of two width of cloth images according to the corresponding relation of key point in reference picture and the individual images, according to this displacement field individual images is out of shape, and the input of the new images after the interpolation as the next iteration process, brain image pixels all in reference picture all become key point, finish the elastic registrating of stereo MRI brain image.

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