CN1952981A - Method for knowledge based image segmentation using shape models - Google Patents

Abstract

A method for segmenting an object of interest from an image of a patient having such object. Each one of a plurality of training shapes is distorted to overlay a reference shape with a parameter Theta<SUB>i </SUB>being a measure of the amount of distortion required to effect the overlay. A vector of the parameters Theta<SUB>i </SUB>is obtained for every one of the training shapes through the minimization of a cost function along with an estimate of uncertainty for every one of the obtained vectors of parameters Theta<SUB>i</SUB>, such uncertainty being quantified as a covariance matrix Sigma<SUB>i</SUB>. A statistical model represented as {circumflex over (f)}<SUB>H </SUB>(Theta,Sigma) is generated with the sum of kernels having a mean Theta<SUB>i </SUB>and covariance Sigma<SUB>i </SUB>. The desired object of interest in the image of the patient is identified by positioning of the reference shape on the image and distorting the reference shape to overlay the obtained image with a parameter Theta being a measure of the amount of distortion required to effect the overlay. An uncertainty is quantified as a covariance matrix Sigma and an energy function E=E<SUB>shape</SUB>+E<SUB>image </SUB>is computed to obtain the probability of the current shape in the statistical shape model E<SUB>shape</SUB>(Theta,Sigma)=-log({circumflex over (f)}<SUB>H</SUB>) and the fit in the image E<SUB>image</SUB>.

Description

Utilize the image partition method based on knowledge of shape

The cross reference of related application

The application requires in the U.S. Provisional Application No.60/698 of submission on July 13rd, 2005, and 826 right of priority is incorporated herein by reference this application in this.

Technical field

The present invention relates generally to the anatomical object dividing method, and relate more specifically to priori with anatomical object and be used for anatomical object and cut apart.

Background technology

As known in the art, many big three-dimensional (3D) volumes that are used in according to imaging data, for example CT data carry out technology in quantitative test, for example anatomy and the pathology of object and comprise object and contiguous Object Segmentation are opened.In in the past 10 years, become more and more general based on the dividing method of shape.At first nineteen ninety-five introduce as T.F.Cootes and C.J.Taylor at " Statistical models of appearance for computervision " (Technical Report, University of Manchester, 2004) described in active shape model (ASM) and active appearance models (AAM) be the very general instrument that is used for the anatomical structure of Medical Image Segmentation.Also see also: J.G.Bosch, S.C.Mitchell, B.P.F.Lelieveldt, F.Nikland, O.Kamp, M.Sonka and J.H.Reiber " Automatic segmentation ofechocardiographic sequences by active appearance motionmodels ", IEEE Trans.Medical Imaging, 21 (11): 1374-1383,2002; Duta and M.Sonka " Segmentation and interpretation of MR brainimages:An improved active shape model ", IEEE Trans.MedicalImaging, 17 (6): 1049-1062,1998; And A.Lundervold, N.Duta, T.Taxt and A.Jain. " Model-guideds egmentation of corpus callosumin MR images " CVPR, 1231-1238 page or leaf, 1999.

More recently, principal component analysis (PCA) also has been applied to the range conversion of the implicit representation of shape, referring to M.Leventon, " the Statistical Shape Influence in Geodesic Active Contours " of E.Grimson and O.Faugeras, IEEE Conference on Computer Vision and Pattern Recognition, the I:316-322 page or leaf, 2000.Based on being equivalent to the recovery geometry cutting apart of shape usually, described geometry is very possible in the model space, and aims at well with the strong feature in the image.The advantage that is better than traditional deformable template based on the method for shape is that their allow restrained deformation process to remain in the space that allows shape, referring to T.McInerney, G.Hamarneh, Deformable organisms for automatic medical imageanalysis (the Medical Image Analysis of M.Shenton and D.Terzopoulos, 6:251-266,2002).Verified these methods are good the trading off between complicacy and shape are summarized.Yet owing to carry out modeling after registration, recording error can be transmitted in the model space.In addition, the supposition of gaussian shape model may be to have a bit restrictive.

Summary of the invention

According to the present invention, provide a kind of method of from the image of patient with objects, cutting apart such object.This method comprises the reference figuration of this object that conversion produces, and mates each training shapes in a plurality of training shapes with the foundation energy function, and this comprises each training shapes distortion that makes in the described training shapes, to utilize parameter Θ _iCover reference figuration, parameter Θ _iBe to realize measuring of deflection that the covering of i training shapes in N the training shapes is required at each lattice point place.This method obtains parameter Θ by each training shapes in the described training shapes of being minimised as of cost function _iVector.This method is the parameter Θ that is obtained _iVector in each vector estimate uncertainly, this uncertainty is quantified as the covariance matrix ∑ _iThis method is represented as for a plurality of training shapes provide

Statistical model, this statistical model is to have mean value Θ _iWith the covariance ∑ _iThe summation of K gaussian kernel.

In one embodiment, cost function is the difference of two squares and (the sum squared difference) between the reference model of the distance map that produces for one of described training shapes and institute's conversion.

In one embodiment, this method additionally comprises: the image that obtains to expect object from patient; Discern the interested expectation object in patient's the image by position reference shape on image, this comprises: the reference figuration that conversion produced, mate the image that is obtained with the foundation energy function, this comprises makes the reference figuration distortion cover the image that is obtained to utilize parameter Θ, and parameter Θ is measuring of the required deflection of this covering of realization; Estimate uncertainty, this uncertainty is quantified as the covariance matrix ∑; The shape item of calculating energy function $E_{\mathrm{shape}}(\mathrm{\&Theta;},\mathrm{\&Sigma;})=-\log \left({\hat{f}}_H\right)$ , to obtain the probability of current shape in the statistical shape model; And the image term E of calculating energy function _Image, with the match of the shape in the evaluation map picture; Make energy function E _Shape+ E _ImageMinimize.More specifically, calculate $E_{\mathrm{shape}}(\mathrm{\&Theta;},\mathrm{\&Sigma;})=-\log \left({\hat{f}}_H\right)$ And E _Image, change Θ, calculate new covariance matrix as ∑ ^-1 _ΘThereby, so that calculate new $E_{\mathrm{shape}}(\mathrm{\&Theta;},\mathrm{\&Sigma;})=-\log \left({\hat{f}}_H\right)$ And E _Image, be minimized until whole energy function.

In one embodiment, $E_{\mathrm{shape}}(\mathrm{\&Theta;},\mathrm{\&Sigma;})=-\log \left({\hat{f}}_H\right)$ Minimize and comprise: calculate $E_{\mathrm{shape}}(\mathrm{\&Theta;},\mathrm{\&Sigma;})=-\log \left({\hat{f}}_H\right)$ And E _ImageChange Θ; Produce new covariance matrix as ∑ _ΘThereby, so that calculate new $E_{\mathrm{shape}}(\mathrm{\&Theta;},\mathrm{\&Sigma;})=-\log \left({\hat{f}}_H\right)$ And E _Image, until E _Shape(Θ, ∑)+E _ImageBe minimized.

In one embodiment, provide a kind of being used for to learn the method for the distortion of this object, comprising: produce the initial reference shape of wanting divided objects from the image library of patient with objects; From expectation object general obtain generally the predetermined quantity of this object image, be N image, wherein N is greater than 1; The reference figuration that conversion produced is with each training shapes in N training shapes of foundation energy function coupling, and this comprises that each the training shapes distortion that makes in N the training shapes is to utilize parameter Θ _iCover reference figuration, parameter Θ _iBe to realize measuring of deflection that the covering of i training shapes in N the training shapes is required at each lattice point place; Each training shapes that is minimised as in N the training shapes by cost function obtains parameter Θ _iVector; Be the parameter Θ that is obtained _iN vector in each vector estimate uncertainly, this uncertainty is quantified as the covariance matrix ∑ _iProvide and be represented as Statistical model, the accumulation of this statistical model utilizes has mean value Θ _iWith the covariance ∑ _iNuclear carry out all information of N training shapes of modeling.

In one embodiment, calculate uncertainty, the probabilistic degree of this paraboloidal width means by supposing that this energy function can be similar to parabola at its minimum value place.

In one embodiment, reference figuration is on reference coordinate system, described reference coordinate system has the FFD grid, this FFD grid has a plurality of lattice points, and wherein covariance matrix provides to the projection on the lattice point and has with the component of reference figuration tangent and have ellipse with the component of reference figuration quadrature.

In one embodiment, this method additionally comprises: the image that obtains to expect object from patient; Discern interested expectation object in patient's the image by position reference shape on image, this comprises: the image that the reference figuration that conversion produced is obtained with foundation energy function coupling, this comprises makes the reference figuration distortion cover the image that is obtained to utilize parameter Θ, and parameter Θ is measuring of the required deflection of this covering of realization; Estimate uncertainty, this uncertainty is quantified as the covariance matrix ∑; Calculating energy function E _Shape, to obtain the probability of current shape in the statistical shape model; And make $E_{\mathrm{shape}}(\mathrm{\&Theta;},\mathrm{\&Sigma;})=-\log \left({\hat{f}}_H\right)$ Minimize, this comprises: calculate E _Shape(Θ, ∑) and ${\mathrm{dE}}_{\mathrm{shape}}(\mathrm{\&Theta;},\mathrm{\&Sigma;})/\mathrm{d\&Theta;}=-d\log \left({\hat{f}}_H\right)/\mathrm{d\&Theta;}$ Change Θ; Utilize the Θ that is changed to produce the covariance matrix that upgrades; Recomputate energy function E _Shape

Use is used for the variational technique of cutting apart based on knowledge of two-dimensional object, wherein is used to indicate shape than high order implicit expression polynomial expression.This method is estimated the uncertainty about the shape of institute's registration, and this uncertainty can be used to the priori technology modeling about objects with the non-parametric density estimation procedure based on bandwidth varying nuclear.This nonlinear model that utilizes uncertainty to measure combines with self-adaptive visual driving data item, and described self-adaptive visual driving data item is intended to separate objects and background.The promising result who obtains for the corpus callosum of cutting apart in the sagittal brain sections of MR center proves the potentiality of this framework.

More specifically, utilize range conversion implicitly to represent shape.In order to produce the model of structures of interest, this method utilization comes registration shape example based on the FFD of batten.This method comprises the probabilistic derivation of measuring that is illustrated in zero contour surface place registration.After dimension reduced, these were measured and the method combination of examining based on bandwidth varying, to obtain the density function to shape family modeling under consideration.Given new image is represented cutting procedure based on the Hamilton-Jacobi formula with the level set framework that changes, wherein the energy function utilization deformed shape of aiming at characteristics of image and the uncertainty of the registration between the model.

Utilize range conversion implicitly to represent shape.In order to produce the model of structures of interest, utilize FFD to come registration shape example based on batten.The main contribution of this paper is the probabilistic derivation of measuring that is illustrated in zero contour surface place registration.After dimension reduced, these were measured and the method combination of examining based on bandwidth varying, to obtain the density function to shape family modeling under consideration.Given new image, represent cutting procedure with the level set framework that changes, (referring to " the Fronts propagating withcurvature-dependent speed:Algorithms based on theHamilton-Jacobi formulation " of S.Osher and J.Sethian, Journal of ComputationalPhysics, 79:12-49,1988) wherein the energy function utilization deformed shape of aiming at and the uncertainty of the registration between the model with characteristics of image.

Accompanying drawing and below explanation in set forth one or more embodiments of the detail of the present invention.Other features of the present invention, purpose and advantage will be according to instructions and accompanying drawings and according to claim and apparent.

Description of drawings

Fig. 1, be thereby that Figure 1A and Figure 1B are according to priori of the present invention, as to be used to produce object so that produce the process flow diagram of process of the statistical shape model of object;

Fig. 2, be Fig. 2 A and Fig. 2 B be according to of the present invention, be used for utilizing the statistical shape model that process produced by Fig. 1 from the process flow diagram of the process of patient's image cutting object;

Fig. 3 be by Fig. 1 process produced, implicit expression is shown than high-order moment with have the set of diagrams of the uncertain callosal registration of estimating;

Fig. 4 helps to understand according to the corpus callosum of process of the present invention and one group of histogram of background area;

Fig. 5 A-5C illustrates and utilizes callosal uncertain cutting apart of estimating; Fig. 5 A illustrates the automatic coarse positioning of model, and Fig. 5 B illustrates cutting apart by the affined transformation of model; Fig. 5 C illustrates the local deformation of utilizing the FFD grid and about cutting apart that the uncertainty of registration/cutting procedure is estimated; And

Fig. 6 illustrates the additional partition result that utilization is measured according to the uncertainty of the present invention's acquisition.

Similar Reference numeral among the different figure is represented similar element.

Embodiment

With reference now to Fig. 1 and 2,, shows the process that is used for cutting apart this object from the image of patient with objects.This process at first comprises the generation of the priori of object, thereby produces the statistical shape model of object, and the step 100 among Fig. 1 is to 114.Then, the statistical shape model that this process utilization is produced is cutting object from patient's image (magnetic resonance image (MRI) (MRI) here), the step 200-208 among Fig. 2.

The generation of statistical shape model

With reference to figure 1, this process produces the initial reference shape of the objects that will cut apart, step 100.This reference figuration model is positioned on reference coordinate system with FFD grid, for example x-y Cartesian coordinate system, this FFD grid has a plurality of (being M here) lattice point.

Then, this process obtain generally from expectation object general this object predetermined quantity, be N image, so that N training shapes to be provided, wherein N is greater than 1, step 102.Reference coordinate system in the step 100 of that each the training shapes initial reference in these training shapes has is a plurality of (being M here) lattice point.

Then, this process is carried out conversion to the reference figuration that produces in step 100, with each training shapes in N the training shapes of foundation energy function coupling acquisition in step 102, step 104.Here, energy function is the reference figuration after the conversion and the function of the measures of dispersion between the training shapes.More specifically, conversion comprises each the training shapes distortion that makes in N the training shapes, so that it utilizes parameter Θ _iCover reference model, described parameter Θ _iBe measuring of deflection (translation vector) of the covering of i training shapes needing in each lattice point place, be used for realizing N training shapes.The conversion of reference model (for example affine or FFD (FFD) conversion) is parameter Θ _iThe smooth function of finite set.By minimizing of this training shapes in suitable cost function, for example N training shapes and the distance between the reference model after the conversion, obtain parameter ' Θ at each training shapes in N the training shapes _i' vector.Therefore, there is parameter Θ in each training shapes in N the training shapes _iVector, wherein like this each vector in the vector has M the element element of each lattice point in M the lattice point (just at), and each element has a pair of component (component on component on the x direction and the y direction).

Then, this process is each the training generation parameter ' Θ in N the training that obtains in step 102 _i' vector, and obtain parameter ' Θ _i' one group of ' N ' individual vector, each vector in N vector has M element, each element in this M element has two components, step 106.

Then, this process is the parameter ' Θ that obtains from step 106 _i' N vector in each vector estimate degree of uncertainty, step 108.Utilize with N training shapes in i training shapes, the Hessian of cost function that just shape " i " is relevant calculate degree of uncertainty.Uncertainty is quantified as covariance matrix ' ∑ _i'.Then, the transformation parameter of supposing the registration of shape ' i ' is followed and is had average Θ _iWith the standard deviation ∑ _iGaussian distribution.Can be by the supposition energy function at its minimum value place with quadric form, para-curve (quadratic function x for example here ^T∑ x) is similar to and calculates uncertainty.(2M dimension) paraboloidal width is equivalent to uncertainty.If parabola is very narrow, then energy is rapid at its minimum value place, and has the little uncertainty about parameter value, energy minimum when this parameter value.When projecting to covariance matrix on the lattice point, can be used in the uncertainty that the ellipse that elongates on bigger probabilistic direction is represented the lattice point place.In the situation of smooth linear profile, one-component and shape tangent, and another component and shape quadrature.

Then, utilize the estimated uncertainty that obtains in step 108, this process is that each training shapes in N the training shapes that obtains in step 102 produces covariance matrix ' ∑ _i', step 110.The statistical model of supposing the expression distortion has the estimated probability density function of summation that utilizes all ' N ' individual nuclears.Nuclear is to be used for the elementary probability distribution that non-parametric density is estimated: it is nonparametric that this statistical model is said to be, because the quantity of theoretical coker (' N ') is unrestricted, and has many more nuclear, and statistical model is just good more.

Then, the predetermined quantity R in the training set of this process removal step 102 in the employed N training shapes, thus stay K training shapes (wherein K is big, and is more much smaller than N), step 112.The R that an is removed image not too helps to produce statistical shape model.A selected K shape is those maximized shapes of likelihood that make whole training set.Application is depended in selection to K; It is to assess the cost (with the K linearity) and if add another sample to trading off between the increase of concentrating the likelihood that is obtained of a selected K shape (nuclear just).

Then, utilize with the covariance ∑ _iBe centered in ' Θ _i' the summation from ' K ' individual gaussian kernel of step 112, this process produces final statistical model, step 114.In fact, ' Θ _i' only comprising the coordinate of FFD grid, global affine transformation is not the part of study.Statistical model provides one group of statistical parameter, for example mean value and with the deviation of mean value, the feature of the class of objects.Statistical model can be represented as then

(equation 3), it is K and has mean value Θ _iWith the covariance ∑ _iThe summation of gaussian kernel.

Cutting object from patient's image

Refer again to Fig. 2, this process is used and reference model identical in step 100, step 200.This process obtains the image (I) of desired object from patient, and this image is arranged in image area, step 202.

This process uses matching technique to discern interested desired object in patient's the image, step 204 then in image area.More specifically, according to utilizing based on the estimated affined transformation of the cutting techniques of fundamental region (utilizing translation, rotation, convergent-divergent and shearing), position reference model on the image that this process is obtained in step 202.That is the overall situation, is affined transformation.

In step 206, except that the previous global change that obtains, use local matching technique.More specifically, this is the FFD grid with the individual lattice point of identical the having of employed FFD grid ' M ' in step 104.The FFD conversion is directly applied to reference model from step 200, and then be applied in the affined transformation that obtains in the step 204, with will be with reference to being transferred to image area from the model territory.

Then, this process is according to the statistical shape model calculating energy function E that obtains in the step 114 _Shape,, and make in the following manner with the probability of the current shape in the acquisition statistical shape model $E_{\mathrm{shape}}(\mathrm{\&Theta;},\mathrm{\&Sigma;})=-\log \left({\hat{f}}_H\right)$ Minimize:

Calculate $E_{\mathrm{shape}}(\mathrm{\&Theta;},\mathrm{\&Sigma;})=-\log \left({\hat{f}}_H\right)$ With ${\mathrm{dE}}_{\mathrm{shape}}(\mathrm{\&Theta;},\mathrm{\&Sigma;})/\mathrm{d\&Theta;}=-d\log \left({\hat{f}}_H\right)/\mathrm{d\&Theta;}$ Change Θ; Utilize the Θ that is changed to produce the covariance matrix that upgrades; Recomputate energy function E _Shape, step 208.

More specifically, be the given one group of transformation parameter of round-robin current iteration, be the current uncertain ∑ of cutting apart calculating based on image _ΘCurrent uncertainty is used to calculating energy function E in conjunction with the current estimation of Θ then _ShapeShape components and obtain the probability of the current shape in the statistical shape model.Want to make and belong to statistical model The probability maximization of profile, this is equivalent to and makes $E_{\mathrm{shape}}(\mathrm{\&Theta;},\mathrm{\&Sigma;})=-\log \left({\hat{f}}_H\right)$ Minimize.Utilize current shape (when current transformation parameter is applied to reference figuration), the picture content E of calculating energy function _ImageThis image term is similar based on the expection shade of the gray scale of the outside of the shape in the class Sihe image of the expection shade of the gray scale of the inside of the shape in the image (I) and object and background.Gross energy is two energy term E _ShapeAnd E _ImageSummation.This process utilizes gradient reduced minimum algorithm how to determine to change transformation parameter to the smaller value of energy.Minimize step according to this and estimate new transformation parameter, and this process iteration.More specifically, calculate $E_{\mathrm{shape}}(\mathrm{\&Theta;},\mathrm{\&Sigma;})=-\log \left({\hat{f}}_H\right)$ And E _Image, changing Θ, new covariance matrix is calculated as ∑ ^-1 _ΘThereby, so that calculate new $E_{\mathrm{shape}}(\mathrm{\&Theta;},\mathrm{\&Sigma;})=-\log \left({\hat{f}}_H\right)$ And E _Image, until total energy function E _ShapeAdd E _ImageBe minimized.

When realizing the cost minimum of a function in step 208, this process withdraws from iterative loop, to produce final segmentation result.

Callosal cutting apart

Be applied to example with top in conjunction with the described process of Fig. 1 and 2 below, here this process is used to cut apart corpus callosum.Corpus callosum is to connect a left side in the brain and the thick nerve fibre bundle of right hemisphere.It is considered to be responsible for the load that balance is crossed over the learning tasks of each hemisphere, makes each hemisphere carry out some task specially.When not learning, it is responsible for two interhemispheric most of communications of route.This is to have researched and developed surgical procedure cutting why to have callosal reason among the patient of serious epilepsy, and drug therapy is invalid for described serious epilepsy.In addition, several studies shows: callosal size and dimension is relevant with various types of cerebral function obstacles, for example dislexia, J.M.Rumsey, M.Casanova, G.B.Mannheim, N.Patronas, N.DeVaughn, S.D.Hamburger, T.Aquino, Corpuscallosum morphology, as measured with MRI, in dyslexic men, Biological Psychiatry, 39 (9): 769-777,1996, or schizophrenia, M.Frumin, P.Golland, R.Kikinis, Y.Hirayasu, D.F.Salisbury, J.Hennen, C.C.Dickey, M.Anderson, F.A.Jolesz, W.E.L.Grimson, R.W.McCarley and M.R.Shenton, Shape differences in the corpus callosumin first-episode schizophrenia and first-episode psychoticaffective disorder, American Journal of Psychiatry, 159:866-866,2002.Therefore, the neurologist is to checking corpus callosum and its form perception interest of analysis.Magnetic resonance imaging (MRI) is a kind of safety and non-invasive instrument that is used to make the corpus callosum imaging.Because manual delineation may be very time-consuming,, we how can be used to cut apart the corpus callosum that hits exactly in the sagittal MR section so proving our algorithm.

Therefore, with reference to figure 1, provide the reference figuration MODEL C _MODEL, step 100.Training set { the C of N shape of expression structures of interest is provided ₁, C ₂..., C _N, step 102.Then, this process is carried out the shape registration based on range conversion (the affine FFD that adds), step 104, this is 11/366 at common unsettled sequence number, 236, that on March 2nd, 2006 submitted to, name be called " Methods forEntity Identification ", the invention people is M.Taron, N.Paragios is described in the patented claim of M.-P.Jolly, this patented claim is transferred to the assignee identical with the present invention, and here the whole themes with this application are incorporated herein by reference.Here, be No.60/664 also with sequence number, 503, on March 23rd, 2005 U.S. Provisional Patent Application that submit to, that be transferred to the assignee identical with the present invention be incorporated herein by reference.

More specifically, modelling task comprises that the probability that recovers this collection represents.In order to remove all posture change from training set, all shapes must be according to affined transformation and common posture registration.Utilize the implicit expression polynomial expression to make the reference figuration MODEL C _MODELWith training set C _iThe local registration of each sample.At first registration process (step 104) will be described, probabilistic calculating will be described then about the model of institute's registration.Uncertainty is measured expression and is still mated C _iMODEL C _MODELThe permission variation range of distortion.These uncertainties are used to the estimation of the probability density function of deforming step 114 then.

By the polynomial registration of implicit expression, step 104

In traditional active shape model (ASM), initial step is used to recover the discretize profile of mould shapes and the tangible consistance between the training example.In this framework, make mould shapes and come each sample non-rigid registration of self-training, and in fact set up statistical shape model according to the parameter of the conversion that is recovered.Utilize the Euclidean distance conversion to represent shape Ci in the implicit expression mode, referring to M.Leventon, the StatisticalShape Influence in Geodesic Active Controus of E.Grimson and Faugeras, IEEE Conferenceon Computer Vision and Pattern Recognition, the I:316-322 page or leaf, 2000, and N.Paragios, M.Rousson and V.Ramesh " MatchingDistance Functions:A Shape-to-Area Variational Approach forGlobal-to-Local Registration ", European Conference onComputer Vision, the II:775-790 page or leaf, 2002.Under the 2D situation, consider the function that on image area Ω, is limited:

${\mathrm{\&phi;}}_{C_i}\left(x\right)=\left\{\begin{array}{cc}0& x\&Element;C_i\\ +D(x,C_i)& x\&Element;R_{C_i}\\ -D(x,C_i)& x\&Element;R_{C_i}^{-}\end{array}\right.$

R wherein _CiBe C _iInstitute's area surrounded.This space is constant for translation, rotation, and also can be modified with the variation of explanation convergent-divergent.This expression is used to solve similarity registration (N.Paragios with the simple type identifier that resembles difference of two squares sum, the Matching Distance Functions of M.Rousson and V.Ramesh: " A Shape-to-AreaVariational Approach for Global-to-Local Registration ", European Conference on Computer Vision, mat woven of fine bamboo strips II:775-790 page or leaf, 2002), or be used for the mutual information of affined transformation, referring to X.Huang, N.Paragios and D.Metaxas " Registration of Structures in ArbitraryDimensions:Implicit Representations, Mutual Information ﹠amp; Free Form Deformations ", Technical Report DCS-TR-0520, Division of Computer﹠amp; Information Science, RutgersUniversity, 2003.

The reservation framework that is used for density Estimation does not put on the reference model that is used for registration to any constraint.In practice, the shape facility of alternative is cut apart.Do not losing under the general situation, can be C _MODELSelect C ₁Smoothed version.Now, make all profiles and the C of training set according to affined transformation _MODELRegistration, and from now on, will be { C ₁, C ₂..., C _NBe expressed as the training set of global registration.

Local registration is conclusive for modelling.

Transformation parameter, step 106

For this reason, be intended to recover to pass through vector theta _iParameterized reversible transformation (differomorphism) L _{Θ i}, described vector theta _iSet up training set C _iEach profile and MODEL C _MODELBetween mapping one to one:

L _Θi:R ²→R ²?and?L _Θi(C _MODEL)≈C _i

Work as L _ΘWhen being selected as having the 2D polynomial expression of coefficient Θ with suitable base, expression formula _ oL _ΘInherit the polynomial unchangeability characteristic of implicit expression, the linear transformation that promptly is applied to Θ relates to the linear transformation that is applied to data space.Here, the simple polynomial expression coiling of this method utilization technology solves the needs of local registration: FFD method (FFD), referring to D.Rueckert, L.I.Sonoda, C.Hayes, D.Hill, " the Nonrigidregistration using free-from deformations:Application tobreast MR images " of M.Leach and D.Hawkes, IEEE Transactions on MedicalImaging, 18:712-721,1999.The essence of FFD is to make the object distortion by the rule control dot matrix that operation is covered on its embedded space.This process utilization cube B batten FFD comes the modeling to local deformation L.Consider the square lattice of M * N point, [{ P ⁰ _{M, n}; (m, n) ∈ [1; M] * [1; N]].In this case, the vector of the parameter Θ of qualification conversion L is the displacement coordinate of control dot matrix.Θ has size 2MN:

Θ＝{δP _m，n}＝{δP ^x _m，n，δP ^y _m，n}；(m，n)∈[1；M]×[1；N]

Limit the displacement of pixel x of the distortion of given control dot matrix according to cube tensor product of B batten, " Free-form deformation of solidgeometric models " referring to T.Sederberg and S.Parry, Proceedings SIGGRAPH ' 86,20:151-160,1986.Because FFD is linear when parameter Θ=δ P, so it can be by introducing X (x) a[2 * 2MN] matrix represents with the form of compactness:

L (Θ; X) ∑ ∑ B _i(u) B _j(v) (p ⁰ _{I, j}+ δ P _{I, j}Wherein (u v) is the coordinate of x to)=x+X (x) Θ, and (B _i, B _j) be a cube B spline base function.

Local registration is equivalent to now and finds best lattice structure so that covered structure overlaps.Owing to the range conversion of structure corresponding to the shape of global alignment, thus can regard the data-driven item to the summation of the difference of two squares (SSD) as, to resume training the Elements C of collection _iAnd MODEL C _MODELBetween deformation domain L (Θ; X) (correspond respectively to range conversion _ _iWith _ _M):

E _data(Θ)＝∫∫ _Ωχ _α(_ _i(x))[_ _i(L(Θ；X))-_M(X)] ²dx (1)

χ wherein _α(_ _i(x)) be that qualification profile width on every side is the indicator function of the band of α.For the systematicness of the registration that further keeps being recovered, can consider additional level and smooth on the deformation domain δ L.Consider to calculate upward effectively level and smooth here:

E _smooth(Θ)＝∫∫ _Ω(|L _xx(Θ；x)| ²+2|L _xy(Θ；x)| ²+|L _yy(Θ；x)| ²)dx

Can drive item and smoothness constraint component integration to data now, to recover the local deformation component by the infinitesimal analysis that changes.The minimum value that is reached is expressed as Θ _iYet, can require the local deformation territory to be not enough to characterize two registrations between the shape.Data are usually destroyed because of noise, and therefore the registration that utilizes deformable model to obtain again may be coarse.Therefore, the recovery uncertainty is measured, referring to K.Kanatani, " Uncertainty modeling andmodel selection for geometrici nference ", IEEE Trans.PatternAnal.Mach.Inte11., 26 (10): 1307-1319,2004, it allows the sign of the permission variation range of registration process was the outstanding condition of accurate shape modeling.

Uncertainty to the registration shape is estimated step 108,110

The target of this process is by revising at first at C.Stewart, " The dual bootstrap iterative closest pointalgorithm with application to retinal image registration " (IEEE Trans.Med.Img. of C.-L.Tsai and B.Roysam, 22:1379-1394,2003) in the method introduced recover the uncertainty of the vector theta of [2MN * 2MN] covariance matrix form.This process considers that it is the zero level collection of range conversion to the quality of the local registration of shape.Therefore, in limiting case, be formulated E _Data, wherein α, be that the size of the limited band around the mould shapes is tending towards 0.The data item of energy function can be represented as now:

E _data(Θ)＝∮_ ² _i(L(Θ；x))dx＝∮_ ² _i(x ²)dx

Wherein represent x '=L (Θ _iX).Consider that q offs normal in C _iOn the nearest point of x '.Because _ _iBe assumed that the Euclidean distance conversion, it also satisfies condition || _ _ _i(x ') ||=1.Therefore, can represent in the following manner single order in the neighborhood of x ' _ _iValue:

_ _i(x′+δx′)＝_ _i(x′)+δx′__ _i(x′)+o(δx′)＝(x′+δx′-q)__ _i(x′)+o(δx′)

Have dot product _ _iThis part represent to reflect the condition of putting curve distance that adopted.Under following supposition, i.e. E when reaching the best _DataBe little, it is approximate to write traditional second order of second energy with following form:

The global minimum of localizing objects function ' E ' be equivalent to find have density exp (E/ β) ' the holotype of stochastic variable.Factor beta changes corresponding to the permission of the energy value around the minimum value.In the present case of second energy (and so Gaussian random variable), pass through ∑ ^-1 _{Θ i}=H _{Θ i}/ β makes the covariance of energy and Hessian directly related.This causes the following formula of covariance:

In the most general situation, can require matrix H _ΘBe irreversible, because registration problems is under constraint.Then, by the use of arbitrarily small positive parameter γ, must be towards Θ _iEstimation of covariance matrix introduce additional constraint:

This causes the covariance matrix of parameter estimation:

Wherein " I " is unit matrix.

Density function and nuclear based on mixed nucleus are selected step 112

All shapes of now having aimed at training set can be used the canonical statistics technology as PCA or ICA, to recover linear Gauss model.Therefore but in the most general situation, the shape that relates to interested especially object non-linearly changes, and the supposition of this such simple parameter model of image height is quite unrealistic.Therefore, in our method, the nonparametric form of probability density function is proposed.

Suppose { Θ ₁... Θ _NBe N vector of the parameter relevant with the registration of N sample of training set.Consider that this group vector is the random sample that extracts from the density function f that describes shape, fixed-bandwidth Density Estimator device comprises:

$\hat{f}\left(\mathrm{\&Theta;}\right)=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\frac{1}{{\left|\right|H\left|\right|}^{-1/2}}K\left(H^{-1/2}(\mathrm{\&Theta;}-{\mathrm{\&Theta;}}_i)\right)$

Wherein H is that symmetry is determined positive quantity (bandwidth matrices), and K represents to have the gaussian kernel placed in the middle of unit covariance.The fixed-bandwidth method is usually owed level and smooth and was produced level and smooth in reverse situation in the region generating with sparse observed reading.

Have endorsing being used to of bandwidth varying this condition is encoded, and for utilizing the variable uncertainty relevant with sample point that frame mode is provided.In the literature, rely on the Density Estimator method that changes bandwidth and be commonly referred to as self-adaptive kernel.Utilize bandwidth match to carry out density Estimation, referring to the Kernel Smoothing of M.Wand and M.Jones, Cha pman﹠amp in the sparse nuclear of data; Ha11, nineteen ninety-five.

In present case, vector { Θ _iWith relevant uncertainty { ∑ _iOccur together.In addition, the some Θ that density function is estimated is corresponding to the model of distortion, and therefore also relevant with measuring of uncertain ∑.In order to illustrate that they are own and the uncertainty of estimation point estimated to sample point, adopt and mix estimator, referring to A.Mittal and N.Paragios, " Motion-basedbackground substraction using adaptive kernel densityestimation ", Computer Vision and Pattern Recognition, volume 2, the 302-309 pages or leaves, 2004:

$\hat{f}(\mathrm{\&Theta;},\mathrm{\&Sigma;})=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}K(\mathrm{\&Theta;},\mathrm{\&Sigma;},{\mathrm{\&Theta;}}_i,{\mathrm{\&Sigma;}}_i)$

$=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\frac{1}{{\left|\right|H({\mathrm{\&Sigma;}}_{\mathrm{\&Theta;}},{\mathrm{\&Sigma;}}_{{\mathrm{\&Theta;}}_i})\left|\right|}^{-1/2}}K{({\mathrm{\&Sigma;}}_{\mathrm{\&Theta;}},{\mathrm{\&Sigma;}}_{{\mathrm{\&Theta;}}_i})}^{-1/2}(\mathrm{\&Theta;}-{\mathrm{\&Theta;}}_i)$

Wherein select H (∑ _Θ, ∑ _{Θ i})=∑ _Θ+ ∑ _{Θ i}As the bandwidth function, (roll up 2 as A.Mittal and N.Paragios at Computer Vision and Pattern Recognition, the 302-309 page or leaf, 2004) in proposed among the Motion-based background substractionusing adaptive kernel density estimation that delivered.

Utilize this estimator, when comparing, reduce slowlyer in big probabilistic direction upper density with other directions.

Statistical shape model, step 112

This measure the part that can be used to be estimated as training set now new samples probability and the nonparametric form of observed density is described.Yet calculating is time-consuming, because the calculating that it causes large matrix to be inverted.Because the quantitative aspects of the sample of cost in training set is linear, so exist by selecting most representative nuclear to reduce the remarkable needs of its radix.

The quality that PRML canonical representation model and data are approximate.Use recurrence suboptimum algorithm to select nuclear, and therefore set up the maximized compact models of likelihood that makes whole training set.

Consideration is from having mean value and the uncertain training set of estimating ${\{X_i=\}\left({\mathrm{\&Theta;}}_i{\mathrm{\&Sigma;}}_i\right)}_{i=1}^k$ The collection Z of K the nuclear that extracts _K={ X ₁, X ₂..., X _K.Log-likelihood according to the whole training set of this model is:

Extract new nuclear X from this training set _K+1, because this nuclear makes and Z _K+1=Z _K∪ X _K+1Relevant amount C _K+1Maximization.Can select identical nuclear several times, so that keep the sequence C of increase _KTherefore, at Z _KThe middle nuclear X that selects _iAlso with weight factor ω _iRelevant.In case finished this selection, just about Z _KEstimate mixed estimator:

${\hat{f}}_H(\mathrm{\&Theta;},\mathrm{\&Sigma;})=\frac{1}{N}\underset{({\mathrm{\&Theta;}}_i{,\mathrm{\&sigma;}}_i,{\mathrm{\&omega;}}_i)\&Element;Z_K}{\mathrm{\&Sigma;}}{\mathrm{\&omega;}}_{i}K(\mathrm{\&Theta;},\mathrm{\&Sigma;},{\mathrm{\&Theta;}}_i,{\mathrm{\&Sigma;}}_i))---\left(3\right)$

Be applied to callosally cut apart step 200-212 based on shape

Let us considers to exist and will reproduce the image I of corpus callosum structure.Recall us and have callosal model (step 200) now: can utilize affined transformation and FFD carry out conversion shape and the distortion shape how to belong to measuring of training shapes family well.

Therefore, obtain image, MRI here, step 202 from patient.Suppose _ _MRange conversion for reference model.As mentioned above, cut apart the callosal overall situation that comprises in describing I and local deformation _ _M(step 204-206).Suppose that A is that the affined transformation and the L (Θ) of model is the local deformation of utilizing FFD of this model, introduced as former.

From now on, suppose known callosal visual characteristic π _CorThe visual characteristic π of () and local peripheral region _Bck().Be equivalent to following energy minimizing about parameter Θ and A callosal cutting apart:

$E_{\mathrm{image}}(A,\mathrm{\&Theta;})=-{\&Integral;\&Integral;}_{R_M}\log \left[{\mathrm{\&pi;}}_{\mathrm{cor}}\left(I(A\left(L\left({\mathrm{\&Theta;}}_{;}x\right)\right)\right)\right]\mathrm{dx}-{\&Integral;\&Integral;}_{\mathrm{\&Omega;}-R_M}\log \left[{\mathrm{\&pi;}}_{\mathrm{bkg}}\left(I\left(A\left(L(\mathrm{\&Theta;},x\right)\right)\right)\right]\mathrm{dx}$

R wherein _MExpression C _MInside.Yet the direct calculating of variation comprises image gradient, and usually owing to the discretize in model territory converges on wrong separating.In the sort of situation,, limit of integration is transformed into image (referring to appendix) by implicitly introducing inverse transformation.To recover the bimodal part in the image space now.This territory R _CorThe following parameter [A, Θ] that depends on conversion of qualification:

R _cor＝A(L(Θ，R _M))y＝A(L(Θ，x))。

The real image item of the energy that will be minimized becomes then:

$E_{\mathrm{image}}(A,\mathrm{\&Theta;})=-\&Integral;{\&Integral;}_{R_M}\log [{\mathrm{\&pi;}}_{\mathrm{cor}}\left(I\left(y\right)\right)\mathrm{dy}-\&Integral;{\&Integral;}_{\mathrm{\&Omega;}-R_M}\log [{\mathrm{\&pi;}}_{\mathrm{bkg}}\left(I\left(y\right)\right)\mathrm{dy}---\left(4\right)$

Wherein consider statistical independence in pixel and supposition level place.In fact, can utilize the Mumford-Shah principle to recover the distribution [π of callosal distribution and peripheral region with the square formula that increases progressively _Cor, π _Bkg], referring to " the Boundary detection byminimizing functionals " of D.Mumford and J.Shah, IEEE Conference on Computer Visionand Pttern Recognition, 22-26 page or leaf, 1985.In present case, utilize expectation maximization (Expectation-Maximization) algorithm as shown in Figure 4, estimate each distribution by the mixing fit image histogram that makes Gauss.The energy term of the nonparametric framework of early introducing based on the utilization of shape also is subjected to influence according to probabilistic covariance matrix of the Model Calculation of institute's conversion partly.Calculate this covariance matrix in the mode that is similar to equation (2), wherein difference is: it can only illustrate the linear structure and the therefore variation of the Θ of the tangential displacement of permission generation profile of the model of institute's conversion:

Wherein

Be the distortion A (L (Θ)) situation under _ _MConversion.Directly calculate and cause:

Wherein ' com ' represents the matrix of complementary divisor.Utilize the energy term E of the symbol following introducing identical then based on shape with symbol in the equation (3) _Shape:

$E_{\mathrm{shape}}(\mathrm{\&Theta;},{\mathrm{\&Sigma;}}_{\mathrm{\&Theta;}})=-\log \left({\hat{f}}_H(\mathrm{\&Theta;},\mathrm{\&Sigma;})\right)$

According to parameter A and Θ, pass through E=E _Image+ E _ShapeVariation calculating and utilize normal gradients to descend and realize making global energy to minimize step 208.

Experimental result

We have been applied to our method callosal the cutting apart in the sagittal brain sections of MR center.

First step is to set up callosal model.Utilize gradient to descend and carry out minimizing of registration energy.Concurrently, we successfully improve the size α (from 0.3 times to 0.05 times of the size of shape) of the band around the profile, and we increase diffeomorphic complicacy ([7 * 12] dot matrix that utilizes rule from affined transformation to FFD) simultaneously.

Fig. 3 illustrates FFD distortion and uncertain oval example.These ellipses are when the covariance matrix ∑ that will (be of a size of 168 * 168) _ΘThe expression of the 2D quafric curve that is obtained when being projected on the reference mark.Therefore it does not allow us to represent correlativity between the reference mark.

By foundation A.Lundervold, N.Duta, the method location initial profile that T.Taxt and A.Jain propose in the Model-guided segmentation of corpuscallosum in MR images among the CVPR (1231-1238 page or leaf, 1999) comes the initialization cutting procedure.Descend by gradient and to carry out energy minimization, estimate PDF π by Gauss's mixing simultaneously _CorAnd π _BkgFig. 4 illustrates the histogram of callosal typical image.How this mixing that illustrates two Gaussian distribution can represent the independent histogram of corpus callosum and background well respectively.(in Fig. 5 and Fig. 6) represented segmentation result together with relevant uncertainty.In Fig. 5, each step of demonstration cutting procedure: leftmost image illustrates the auto-initiation of profile, and middle image is illustrated in and has recovered affined transformation profile afterwards, and the image on the right illustrates local deformation.The method that Fig. 6 illustrates additional result and we are shown can be handled the big variation of callosal different shape and picture contrast.Result in the lower left quarter image is not desirable as can be seen.Usually, failure may be since shape constraining is enough strong and image in the contrast domination fact of being out of shape.And, may be to utilize current probability density function (Probability Density Function (PDF)) to catch this specific callosal shape, because it has been reduced to only 10 nuclears.

Conclusion

Described to be used for utilizing and to have illustrated that the nonparametric bandwidth varying of the error in registration and the cutting procedure examines the method that priori is described at cutting procedure.This method can produce the extraordinary model of objects and produce extraordinary segmentation result.Yet the nuclear system of selection that proposes has above demonstrated some restrictions in practice.Therefore the strong needs that have the more effective and compact estimator of setting up the change of shape PDF that illustrates that these uncertainties are measured.

Notice that it also is important that this method can be expanded to higher dimension.In 3D, set up model and cut apart have big variable to as if the next procedure of our research work.

At last, but quite important, probabilistic introducing of directly measuring in image as the part of cutting procedure will provide the part of degree of confidence to measure, and can be considered to based on the key breakthrough in the field of the object extraction of knowledge.

Appendix

In this section, we provide energy term E _ImageSome further investigations of infinitesimal analysis of derivative.At first need to introduce the contrary differomorphism that the Heaviside that is labeled as H distributes and is labeled as the AoL (Θ) of G (Θ).Therefore this differomorphism checking:

A(L(Θ，G(Θ，y)))＝y (5)

For simpler symbol, we also propose:

D(x，y)＝-H(_ _M(x))log(π _cor(I(y)))-(1-H(_ _M(X)))log(π _bkg(I(y)))

So the image term of energy (equation 4) can be rewritten as:

$E_{\mathrm{image}}\left(\mathrm{\&Theta;}\right)=\underset{\mathrm{\&Omega;}}{\&Integral;}D(G(\mathrm{\&Theta;},y),y)\mathrm{dy}$

When equation (5) during to the Θ differentiate and the expression formula substitution dE that will obtain at dG/d Θ _Image(Θ)/during the expression formula of d Θ, obtain following formula:

$\frac{{\mathrm{dE}}_{\mathrm{image}}\left(\mathrm{\&Theta;}\right)}{\mathrm{d\&Theta;}}=-\underset{\mathrm{\&Omega;}}{\&Integral;}\frac{\&PartialD;D}{{\&PartialD;x}^T}(G(\mathrm{\&Theta;},y),y){\left[\frac{\&PartialD;(\mathrm{AoL}}{{\&PartialD;x}^T}(G(\mathrm{\&Theta;},y),\mathrm{\&Theta;})\right]}^{-1}\frac{\&PartialD;\left(\mathrm{AoL}\right)}{{\&PartialD;\mathrm{\&Theta;}}^T}\left(G(\mathrm{\&Theta;},y)\right)\mathrm{dy}$

(Θ y) changes integration variable according to differomorphism x=G now

$\frac{{\mathrm{dE}}_{\mathrm{image}}\left(\mathrm{\&Theta;}\right)}{\mathrm{d\&Theta;}}=-\underset{\mathrm{\&Omega;}}{\&Integral;}\frac{\&PartialD;D}{{\&PartialD;x}^T}(x,A(L(\mathrm{\&Theta;},x),y)\mathrm{com}{\left[\frac{\&PartialD;\left(\mathrm{AoL}\right)}{{\&PartialD;x}^T}(x,\mathrm{\&Theta;})\right]}^T\frac{\&PartialD;\left(\mathrm{AoL}\right)}{{\&PartialD;\mathrm{\&Theta;}}^T}(x,\mathrm{\&Theta;})\mathrm{dx}$

Wherein ' com ' represents the matrix of complementary divisor.When the first variable explicitly with respect to it calculated the partial derivative of D, this integration further was simplified to the curvilinear integral along reference model:

$\frac{{\mathrm{dE}}_{\mathrm{image}}\left(\mathrm{\&Theta;}\right)}{\mathrm{d\&Theta;}}=-\underset{C_{\mathrm{mode}t}}{\&Integral;}\tilde{D}\left(A\left(L(\mathrm{\&Theta;},x)\right)\right){[\mathrm{com}\left(\frac{\&PartialD;\left(\mathrm{AoL}\right)}{{\&PartialD;\mathrm{\&Theta;}}^T}(x,\mathrm{\&Theta;})\right)\&CenterDot;\&dtri;{\mathrm{\&phi;}}_M\left(x\right)]}^T\frac{\&PartialD;\left(\mathrm{AoL}\right)}{{\&PartialD;\mathrm{\&Theta;}}^T}(x,\mathrm{\&Theta;})\mathrm{dx}$

Wherein

Be restricted to:

$\tilde{D}\left(y\right)=-\log \left({\mathrm{\&pi;}}_{\mathrm{cor}}\left(I\left(y\right)\right)\right)+\log \left({\mathrm{\&pi;}}_{\mathrm{bkg}}\left(I\left(y\right)\right)\right)$

This expression formula of derivative only relates to the profile in the model space.Resolve the entire image territory during iteration each time that therefore need employed gradient does not descend in our embodiment.On the contrary, our scan model profile only when iteration each time.Have only and work as at π _CorAnd π _BkgThe parsing of image is only necessary (per 20 iteration) when reappraising the parameter of Gaussian Mixture.

A plurality of embodiment of the present invention has been described.However, be understood that and under the situation that does not deviate from the spirit and scope of the present invention, carry out various modifications.Therefore, in the scope of other embodiment claim below.

Claims (9)

1, a kind of method that is used for cutting apart from the image of patient with objects this object comprises:

The reference figuration of this object that conversion produced mates each training shapes in a plurality of training shapes with the foundation energy function, and this comprises that each training shapes distortion that makes in the described training shapes is to utilize parameter Θ _iCover reference figuration, parameter Θ _iBe to realize measuring of deflection that the covering of i training shapes in N the training shapes is required at each lattice point place;

Obtain parameter Θ by each training shapes in the described training shapes of being minimised as of cost function _iVector;

Be the parameter Θ that is obtained _iVector in each vector estimate uncertainly, this uncertainty is quantified as covariance matrix Σ _i

For providing, a plurality of training shapes are represented as

Statistical model, this statistical model is to have mean value Θ _iWith covariance Σ _iThe summation of K gaussian kernel.

2, the method for claim 1, wherein cost function be between the reference model of the distance map that produces for one of described training shapes and institute's conversion the difference of two squares and.

3, the method for claim 1 additionally comprises:

Obtain to expect the image of object from patient;

Discern the interested expectation object in patient's the image by position reference shape on this image, this comprises:

The reference figuration that conversion produced, with the image that foundation energy function coupling is obtained, this comprises makes the reference figuration distortion cover the image that is obtained to utilize parameter Θ, and parameter Θ is measuring of the required deflection of this covering of realization;

Estimate uncertainty, this uncertainty is quantified as covariance matrix Σ;

The shape item of calculating energy function $E_{\mathrm{shape}}(\mathrm{\&Theta;},\mathrm{\&Sigma;})=-\log \left({\hat{f}}_H\right),$ To obtain the probability of current shape in the statistical shape model; And

The image term E of calculating energy function _Image, with the match of the shape in the evaluation map picture;

Make energy function E _Shape+ E _ImageMinimize.

4, method as claimed in claim 3 wherein makes $E_{\mathrm{shape}}(\mathrm{\&Theta;},\mathrm{\&Sigma;})=-\log \left({\hat{f}}_H\right)$ Minimize and comprise:

Calculate $E_{\mathrm{shape}}(\mathrm{\&Theta;},\mathrm{\&Sigma;})=-\log \left({\hat{f}}_H\right)$ And E _Image

According to E _Shape+ E _ImageDerivative change Θ;

Produce new covariance matrix as Σ _ΘThereby, so that calculate new $E_{\mathrm{shape}}(\mathrm{\&Theta;},\mathrm{\&Sigma;})=-\log \left({\hat{f}}_H\right)$ And E _Image, until E _Shape(Θ, Σ)+E _ImageBe minimized.

5, the method for claim 1, wherein cost function is the distance between the reference model of such training shapes in the described training shapes and institute's conversion.

6, be used to learn the method for the distortion of this object that obtains from the image library of patient with objects, comprise:

Produce the initial reference shape of wanting divided objects;

From expectation object general obtain generally the predetermined quantity of this object image, be N image, wherein N is greater than 1;

The reference figuration that conversion produced is with each training shapes in N training shapes of foundation energy function coupling, and this comprises that each the training shapes distortion that makes in N the training shapes is to utilize parameter Θ _iCover reference figuration, parameter Θ _iBe to realize measuring of deflection that the covering of i training shapes in N the training shapes is required at each lattice point place;

Each training shapes that is minimised as in N the training shapes by cost function obtains parameter Θ _iVector;

Be the parameter Θ that is obtained _iN vector in each vector estimate uncertainly, this uncertainty is quantified as covariance matrix Σ _i

Provide and be represented as

Statistical model, the accumulation of this statistical model utilizes has mean value Θ _iWith covariance Σ _iNuclear carry out the information of N training shapes of modeling.

7, method as claimed in claim 6 is wherein calculated uncertainty, the probabilistic degree of this paraboloidal width means by supposing that this energy function can be similar to parabola at its minimum value place.

8, method as claimed in claim 7, wherein reference figuration is on reference coordinate system, described reference coordinate system has overlapping FFD grid, this FFD grid has a plurality of lattice points, described lattice point has the position of representing with vector theta, wherein covariance matrix is represented as the ellipse that elongates on bigger probabilistic direction to the projection on the lattice point, and wherein under the situation of smooth linear profile, one-component and reference figuration tangent, and another component and reference figuration quadrature.

9, method as claimed in claim 6 additionally comprises:

Obtain to expect the image of object from patient;

Discern the interested expectation object in patient's the image by position reference shape on image, this comprises:

The image that the reference figuration that conversion produced is obtained with foundation energy function coupling, this comprises makes the reference figuration distortion cover the image that is obtained to utilize parameter Θ, and Θ is measuring of the required deflection of this covering of realization;

Estimate uncertainty, this uncertainty is quantified as covariance matrix Σ;

Calculating energy function E _Shape, to obtain the probability of current shape in the statistical shape model; And

Make E=E _Shape+ E _ImageMinimize, this comprises:

Calculate $E_{\mathrm{shape}}(\mathrm{\&Theta;},\mathrm{\&Sigma;})=-\log \left({\hat{f}}_H\right);$

Calculate E _Image

Change Θ;

Utilize the Θ that is changed to produce the covariance matrix that upgrades;

Recomputate energy function E=E _Shape+ E _Image

Images