CN1870006A - Effective nuclear density assess for horizontal collection divided shapes and brightness prior - Google Patents

Abstract

Methods and systems for image segmentation are disclosed. A nonlinear statistical shape model of an image is integrated with a non-parametric intensity model to estimate characteristics of an image and create segmentations of an image based on Bayesian inference from characteristics of prior learned images based on the same models

Description

Be used for shape that level set cuts apart and effective Density Estimator of brightness prior

The statement of relevant case

It is the rights and interests of 60/672,649 U.S. Provisional Application that the application requires in the application number that on April 19th, 2005 submitted to, and this application is incorporated herein by reference.

Technical field

The present invention relates to be used for the system and method for processing digital images.More specifically, the present invention relates to make the objects in the image and the image segmentation of the background separation of this object in image.

Background technology

Cutting apart is the problem that often runs in Flame Image Process.It is even more important when medical imaging, wishes under the situation of imaging once to extract object, for example organ or tumour to be used for further processing from image.

There are many different dividing methods to use.The effect of all dividing methods changes according to quality, application and many other factors of view data.

Cutting apart of medical image is especially difficult.In this field, the data of enormous quantity make cuts apart the difficulty that becomes.In addition, the quality of the view data that obtains from medical imaging devices is always not optimal.In addition, may be used to instruct diagnosis or treatment plan owing to cut apart, so the quality of cutting apart is normally very important.

Therefore, need new and improved method and system, these method and systems will produce cutting apart of image and image volume.

Summary of the invention

The invention provides a kind of method of using in as data one or more priori examples of object to come cutting object at set of diagrams.According to an aspect of the present invention, step comprises: determine the non-parametric estmation of characteristic of one or more priori examples of object in the subspace that one or more priori examples of object are crossed over, utilize the non-parametric estmation of one or more priori and by carrying out Level Set Method the cutting apart of alternative in this set of image data of optimizing Bayes's expression formula in the Bayes's expression formula that is subjected to this set of image data restriction.

This characteristic can be brightness.It also can be a shape.The characteristic of one or more priori examples of object can be based on the mean value of the characteristic relevant with each priori example in the priori example of object.The characteristic of one or more priori examples of object can be based on distance function.This expression formula can be an energy function.The characteristic of one or more priori examples of object can be translation or rotational invariants.The characteristic of one or more priori examples of object can be based on density function, for example cuclear density.

This expression formula can be:

$E(\mathrm{\α},h,\mathrm{\θ})=-{\∫}_{\mathrm{\Ω}}{H}_{\mathrm{\φ}}\log p_{\mathrm{in}}\left(I\right)+(1-H_{\mathrm{\φ}})\log P_{\mathrm{out}}\left(I\right)\mathrm{dx}-\log \left(\frac{1}{\mathrm{N\σ}}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}K\left(\frac{\mathrm{\α}-{\mathrm{\α}}_i}{\mathrm{\σ}}\right)\right),$

One aspect of the present invention provides the effective image partition method that utilizes level set to cut apart and utilize the priori of wanting divided image.

Another aspect of the present invention provides the statistics shape prior based on the precision of the efficient of PCA (based on principal component analysis (PCA)) method and nonparametric statistics shape in conjunction with low-dimensional.

Another aspect of the present invention is that the statistical property for the object in the image provides method of estimation.

Another aspect of the present invention is to cut apart for non-parametric level set distance function is provided.

Another aspect of the present invention is to come the distribution of shapes of object is carried out modeling by Density Estimator.

Another aspect of the present invention provides the Bayesian inference of level set dividing method as known priori.

Another aspect of the present invention provides the method that the probability brightness model that provides by the Density Estimator of using by the Luminance Distribution of the previous observation of known priori utilizes the monochrome information in the image best.

Another aspect of the present invention is to be provided for the method that level set that knowledge drives is cut apart by comprehensive several aspects of the present invention.

Description of drawings

Fig. 1 represents medical image and relevant luminance graph.

Fig. 2 represents different density maps.

Fig. 3 represents the effect of the shape interpolation of linear shape interpolation relative nonlinear.

Fig. 4 represents the effect of different prior models.

The image that Fig. 5 indicated object is cut apart.

Other image that Fig. 6 indicated object is cut apart.

Fig. 7 has illustrated the inventive method according to an aspect of the present invention.

Fig. 8 represents the figure of an image segmentation system.

Embodiment

The initial level set that proposes is handled as the method for propagating the interface in time.A finite element method for the simulation of Raleigh-Taylorinstability (Springer Lect.Notes in Math. referring to for example A.Dervieux and F.Thomasset, 771:145-158,1979) and Fronts propagation with curvature dependent speed:Algorithms based onHamilton-Jacobi formulations (the J.of Comp.Phys. of S.I.Osher and J.A.Sethian, 79:12-49,1988).

As the framework of image segmentation, Level Set Method has become and has become more and more popular.Key idea is with image area Ω  R ³In interface Γ  Ω impliedly be expressed as imbedding function φ: R ³The zero level collection of → Ω:

Γ＝{x∈Ω|φ(x)＝0} (1)

And launch Γ by expansion (propagate) imbedding function φ according to suitable partial differential equation.At first this level set form being applied to image segmentation is at V.Caselles, F.Catt é, T.Coll, with F.Dibos in 1993 at Numer.Math., the A geometric model for active contours in imageprocessing that delivers on the 66:1-31, R.Malladi, J.A.Sethian, with B.C.Vemuri in 1994 at SPIE Conferenceon Geometric Methods in Computer Vision II, volume 2031, the Atopology independent shape modeling scheme that delivers on the 246-258 page or leaf, and S.Kichenassamy, A.Kumar, P.J.Giver, A.Tannenbaum, with A.I.Yezzi in nineteen ninety-five at Proc.IEEE Intl.Conf.on Comp.Vis., the 810-815 page or leaf, Boston proposes among the Gradient flows and geometric active contourmodels that delivers on the USA.Two key advantages that are better than propagating at clear and definite interface are that the border Γ of specific parameterized independence and expression impliedly can stand as division and the fact of the change in topology merging.This makes this framework be fit to very much cutting apart of several objects or a plurality of continuous object.The publication number of Nikolaos Paragyios be 2005/0169533, exercise question is PRIOR KNOWLEDGE, the U.S. Patent application of LEVEL SET REPRESENTATIONAND VISUAL GROUPING has been described a kind of shape prior knowledge in the level set Object Segmentation method and method of coming detected object in image with random fashion use priori of comprising, at this this patented claim intactly is incorporated herein by reference.Below the concise and to the point Level Set Method of describing.

Cutting apart preferably among the present invention carried out according to the Level Set Method at the expansion interface (for example, curve) of flow process by employing.The flow process of the propagation of control curve can be by object function, recover such as minimizing of energy function.In order to introduce the level set representations method, consider the parametric line that launches according to the equation of motion that on the conventional direction (for example curvature) of curve, provides.This flow process can adopt Lagrangian method to realize.Utilize the selection at reference mark to represent profile with discrete form.Curve location can be upgraded by the Equation of Motion of describing curve and each reference mark thereof is found the solution.Under most of common situations, this technology can not change the topology of the curve of expansion, and may need the curve that launches is carried out again parametrization.Level Set Method is introduced in the fluid dynamics field at first, and is the emerging technology that is used to handle the different application aspect imaging, vision, drawing.Level Set Method is represented the curve that launches with the zero level on plane.Such expression is that imply, essence and printenv.The purpose based on the dividing method of knowledge that shape drives is that recovery has the structure of consistent geometric format when compare with prior model.Need be when introducing spherical form driving constraint to the priori modeling.This is equivalent with the expression of extracting structures of interest from one group of training example.The selection of expression is relevant with the form of the priori that will be introduced into.Modeling is an importance of the cutting techniques of shape driving.According to the embodiment of present disclosure, realize that formulism illustrates the priori based on the Level Set Method of the object extraction of knowledge that is being used for that shape drives.Utilize the random distance function to come indicated object.Apply constraint in the Bayes' theorem mode, in order in the plane of delineation that belongs to the shape family that produces by prior model, to seek geometry to dividing processing.

When Medical Image Segmentation, have to handle noise, lack or misleading image information usually.For some imaging pattern, for example ultrasound wave or CT, structures of interest is being more or less the same with its background aspect its Luminance Distribution.An illustrative example in Fig. 1, having represented this respect.Therefore only based on image information cutting object accurately.In recent years, therefore researchers have proposed to utilize the statistics shape prior to come the enhanced level diversity method.Under the situation that provides one group of training shapes, can utilize that to cut apart about which more or less may be the information of priori.This prior shape information is proved to be the thorough segmentation result that has improved when having noise or blocking.For example referring to following publication: M.Leventon, W.Crimson and O.Faugeras in 2000 at CVPR, volume 1, the 316-323 page or leaf Hilton Head Island, the Statisticalshape influence in geodesic active contours that delivers on the SC; A.Tsai, A.i.Yezzi and A.S.Willsky in 2003 at IEEE Trans.on Medical Imaging 22 (2): the A shape-basedapproach to the segmentation of medical imagery using level sets that delivers on the 137-154; D.Cremers, S.J.Oshcr and S.Soatto in 2004 at Pattern Recognition, volume 3175 of LNCS, the Kernel density estimation and intrinsic alignment forknowledge-driven segmentation:Teaching level sets to walk that delivers on the 36-44 page or leaf .Springer; Rousson, N.Paragios and R.Deriche in 2004 at MICCAL, the Implicit active shapemodels for 3d segmentation in MRI imaging that delivers on the 209-216 page or leaf; E.B.Dam, F.T.Fletcher, S.Pizer, C.Tracton and J.Rosenman in September, 2004 at MICCAI, volume 2217 of LNCS, the Prostate shape modeling based on principal geodesic analysisbootstrapping that delivers on the 1008-1016 page or leaf; And D.Freedman, R.J.Radke, T.Zhang, Y.Jeong, D.M.Lovelock and G.T.Chen in March, 2005 at IEEE Trans Med Imaging, 24 (3): the Model-based segmentation of medical imagery by matching distributions that delivers on the 281-292.Great majority in these methods all are based on the training shapes of encoding by signed distance function and form Gaussian distribution this hypothesis.This has two shortcomings: at first, the space of signed distance function is not a linear space, and therefore, the linear combination of average shape and natural mode generally no longer is signed distance function.Secondly, even this space is a linear space, the reason that the sample shape group that provides should distribute according to gaussian density also is indefinite.In fact, as will demonstrating as one aspect of the present invention, they are not Gaussian distribution usually.Recently, proposed in the space of level set function, to adopt non-parametric density estimation [3] to carry out modeling with nonlinear Distribution to training shapes.(term " non-linear " relates to the fact that multiple admissible shape is not only the subspace of linearity).Though this addresses the aforementioned drawbacks, sacrificed the work efficiency in low n-dimensional subspace n (forming) for the problem of infinite dimension optimization by initial minority natural mode.

The ultrasonography of the image 101 expression hearts among Fig. 1.Image 102 expressions are corresponding to the histogram of the empirical probability of the brightness inside and outside the left ventricle.Image 103 expression prostate CT, image 104 expressions are corresponding to the histogram of the empirical probability of the brightness inside and outside the prostate.These structures based on being cutting apart of zone challenging problem, because object has similar histogram with background.

In the present invention, the dividing method of knowledge driving and the framework of system are provided.According to an aspect of the present invention, this framework is based on Level Set Method.According to another aspect of the present invention, this framework is in conjunction with the contribution of three aspects: at first, it provides the statistics shape prior, this statistics shape prior in conjunction with low-dimensional based on the efficient of the method for PCA and the degree of accuracy of nonparametric statistics shape.Crucial aspect is to carry out Density Estimator in linear subspaces, and these linear subspaces are enough greatly to embed all training datas.Secondly, provide a kind of mode to estimate the method for posture and translation parameters with more multidata driving.The 3rd, the monochrome information in the image is used best by the given probability brightness model of Density Estimator by before observed Luminance Distribution.With the example of furnishing an explanation property, the effective Object Segmentation by the method that is provided in the present invention will be provided these examples.

Level set as Bayesian inference is cut apart

If provide image I: Ω → R, then the target cut apart of level set can be formulated as the estimation of best equation: φ: the Ω → R of embedding.In Bayesian frame, this can distribute by the maximization posteriority and calculate:

P(φ|I)∝P(I|φ)P(φ) (2)

(2) problem that maximization causes infinite dimension to be optimized.Provide one group by signed distance function { φ _i} _I=1...NThe training shapes that is encoded, people such as Tsai have proposed by optimization problem being defined as the finite dimensional subspace of being crossed over by training shapes segmentation problem to be reduced to the segmentation problem that finite dimension is optimized.Referring to A.Tsai, A.J.Yezzi and A.S.Willsky in 2003 at IEEE Trans.on Medical Imaging, 22 (2): the A shape-based approach to the segmentation of medical imagery using level sets that delivers on the 137-154.

In the present invention, this concise representation method of imbedding function is useful.Suppose on the space of signed distance function apart from d as giving a definition: d ²(φ ₁, φ ₂)=∫ _Ω(φ ₁(x)-φ ₂(x)) ²Dx, the present invention adjusts this group training shapes according to translation and rotation.Subsequently, it is defined as level set function φ the parametric representation of following form:

${\mathrm{\φ}}_{\mathrm{\α},h,\mathrm{\θ}}\left(x\right)={\mathrm{\φ}}_0(R_{\mathrm{\θ}}x+h)+\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\α}}_i{\mathrm{\Ψ}}_i(R_{\mathrm{\θ}}x+h)---\left(3\right)$

Wherein ${\mathrm{\φ}}_0\left(x\right)=\frac{1}{N}{\mathrm{\Σ}}_{i=1}^N{\mathrm{\φ}}_i\left(x\right)$ The expression average shape, { Ψ _i(x) } _I=1...nBe the natural mode that distributes, n＜N is the dimension of the subspace crossed over of N training shapes.Parameter vector α=(α ₁... α _n) to the warpage modeling; And parameter h ∈ R ³With θ ∈ [0,2 π] ³Translation and rotation modeling to respective shapes.In the subspace, carry out the estimation of priori or training objects, this means the whole space of in step according to aspects of the present invention, not using priori occupied.The subspace is crossed over by n dimension less than N the dimension in whole space.

Therefore, the infinite dimension Bayesian inference problem in (2) is reduced to finite dimension Bayesian inference problem, wherein conditional probability

P (α, h, θ | I) (θ) (θ) (4) are optimized with regard to form parameter α, conversion parameter h and θ to P to ∝ P for α, h for I| α, h.Below, suppose consistent priori about these conversion parameters, promptly P (α, h, θ)=P (α).In the part below, propose three kinds of solutions as an aspect of of the present present invention and come this shape prior is carried out modeling.

Effective nonparametric statistics shape

Provide one group of training shapes { φ that is in line _i} _I=1...N, wherein each can be with their corresponding shape vector { α _i} _I=1...NRepresent.In this representation, statistics shape the destination of study is to infer statistical distribution P (α) from these sample shape.Two solutions that proposed are based on training shapes can be with evenly distributing [15,13]: P (α)=constant or Gaussian distribution are (referring to M.Leventon, W.Crimson and O.Faugeras in 2000 at CVPR, volume 1, the 316-323 page or leaf, Hilton Head Island, the Statistical shape influence in geodesic active contours that delivers on the SC) hypothesis of approaching:

$P\left(\mathrm{\α}\right)\∝\exp (-{\mathrm{\α}}^T{\mathrm{\Σ}}^{-1}\mathrm{\α}),$ Wherein $\mathrm{\Σ}=\frac{1}{N}\underset{i}{\mathrm{\Σ}}{\mathrm{\α}}_i{\mathrm{\α}}_i^T.---\left(5\right)$

In the present invention, the non-parametric density estimation is used to approach the distribution of shapes in the linear subspaces.Referring to F.Rosenblatt in 1956 at Annals of Mathematical Statistics, the Remarks on some nonparametric estimates of a density function that delivers on the 27:832-837.The present invention comes distribution of shapes is carried out modeling by Density Estimator:

$P\left(\mathrm{\α}\right)=\frac{1}{\mathrm{N\σ}}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}K\left(\frac{\mathrm{\α}-{\mathrm{\α}}_i}{\mathrm{\σ}}\right),$ Wherein $K\left(u\right)=\frac{1}{\sqrt{2\mathrm{\π}}}\exp (-\frac{u^2}{2}).---\left(6\right)$

Exist the width cs be used to kernel function automatically to estimate the whole bag of tricks of suitable value, scope from k Nearest Neighbor Estimates to cross validation and bootstrapping.According to of the present invention-individual aspect, σ is set to average nearest neighbor distance simply: ${\mathrm{\σ}}^2=\frac{1}{N}{\mathrm{\Σ}}_{i=1}^N{\min }_{j\≠i}{|{\mathrm{\α}}_i-{\mathrm{\α}}_j|}^2.$

In the context based on the image segmentation of level set, Density Estimator amount (6) has two and is better than all advantages of even Gaussian distribution:

Evenly the hypothesis of distribution or Gaussian distribution normally satisfies.This is illustrated at one group of sample shape profile in Fig. 3.On the other hand, known Density Estimator amount is approached any distribution.Under the hypothesis of appropriateness, it is proved to be under the limiting case of infinite sample size and converges on actual distribution.(referring to B.W.Silverman in 1992 at Chapman and Hall, the Density estimation for statistics anddata analysis that delivers on the London.)

The space of known signed distance function is not a linear space.Therefore, as the average shape φ in (3) ₀With the linear combination of natural mode be not signed distance function usually.So, can not expect that by function phi (x) even or that Gaussian distribution is supported be signed distance function.On the other hand, Density Estimator amount (6) is supported in sample shape vector α _iNear shape vector α.Through structure, these vectors meet signed distance function.In fact: under the limiting case of infinite sample size, the distribution of being inferred by Density Estimator amount (6) is towards the convergence in distribution about a plurality of signed distance functions.

Fig. 2 represents that three kinds are used for one group of leap R ³The synoptic diagram of the method for the sample data of middle two-dimensional sub-spaces.The Density Estimator amount is the clearest catches distribution.The zone of the high probability density of darker each model of shadow representation.Because the Density Estimator amount does not rely on the ad hoc hypothesis about distribution shape, so the Density Estimator amount is matched with training data more neatly.In Fig. 2, the density Estimation figure of image 201 expression uniform densities, the density Estimation figure of image 202 expression gaussian densities, and the density Estimation figure of image 203 expression cuclear density.Fig. 3 represents the 3D projection at the people's of one group of walking the estimation shape density that profile calculated.Image 303 and the warpage of 304 expressions by taking a sample along the geodesic line of the cuclear density in the uniform density in 303 and 304.These show that kernel estimator more accurately catches the distribution of effective shape.In 49 training shapes of image 301 expression among Fig. 36.The 3D projection of the contour surface of (48 dimension) distribution of shapes that image 302 expressions among Fig. 3 are estimated.This distribution of shapes is clearly neither evenly distribution neither Gaussian distribution.Image 303 among Fig. 3 and 304 expressions are along the distortion between two sample shape of the caused geodesic line (geodesics) that distributed by even distribution among Figure 30 3 and the nuclear among Figure 30 4.The evenly distortion that distributes and cause leg to disappear and reappear and do not capture arm motion.Non-linear sampling provides intermediate shape more true to nature.Select people's profile, because they show more significant shape variable than most of medical structure of being analyzed.

Similar with shape study, in example, be used for learning the Density Estimator of conditional probability of the luminance function I of (4).N.Paragios and R.Deriche in 2002 at Int.J.of Computer Vision, 46 (3): proposed similar calculating in advance among the Geodesic active regions and level set methods for supervisedtexture segmentation that delivers on the 223-247 by the Luminance Distribution of mixture model.Provide the training image of one group of pre-segmentation, provide the Luminance Distribution p of object and background by corresponding level and smooth brightness histogram _InAnd p _OutDensity Estimator.This has two advantages: at first, the Density Estimator amount does not rely on the ad hoc hypothesis about distribution shape.Fig. 1 represents that the Luminance Distribution of ultrasound wave and CT image can not approach well with Gauss or laplace model.Secondly, estimate to compare with uniting of Luminance Distribution [2], this simplifies segmentation procedure, and this segmentation procedure no longer needs the renewal of brightness model.And we find that segmentation procedure is more sane to initialization in numerous experiments.

Energy theoremization and minimizing

Maximization in (2) posterior probability or minimize its negative logarithm equivalently and will produce the most probable of given image and cut apart.Under the situation of the nonparametric model of shape of Jie Shaoing and brightness, this causes the energy of following form in the above

E(α，h，θ)＝-logP(I|α，h，θ)-logP(α) (7)

Nonparametric brightness model allows first of expression and equation (6) to provide second exactly.Utilize Heaviside (Heaviside) step function H and short hand (short hand) H _φ=H (φ _{α, h, θ}(x)), finish with following formula:

$E(\mathrm{\α},h,\mathrm{\θ})=-{\∫}_{\mathrm{\Ω}}{H}_{\mathrm{\φ}}\log p_{\mathrm{in}}\left(I\right)+(1-H_{\mathrm{\φ}})\log p_{\mathrm{out}}\left(I\right)\mathrm{dx}-\log \left(\frac{1}{\mathrm{N\σ}}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}K\left(\frac{\mathrm{\α}-{\mathrm{\α}}_i}{\mathrm{\σ}}\right)\right).$

Utilize $e\left(x\right)=\left[\log \frac{p_{\mathrm{out}}\left(I\left(x\right)\right)}{p_{\mathrm{in}}\left(I\left(x\right)\right)}\right],K_i=K\left(\frac{\mathrm{\α}-{\mathrm{\α}}_i}{\mathrm{\σ}}\right)$ And Ψ=(Ψ ₁..., Ψ _n), obtain following system with paired gradient decline equation:

$\left\{\begin{array}{c}\frac{\mathrm{d\α}}{\mathrm{dt}}=\underset{\mathrm{\Ω}}{\∫}\mathrm{\δ}\left({\mathrm{\φ}}_{\mathrm{\α},h,\mathrm{\θ}}\left(x\right)\right)\mathrm{\Ψ}(R_{\mathrm{\θ}}x+h)e\left(x\right)\mathrm{dx}+\frac{1}{{\mathrm{\σ}}^2}\frac{{\mathrm{\Σ}}_{i=1}^N({\mathrm{\α}}_i-\mathrm{\α})K_i}{{\mathrm{\Σ}}_{i=1}^N{K}_i},\\ \frac{\mathrm{dh}}{\mathrm{dt}}=\underset{\mathrm{\Ω}}{\∫}\mathrm{\δ}\left({\mathrm{\φ}}_{\mathrm{\α},h,\mathrm{\θ}}\left(x\right)\right)\▿{\mathrm{\φ}}_{\mathrm{\α},h,\mathrm{\θ}}\left(x\right)e\left(x\right)\mathrm{dx},\\ \frac{\mathrm{d\θ}}{\mathrm{dt}}=\underset{\mathrm{\Ω}}{\∫}\mathrm{\δ}\left({\mathrm{\φ}}_{\mathrm{\α},h,\mathrm{\θ}}\left(x\right)\right)(\▿{\mathrm{\φ}}_{\mathrm{\α},h,\mathrm{\θ}}\left(x\right)\·{\▿}_{\mathrm{\θ}}\mathrm{Rx})e\left(x\right)\mathrm{dx}.\end{array}\right.----\left(8\right)$

In all equatioies, the Di Lake delta function occurs as the factor in the integration on the image area Ω.This permission is limited to all calculating in the arrowband around the zero crossing of φ.When translation expansion and pose parameter h and θ were only driven by data item e (x), shape vector α was with along with being drawn towards each training shapes to the distance of respective shapes again by the intensity of exponential damping.

Experimental result and checking

Method of the present invention has been applied to the cutting apart of different objects in the medical image, wherein will be used for explanation and verify method of the present invention cutting apart of the different objects in the medical image.Illustrative example is cut apart about the prostate in cardiac segmentation in the ultrasonography and the 3D CT image.

Cardiac segmentation in the ultrasonography

The shape prior that Fig. 4 represents to utilize the training image cut apart according to one group of 21 craft to construct is cut apart the experimental result that left ventricle obtains in 2D cardiac ultrasonic wave train.Compare with cut apart (image 402 among Fig. 4) that adopt even priori, the nonparametric statistics shape prior allows accurately to limit cuts apart (image 403 among Fig. 4).This becomes obvious especially in the too weak field of data item.The number percent of object pixel that has calculated the object pixel of correct classification and mis-classification is as quantitatively estimating.During energy minimization, by adopting nuclear priori, the number percent of the pixel of correct classification brings up to 90% from 56%, and the wrong number percent of determining is reduced to 2.7% from 27%.Adopt even priori, the pixel of the correct classification of acquisition 92%, but the wrong number percent of determining is increased to 42%.Only the border is launched to be limited to the linear subspaces that training shapes crosses over and be not enough to provide accurate segmentation result.

Prostate in the 3D CT image is cut apart

As another illustrative example, the prostate image (having seminal vesicle), the prostatic nonparametric 3D shape that utilize from 12 manual extraction of two different patients' collections have been researched and developed.Fig. 5 represents to use 2 patients' of same shape prostate to cut apart.Comprise that every tabulation in the row 501,502,503 and 504 of two images shows first patient (left side two row 501 and 502) and second patient's (back two row 503 and 504) the same crown and axial slices of cutting apart.First row 501 are also represented manual cut apart (black profile).Compare with work on hand, next adopted the single shape of cutting apart that is used for from different patients' image.Adopted by what from the training stage, remove image of interest and stayed one (leave-one-out) strategy.Fig. 6 represents to adopt this tactful some results' that obtain 2D section.It illustrates adopts cutting apart of nuclear priori (white line) and employing alternative method (black line) acquisition.Click initialization along with intraorganic, method of the present invention causes the stable state solution less than 20 seconds.The organ voxel of 86% successful classification and the organ voxel of 11% mis-classification have been obtained.This advantageously with at D.Freedman, R.J.Radke, T.Zhang, Y Jeong, D.M.Lovelock and G.T.Chen in March, 2005 at IEEE Trans Med Imaging, 24 (3): the inner result of the patient that reported among the Model-based segmentation of medical imagery by matching distributions that delivers among the 281-292 forms comparison.

Fig. 5 provides and has cut apart by hand and utilize all even Gauss of distribution of shapes to approach the qualitative comparison of cutting apart that is obtained.

Proposed to be used to create and use and be used for the method for effectively and accurately adding up shape prior that level set is cut apart, wherein level set is cut apart based on the non-parametric density in the linear subspaces of crossing at one group of training data and is estimated.What proposed in addition, is that the many-sided dividing method of the present invention adopts the non-parametric estmation of Luminance Distribution and effective optimization of posture and translation parameters.Proposed to verify here this method, heart ultrasonic image and the segmentation precision of prostate 3D CT image and the illustrative of speed quantitatively estimate.The example that is proposed shows that the nonparametric shape prior of being advised is better than the shape prior that level set is cut apart that is used for of suggestion in the past.

Fig. 7 has illustrated the summary of one aspect of the present invention.The first step 701 in the segmentation procedure is to set up the nonparametric model that allows to describe according to Level Set Method image.The model that is used for the present invention is the Density Estimator of approaching as the nonparametric of distribution of shapes.Next step 702 comprises the shape of learning one group of priori.Here, the Density Estimator of the training image of pre-segmentation is provided by level and smooth brightness histogram.The Density Estimator of divided image is produced in step 703.In step 704, provide energy function E (α, h, θ), this energy function can with Bayes's form be represented as E (α, h, θ)=-logP (I| α, h, θ)-logp (α).The maximization of the posterior probability by the minimization of energy expression formula will obtain most probable cutting apart (looking like priori), and this provides in step 704.

For the dividing method of a part of the present invention can be carried out by system as shown in Figure 8.For this system provides the data 801 of expression with divided image and priori image.Providing to carry out adopts the inventive method to learn and instruction set or the program 802 of the method cut apart, and with itself and data combination, processor 803 can be handled the instruction 802 that is applied to data 801 and show split image on display 804 in processor 803.This processor can be can execute instruction 802 a calculation element of specialized hardware, GPU, CPU or any other.Input media 805, for example mouse or tracking ball or other input medias allow the user to select initial object and start segmentation procedure.Therefore, system as shown in Figure 8 is provided for adopting Level Set Method and shape and brightness prior to come the interactive system of cutting object from image.

Following list of references provides background information related to the present invention usually, and therefore be introduced into as a reference: [1] V.Caselles, F.Catt é, T.CoIl and F.Dibos in 1993 at Numer.Math., the A geometric model for active contours in image processing that delivers among the 66:1-31; [2] T.F.Chan and L.A.Vese in calendar year 2001 at IEEE Trans.Image Processing, 10 (2): the Active contours without edges that delivers among the 266-277; [3] D.Cremers, S.J.Osher and S.Soatto in 2004 at Pattern Recognition, volume 3175 of LNCS, the Kerneldensity estimation and intrinsic alignment for knowledge-driven segmentation:Teachinglevel sets to walk that delivers among the 36-44 page or leaf .Springer; [4] E.B.Dam, F.T.Fletcher, S.Pizer, C.Tracton and J.Rosenman in September, 2004 at MICCA, volume 2217 of LNCS, the Prostateshape modeling based on principal geodesic analysis bootstrapping that delivers in the 1008-1016 page or leaf; [5] A.Dervieux and F.Thomasset in 1979 at Springer Lect.Notes in Math., the A finiteelement method for the simulation of Raleigh-Taylor instability that delivers among the 771:145-158; [6] D.Freedman, R.J.Radke, T.Zhang, Y.Jeong, D.M.Lovelock and G.T.Chen in March, 2005 at IEEE TransMed Imaging, 24 (3): the Model-based segmentation of medical imagery bymatching distributions that delivers among the 281-292; [7] S.Kichenassamy, A.Kumar, P.J.Giver, A.Tannenbaum and A.J.Yezzi in nineteen ninety-five at Proc.IEEE Intl.Conf.on Comp.Vis., the 810-815 page or leaf, Boston, the Gradient flows and geometric active contour models that delivers among the USA; [8] M.Leventon, W.Crimson and O.Faugeras in 2000 at CVPR, volume 1, the 316-323 page or leaf, Hilton HeadIsland, the Statistical shape influence in geodesic active contours that delivers among the SC; [9] R.Malladi, J.A.Sethian and B.C.Vemuri in 1994 at SPIE Conference on Geometric Methods inComputer Vision II, the A topology independentshape modeling scheme that delivers in the volume 2031. 246-258 pages or leaves; [10] 5.J.Osher and J.A.Sethian in 1988 at J.of Comp.Phys., the Fronts propagation with curvature dependent speed:Algorithms basedon Hamilton-Jacobi formulations that delivers among the 79:12-49; [11] N.Paragios and R.Deriche in 2002 at Int.J.ofComputer Vision, 46 (3): the Geodesic active regions and level setmethods for supervised texture segmentation that delivers among the 223-247; [12] F.Rosenblatt in 1956 at Annals ofMathematical Statistics, the Remarks on some nonparametric estimatesof a density function that delivers among the 27:832-837; [13] M.Rousson, N.Paragios and R.Deriche in 2004 at MICCAI, the Implicit active shape models for 3d Segmentation inMRI imaging that delivers in the 209-216 page or leaf; [14] B.W.Silverman in 1992 at Chapman and Hall, the Density estimation for statistics and data analysis that delivers among the London; [15] A.Tsai, A.J.Yezzi and A.S.Willsky in 2003 at IEEE Trans.on Medical Imaging, 22 (2): the Ashape-based approach to the segmentation of medical imagery using level sets that delivers among the 137-154.

Here anyly should be considered to quoting to voxel to quoting also of term pixel.

Though illustrate, describe and pointed out as being applied to the preferred embodiments of the present invention, basic novel feature of the present invention, but it should be understood that those skilled in the art can aspect the form of described device and the details and operating aspect make various omissions, substitute and change and do not break away from spirit of the present invention.Therefore, only should as indicated, limit the present invention by the scope of appended claim.

Claims (22)

1, a kind of method of utilizing in as data one or more priori examples of object to come cutting object at set of diagrams comprises:

In the subspace that one or more priori examples of object are crossed over, determine the non-parametric estmation of characteristic of one or more priori examples of object;

In the Bayes's expression formula that is subjected to this set of image data restriction, utilize the non-parametric estmation of one or more priori; And

Level Set Method by carry out optimizing Bayes's expression formula the cutting apart of alternative in this set of image data.

2, the method for claim 1, wherein described characteristic is brightness.

3, the method for claim 1, wherein described characteristic is a shape.

4, the method for claim 1, wherein the characteristic of one or more priori examples of object based on the mean value of the characteristic relevant with each priori example in the priori example of object.

5, the method for claim 1, wherein the characteristic of one or more priori examples of object based on distance function.

6, the method for claim 1, wherein described expression formula is an energy function.

7, the method for claim 1, wherein the characteristic of one or more priori examples of object is translation and rotational invariants.

8, the method for claim 1, wherein the characteristic of one or more priori examples of object based on density function.

9, the method for claim 1, wherein density function is a cuclear density.

10, the method for claim 1, wherein the Density Estimator amount of priori is level and smooth brightness histogram.

11, the method for claim 1, wherein described expression formula is provided with according to following formula:

$E(\mathrm{\α},h,\mathrm{\θ})=-{\∫}_{\mathrm{\Ω}}{H}_{\mathrm{\φ}}\log p_{\mathrm{in}}\left(I\right)+(1-H_{\mathrm{\φ}})\log p_{\mathrm{out}}\left(I\right)\mathrm{dx}-\log \left(\frac{1}{\mathrm{N\σ}}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}K\left(\frac{\mathrm{\α}-{\mathrm{\α}}_i}{\mathrm{\σ}}\right)\right).$

12, a kind of being used for utilizes one or more priori examples of object to come the system of cutting object at set of diagrams as data, comprising:

Processor;

The computer software that on this processor, can move, this computer software can:

The non-parametric estmation of the characteristic of one or more priori examples of definite object in the subspace that one or more priori examples of object are crossed over;

In the Bayes's expression formula that is subjected to this set of image data restriction, utilize the non-parametric estmation of one or more priori; And

Level Set Method by carry out optimizing Bayes's expression formula the cutting apart of alternative in this set of image data.

13, system as claimed in claim 12, wherein, described characteristic is brightness.

14, system as claimed in claim 12, wherein, described characteristic is a shape.

15, system as claimed in claim 12, wherein, the characteristic of one or more priori examples of object is based on the mean value of the characteristic relevant with each priori example in the priori example of object.

16, system as claimed in claim 12, wherein, the characteristic of one or more priori examples of object is based on distance function.

17, system as claimed in claim 12, wherein, described expression formula is an energy function.

18, system as claimed in claim 12, wherein, the characteristic of one or more priori examples of object is translation and rotational invariants.

19, system as claimed in claim 12, wherein, the characteristic of one or more priori examples of object is based on density function.

20, system as claimed in claim 12, wherein, density function is a cuclear density.

21, system as claimed in claim 12, wherein, the Density Estimator amount of priori is level and smooth brightness histogram.

22, system as claimed in claim 12, wherein, described expression formula is provided with according to following formula:

$E(\mathrm{\α},h,\mathrm{\θ})=-{\∫}_{\mathrm{\Ω}}{H}_{\mathrm{\φ}}\log p_{\mathrm{in}}\left(I\right)+(1-H_{\mathrm{\φ}})\log p_{\mathrm{out}}\left(I\right)\mathrm{dx}-\log \left(\frac{1}{\mathrm{N\σ}}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}K\left(\frac{\mathrm{\α}-{\mathrm{\α}}_i}{\mathrm{\σ}}\right)\right).$

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