CN106023138B - A kind of global probability fiber tracking method based on spherical convolution - Google Patents

A kind of global probability fiber tracking method based on spherical convolution Download PDF

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CN106023138B
CN106023138B CN201610292345.8A CN201610292345A CN106023138B CN 106023138 B CN106023138 B CN 106023138B CN 201610292345 A CN201610292345 A CN 201610292345A CN 106023138 B CN106023138 B CN 106023138B
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fiber
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distribution
probability
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CN106023138A (en
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冯远静
何建忠
吴烨
张军
徐田田
周思琪
黄奕奇
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Yuenaoyunfu Medical Information Technology Zhejiang Co ltd
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Zhejiang University of Technology ZJUT
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    • G06T7/0012—Biomedical image inspection
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    • G06T2207/10088—Magnetic resonance imaging [MRI]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
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Abstract

A kind of global probability fiber tracking method based on spherical convolution, the fiber orientation distribution in the convolutional calculation unit sphere of diffusion signal and receptance function is used first, original fiber orientation distribution fODF is replaced by spherical surface Gauss kernel method again, obtains one group of new fODF；Global probability fiber tracking based on group's track algorithm calculates Posterior distrbutionp after obtaining prior probability and observation density；The summation and average value of global fiber function are calculated on the basis of learning Posterior distrbutionp, sets up tracking initiation point and starts to track, by selecting optimum orientation to obtain relatively accurate fibre structure.The present invention provides a kind of effective consideration local fiber distribution of orientations, the higher global probability fiber tracking method based on spherical convolution of precision.

Description

A kind of global probability fiber tracking method based on spherical convolution
Technical field
The present invention relates to the medical imaging under computer graphics, Nervous System Anatomy field, especially a kind of fiber tracking Method.
Background technology
Fibre straighteness is the unique work for obtaining neuromechanism and dissecting link information based on Magnetic Resonance Diffusion Weighting molding Tool；It estimates possible fiber path by tracking the diffusion directions that local tensors are orientated；Fiber path is with a complex web Nerve fibre bundle in the form performance human brain of network chart, and nuerological pathology and sick crowd are investigated by it；Practical card Bright, in certainty tracking technique, fiber path remains diversification, can not be divided in noise, and head movement and image are pseudo- The uncertainty of track is reconstructed under the influence of shadow；In order to overcome these limitations, fibre straighteness method to be developed to quantify With the uncertainty of visualization and fiber path；Researcher began to use some fine angular resolution diffusion imaging methods in recent years To realize probabilistic algorithm.
Invention content
In order to which overcome existing fiber tracking mode can not consider the lower deficiency of local fiber distribution of orientations, precision, this A kind of effective consideration local fiber distribution of orientations of invention offer, the higher global probability fiber tracking based on spherical convolution of precision Method.
The technical solution adopted by the present invention to solve the technical problems is：
A kind of global probability fiber tracking method based on spherical convolution, includes the following steps：
1) diffusion model is estimated
Estimate spherical convolution SD, S (g)/S by solving a linear system and the recycling spherical surface Gauss nuclear issue0With N number of ladder Spend convolution of the direction g approximations by receptance functionAnd the fiber orientation distribution in unit sphereIt indicates：
Wherein,It is sample convolution direction, defining receptance function is：
δ is the product of diffusion time and diffusion coefficient, therefore passes through S (g)/S0WithObtain fiber orientation distributionEstimated by minimizing following energy：
One linear system is expressed as by non-negative least square method；It is j-th of fiber orientation distribution, passes through ball It is each that face Gauss kernel method substitutes the humorous recycling of ballTo the machine direction distribution function regainedIn：
Wherein,σ is width parameter；
2) global probability fiber tracking, process are as follows：
From x on the c of path0Point arrives xnPoint global cost function be approximately under the action of α：
Cost function p (vi,xi) it is xiPoint choice direction viProbability；For each step, direction viIt is from probability density letter Number p (vi|vi-1, Φ) and sampling obtains, and it is to be indicated by a Bayesian frame：
Wherein, Φ is the observed value of one group of three-dimensional diffusion weighted imaging volume, and p (Φ) is a fixed standard of the system The factor, distribution p (vi|vi-1) be defined as priori conditions and obtained by a simple group distribution；Observing and nursing p (Φ |vi) generation For in formula (4)
After priori and observation density are all calculated, Posterior distrbutionp p (vi|vi-1, Φ) and it is obtained by formula (6)；Finally, Using Markov monte carlo method from p (vi|vi-1, Φ) and draw the random sample of machine direction；Define EsumAnd EaveMake Connection is measured for two from a-quadrant to B area, has respectively represented the summation and average value of global fiber function：
EaveThe quantity for representing point, for every fiber average probability, EaveIndicate the average value in path, but it may also be answered For excessively high EsumValue and mistake indicate some short or dead paths, and EsumExplicitly indicate that the summation in path, positive correlation Property may come from some unreasonable paths；So needing two global measurings for selecting optimal path；
3) group's track algorithm is executed, process is as follows：
M particle is distributed in starting point and propagate as time goes by one path；In step number t-1, that is, vi(t-1) and xi (t-1), under i=1....m and step-length α, the function that particle is previous step sequentially is propagated in next step, i.e.,：
xi(t+1)=xi(t)+αvi(t), i=1 ..., m (10)
Refer to local fiber be orientated in step t from formula (6) andSampled representation whole world fiber-wall-element model；It is It is selected according to the adaptive value of all particles：It is parameter for each iteration k, k, d top fibers descending is stored asWithD is parameter；According to EsumAnd EaveThe two ring The measurement answered, therefore best fiber fk：
WithThe summation and average value of best fiber are respectively represented, p is coefficient；All voxel x1,2,...,mIt is every A fiber fkIt is stored in and achieves in Γ：
Wherein, m>0,n>0,It is the fiber-wall-element model that voxel x is passed through in n path；N=0 represents the voxel in formula (12) In while be extraIt is suitable；Assuming that a particle propagation passes through current point xiIt is v with the vector before iti-1, one Best orientation viThen it is and vi-1Lowest difference fromIt obtains, formula is
The present invention technical concept be：The fiber in the convolutional calculation unit sphere of diffusion signal and receptance function is used first Distribution of orientations, then original machine direction distribution function is replaced by spherical surface Gauss kernel method, obtain one group of new fiber side To distribution function.
Global probability fiber tracking based on group's track algorithm calculates posteriority after obtaining prior probability and observation density Distribution；The summation and average value of global fiber function are calculated on the basis of learning Posterior distrbutionp.Set up tracking initiation point Start to track, by selecting optimum orientation to obtain relatively accurate fibre structure.
Beneficial effects of the present invention are mainly manifested in：Effectively consider that local fiber distribution of orientations, precision are higher；The side of cooperation Formula obtains best fibre structure.
Specific implementation mode
The invention will be further described below.
A kind of global probability fiber tracking method based on spherical convolution, includes the following steps：
1) diffusion model is estimated
Estimate spherical convolution SD, S (g)/S by solving a linear system and the recycling spherical surface Gauss nuclear issue0With N number of ladder Spending direction g can the approximate convolution by receptance functionAnd the fiber orientation distribution machine direction in unit sphere point Cloth function,It indicates：
Wherein,It is sample convolution direction, defining receptance function is：
δ is the product of diffusion time and diffusion coefficient, therefore passes through S (g)/S0WithObtain fiber orientation distribution fibre Direction distribution function is tieed up,Estimated by minimizing following energy：
One linear system is expressed as by non-negative least square method；It is j-th of fiber orientation distribution fiber side To distribution function, finally in order to prevent to the susceptibility of noise, it is each that the humorous recycling of ball is substituted by spherical surface Gauss kernel method To the machine direction distribution function regainedIn：
Wherein,σ is width parameter, and numerical value construction is insufficient to prevent from merging Or angular resolution reduces.
2) global probability fiber tracking, process are as follows：
From x on the c of path0Point arrives xnPoint global cost function be approximately under the action of α：
Cost function p (vi,xi) it is xiPoint choice direction viProbability；For each step, direction viIt is from probability density letter Number p (vi|vi-1, Φ) and sampling obtains, and it is to be indicated by a Bayesian frame：
Wherein, Φ is the observed value of one group of three-dimensional diffusion weighted imaging volume, and p (Φ) is a fixed standard of the system The factor, distribution p (vi|vi-1) be defined as priori conditions and obtained by a simple group distribution；Observing and nursing p (Φ |vi) generation For in formula (4)
After priori and observation density are all calculated, Posterior distrbutionp p (vi|vi-1, Φ) and it is obtained by formula (6)；Finally, Using Markov monte carlo method from p (vi|vi-1, Φ) and draw the random sample of machine direction；Define EsumAnd EaveMake Connection is measured for two from a-quadrant to B area, has respectively represented the summation and average value of global fiber function：
EaveThe quantity for representing point, for every fiber average probability, EaveIndicate the average value in path, but it may also be answered For excessively high EsumValue and mistake indicate some short or dead paths, and EsumExplicitly indicate that the summation in path, positive correlation Property may come from some unreasonable paths；So needing two global measurings for selecting optimal path；
3) group's track algorithm is executed, process is as follows：
M particle is distributed in starting point and propagate as time goes by one path；In step number t-1, that is, vi(t-1) and xi (t-1), under i=1....m and step-length α, the function that particle is previous step sequentially is propagated in next step, i.e.,：
xi(t+1)=xi(t)+αvi(t), i=1 ..., m (10)
Refer to local fiber be orientated in step t from formula (6) andSampled representation whole world fiber-wall-element model；It is root Selected according to the adaptive value of all particles：It is parameter for each iteration k, k, d top fibers descending is stored asWithD is parameter；According to EsumAnd EaveThe two ring The measurement answered, therefore best fiber fk：
WithThe summation and average value of best fiber are respectively represented, p is coefficient；All voxel x1,2,...,mIt is every A fiber fkIt is stored in and achieves in Γ：
Wherein, m>0,n>0,It is the fiber-wall-element model that voxel x is passed through in n path；N=0 represents the voxel in formula (12) In while be extraIt is suitable；Assuming that a particle propagation passes through current point xiIt is v with the vector before iti-1, one Best orientation viThen it is and vi-1Lowest difference fromIt obtains, formula is

Claims (1)

1. a kind of global probability fiber tracking method based on spherical convolution, it is characterised in that：Include the following steps：
1) diffusion model is estimated
Estimate spherical convolution SD, S (g)/S by solving a linear system and the recycling spherical surface Gauss nuclear issue0With N number of gradient side To g approximations by the convolution of receptance functionAnd the fiber orientation distribution in unit sphereIt indicates：
Wherein,It is sample convolution direction, defining receptance function is：
δ is the product of diffusion time and diffusion coefficient, therefore passes through S (g)/S0WithObtain fiber orientation distributionIt is logical It crosses and minimizes following energy to estimate：
One linear system is expressed as by non-negative least square method；It is j-th of fiber orientation distribution, passes through spherical surface height It is each that this kernel method substitutes the humorous recycling of ballTo the machine direction distribution function regainedIn：
Wherein,σ is width parameter；
2) global probability fiber tracking, process are as follows：
From x on the c of path0Point arrives xnPoint global cost function be approximately under the action of α：
Cost function p (vi,xi) it is xiPoint choice direction viProbability；For each step, direction viIt is from probability density function p (vi|vi-1, Φ) and sampling obtains, and it is to be indicated by a Bayesian frame：
Wherein, Φ be one group of three-dimensional diffusion weighted imaging volume observed value, p (Φ) be the system a fixed standard because Son, distribution p (vi|vi-1) be defined as priori conditions and obtained by a simple group distribution；Observing and nursing p (Φ |vi) replace In formula (4)
After priori and observation density are all calculated, Posterior distrbutionp p (vi|vi-1, Φ) and it is obtained by formula (6)；Finally, using horse Er Kefu monte carlo methods are from p (vi|vi-1, Φ) and draw the random sample of machine direction；Define EsumAnd EaveAs from A Two of region to B area measure connection, have respectively represented the summation and average value of global fiber function：
EaveThe quantity for representing point, for every fiber average probability, EaveIndicate the average value in path, but it may also should be High EsumValue and mistake indicate some short or dead paths, and EsumExplicitly indicate that the summation in path, positive correlation can It can come from some unreasonable paths；So needing two global measurings for selecting optimal path；
3) group's track algorithm is executed, process is as follows：
M particle is distributed in starting point and propagate as time goes by one path；In step number t-1, that is, vi(t-1) and xi(t- 1), under i=1....m and step-length α, the function that particle is previous step sequentially is propagated in next step, i.e.,：
xi(t+1)=xi(t)+αvi(t), i=1 ..., m (10)
Refer to local fiber be orientated in step t from formula (6) andSampled representation whole world fiber-wall-element model；It is according to institute There is the adaptive value of particle to select：It is parameter for each iteration k, k, d top fibers descending is stored asWithD is parameter；According to EsumAnd EaveThe two ring The measurement answered, therefore best fiber fk：
WithThe summation and average value of best fiber are respectively represented, p is coefficient；All voxel x1,2,...,mEach fibre Tie up fkIt is stored in and achieves in Γ：
Wherein, m>0,n>0,It is the fiber-wall-element model that voxel x is passed through in n path；N=0 represents the voxel While extraIt is suitable；Assuming that a particle propagation passes through current point xiIt is v with the vector before iti-1, one best Orientation viThen it is and vi-1Lowest difference fromIt obtains, formula is
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US6697538B1 (en) * 1999-07-30 2004-02-24 Wisconsin Alumni Research Foundation Apparatus for producing a flattening map of a digitized image for conformally mapping onto a surface and associated method
CN103970929A (en) * 2013-12-23 2014-08-06 浙江工业大学 High-order diffusion tensor mixture sparse imaging method for alba fiber tracking

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US6697538B1 (en) * 1999-07-30 2004-02-24 Wisconsin Alumni Research Foundation Apparatus for producing a flattening map of a digitized image for conformally mapping onto a surface and associated method
CN103970929A (en) * 2013-12-23 2014-08-06 浙江工业大学 High-order diffusion tensor mixture sparse imaging method for alba fiber tracking

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