CN102663755B - Method for cutting nuclear magnetic resonance image with uniform gray levels - Google Patents

Abstract

The invention relates to a method for cutting a nuclear magnetic resonance image with uniform gray levels. The method comprises the following steps: firstly, blocking out a closed curve on a nuclear magnetic resonance image with nonuniform gray levels, and secondly, performing iterative evolution on an object in the nuclear magnetic resonance image with nonuniform gray levels through a region-based active contour model, so as to obtain the contour curve of the object. The region-based active contour model takes local and global gray level information of the nuclear magnetic resonance image into account, and the method has the advantages of high operational speed, robustness of active contour initialization, high anti-noise property and accurate cutting result.

Description

A kind of dividing method for the inhomogeneous nuclear magnetic resonance image of gray scale

Technical field

The present invention relates to a kind of dividing method of nuclear magnetic resonance image, particularly a kind of dividing method for the inhomogeneous nuclear magnetic resonance image of gray scale, belongs to medical image analysis field.

Background technology

Magnetic resonance imaging (Magnetic Resonance Image, MRI) is the important supplementary means of medical diagnosis on disease, is also one of the study hotspot in Medical image analysis field.It has and there is no radiocontamination, resolution is high, imaging parameters is many, can random layer bedding fault, to human body without advantages such as electric radiation damages, on clinical medicine, be widely used.Along with people are more and more higher to the requirement of nuclear magnetic resonance image quantitative test, such as in to the research of the degeneration cerebral disease such as such as senile dementia, multiple sclerosis and schizophrenia, except the space distribution and Iterim Change of research grey matter, white matter, white matter damage and cerebrospinal fluid, the accurate measurement of these volume of tissue is also absolutely necessary.Because these sacred diseases have changed normal volume and the areal distribution thereof of human brain soft tissue (grey matter, white matter) and cerebrospinal fluid.A prerequisite of these application is cut apart accurately to brain nuclear magnetic resonance image exactly.But in actual applications, the nuclear magnetic resonance image obtaining due to Magnetic resonance imaging equipment is subject to the factor such as otherness and partial volume effect between the inhomogeneous and different tissues of noise, radio-frequency field, make signal occur to obscure, the gradation uniformity variation of result images, the pixel grey scale that shows as same tissue on image is slow, level and smooth variation along space, the namely problem of biased field, therefore relies on merely tradition to cut apart image based on overall gray-scale value and cannot meet accuracy requirement.

Image partition method has a lot, at present because active contour model can incorporate in a unified process by the priori about target shape with from the knowledge of image, is the focus method that present image is cut apart field.

Based on active contour model, the classical CV model that Chan and Vese propose, supposes that image is divided into two parts of target and background that average does not wait, and splits target from background.This model and afterwards the CV parted pattern of the leggy of proposition are often called as piece-wise constant (piecewise constant, PC) model, owing to using the inside and outside whole half-tone informations of profile, therefore obtain fine to the larger image of noise and weak boundary image endure.But the intensity profile of PC model hypothesis image is that in the time there is gray scale non-uniform phenomenon in image, PC model can produce erroneous segmentation uniformly.Can not overcome the shortcoming of gray scale unevenness in order to overcome PC model, Vese and Chan and Tsai etc. have proposed sectionally smooth (piecewise smooth, PS) model.But PS model is owing to will additionally solving two partial differential equation when each iteration level set function, and calculated amount is larger.In addition,, in order to ensure that in evolutionary process, horizontal energy collecting remains symbolic distance function, when each iteration, need to reinitialize.Recently, Li etc. has proposed the new inhomogeneous dividing method of processing brain nuclear magnetic resonance image gray scale.First this method has defined a K mean cluster objective function in gradation of image neighborhood, then this objective function is incorporated into whole image area, and is incorporated in variation level set framework.By introducing the local gray level information of image, the result that this method can produce.The more method with Li etc. has the algorithm of identity function to be also suggested, but they are sometimes more responsive to the initialization of active profile, and therefore effect is not remarkable especially.

2 important prior arts that relate in the present invention are that the people such as CV model and Li are at document " A variational level set approach to segmentation and bais correction of images with intensity inhomogeneity " (Li C, Huang R, Ding Z, Gatenby C, Metaxas D, Gore J.A variational level set approach to segmentation and bais correction of images with intensity inhomogeneity.In:Processing of medical image computing and computer aided intervention MICCAI 2008, Part II, LNCS 5242, pp.1083-1091, 2008.) the middle active contour model based on cluster proposing, be specially:

(1) CV model

Suppose

image area, be a gray-scale map, the x in I (x) represents gray-scale value, is a constant in image area Ω, and the energy functional of this model is as follows:

$E(c_1^{\mathrm{cv}},c_2^{\mathrm{cv}},C)={\mathrm{\λ}}_1{\∫}_{\mathrm{inside}\left(C\right)}{|I\left(x\right)-c_1^{\mathrm{cv}}|}^2\mathrm{dx}+{\mathrm{\λ}}_2{\∫}_{\mathrm{outside}\left(C\right)}{|I\left(x\right)-c_2^{\mathrm{cv}}|}^2\mathrm{dx}+v\·\mathrm{Length}\left(C\right)---\left(1\right)$

Wherein,

represent the gray-scale value of target;

represent the gray-scale value of background; C represents curve; λ ₁, λ ₂, v is constant; Inside (C) represents the inside of curve C; Outside (C) represents the outside of curve C.

This model adopts variation level diversity method, introduces Heaviside function, can be the functional about imbedding function u by this model modification, as shown in formula (2):

$E(c_1^{\mathrm{cv}},c_2^{\mathrm{cv}},u)=v\underset{\mathrm{\Ω}}{\∫\∫}\mathrm{\δ}\left(u\right)|\▿u|\mathrm{dxdy}+{\mathrm{\λ}}_1\underset{\mathrm{\Ω}}{\∫\∫}{(I-c_1^{\mathrm{cv}})}^{2}H\left(u\right)\mathrm{dxdy}$ (2)

$+{\mathrm{\λ}}_2\underset{\mathrm{\Ω}}{\∫\∫}{(I-c_2^{\mathrm{cv}})}^2(1-H\left(u\right))\mathrm{dxdy}$

Wherein, u represents the imbedding function of curve C; δ (u) is Heaviside function derivative; it is the gradient of imbedding function u; H (u) is Heaviside function.

with

under fixing condition, u minimizes formula (2) relatively, obtains formula (3):

$\frac{\∂u}{\∂t}={\mathrm{\δ}}_{\mathrm{\ϵ}}[v\mathrm{div}\left(\frac{\▿u}{|\▿u|}\right)-{\mathrm{\λ}}_1{(I-c_1^{\mathrm{cv}})}^2+{\mathrm{\λ}}_2{(I-c_2^{\mathrm{cv}})}^2]---\left(3\right)$

Wherein, t represents the time; δ _εrepresent the normalization of δ (u); Div represents divergence operator.

By formula (3), ask steady state solution, can obtain segmentation result.

The shortcoming of CV model is: if the gray scale in inside (C) and outside (C) is inhomogeneous, and optimal value

with

will depart from actual value far away, will make like this segmentation result of CV model inaccurate.

(2) active contour model based on cluster

The universal model of the uneven image of gray scale is defined as follows:

I＝bJ+n (4)

Wherein, I is the image collecting; J is true picture; The gray scale unevenness of b representative image, is a kind of deviation territory, conventionally uses a matrix representation; N is noise.There are following two hypothesis for true picture J and deviation territory b:

(I) deviation territory b slowly changes in whole image area;

(∏) true picture J is approximately constant in every zonule, that is: for x ∈ Ω _i,

be the subdomain of image area Ω, have J (x) ≈ c _i, N is positive integer, c _irepresent the gray-scale value in i region in true picture J.

Based on hypothesis (I) and (∏), the active contour model based on cluster centered by each some x, has defined a circular neighborhood O in image area Ω in the radius ρ relatively little with _x:

in each pocket, there is following approximation:

b(y)J(y)≈b(x)c _i，y∈O _x∩Ω _i (5)

Wherein, b (x) c _ibe considered to circular neighborhood O _xbeing similar to of cluster centre.In order to predict b (x) c _i, circular neighborhood O _xgray scale I (y) be divided into N class.Like this, just can use the K means clustering algorithm of standard to carry out cluster.So definition local recovery canonical function is as shown in formula (6):

$E_x=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\∫}_{O_x\∩{\mathrm{\Ω}}_i}K(x-y){|I\left(y\right)-b\left(x\right)c_i|}^2\mathrm{dy}---\left(6\right)$

Wherein, E _xfor localized target function; K is a non-negative gauss kernel function, and it defines as shown in formula (7); B (x) c _iit is the cluster centre that will predict.

$K\left(\mathrm{\ω}\right)=\left\{\begin{array}{cc}\frac{1}{a}{e}^{-{\left|\mathrm{\ω}\right|}^2/2{\mathrm{\σ}}^2}& \mathrm{for}\left|\mathrm{\ω}\right|\≤\mathrm{\ρ}\\ 0& \mathrm{otherwise}\end{array}\right.---\left(7\right)$

Wherein, a is a constant, and ω is the average of gaussian kernel function, and σ is variance.

Localized target function E in formula (6) _xcan be write as following form:

$E_x=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\∫}_{{\mathrm{\Ω}}_i}K(x-y){|I\left(y\right)-b\left(x\right)c_i|}^2\mathrm{dy}---\left(8\right)$

In order to find the optimal subset of whole image area Ω, for all x, the functional E of energy minimization _xcan be defined as follows:

$E\stackrel{\mathrm{\Δ}}{=}\∫\left(\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\∫}_{{\mathrm{\Ω}}_i}K(x-y){|I\left(y\right)-b\left(x\right)c_i|}^2\mathrm{dy}\right)\mathrm{dx}---\left(9\right)$

Wherein, E is global objective function, i.e. objective function on whole image area Ω.

Work as N=2, image area Ω is divided into two parts

and these two parts can use the region being separated by zero level set function φ to replace,

with

use Heaviside function, formula (10) can be expressed as follows:

$E(\mathrm{\φ},b,c)=\∫(\underset{i=1}{\overset{2}{\mathrm{\Σ}}}\∫K(x-y){|I\left(y\right)-b\left(x\right)c_i|}^2{M}_i\left(\mathrm{\φ}\left(y\right)\right)\mathrm{dy})\mathrm{dx}---\left(10\right)$

Wherein, global objective function when E (φ, b, c) represents N=2; C is the local gray-value of true picture; M ₁(φ (x))=H (φ (x)), M ₂(φ (x))=1-H (φ (x)).

For fixing zero level set function φ and local gray-value c, the optimum deviation territory b that minimizes formula (10) is expressed as follows:

$b=\frac{\left({\mathrm{IJ}}^{\left(1\right)}\right)*K}{J^{\left(2\right)}*K}---\left(11\right)$

Wherein, * represents convolution algorithm, $J^{\left(1\right)}={\mathrm{\Σ}}_{i=1}^N{c}_i{M}_i\left(\mathrm{\φ}\right),$ $J^{\left(2\right)}={\mathrm{\Σ}}_{i=1}^N{c}_i^2{M}_i\left(\mathrm{\φ}\right),$ K is a non-negative gauss kernel function, as shown in formula (7).

For fixing zero level set function φ and deviation territory b, the optimum local gray-value c that minimizes formula (10) is expressed as follows:

Based on the universal model of Description Image gray scale unevenness, integrate topography's half-tone information, adopt the described model of formula (10) can correctly cut apart the inhomogeneous image of several gray scales, but because meeting produces local minimum problem, cause it to not robust of the initialization of profile, therefore just can not get in some cases segmentation result accurately.

Summary of the invention

The object of the invention is the defect in order to solve prior art, overcome the problem that the inhomogeneous nuclear magnetic resonance image of medical science gray scale can not Accurate Segmentation, propose a kind of method of cutting apart for the inhomogeneous nuclear magnetic resonance image of gray scale.

The inventive method is achieved through the following technical solutions.

For a dividing method for the inhomogeneous nuclear magnetic resonance image of gray scale, its concrete implementation step is as follows:

Step 1, the inhomogeneous nuclear magnetic resonance image of gray scale is carried out to initialization operation, on the inhomogeneous nuclear magnetic resonance image of gray scale, sketch out a closed curve.

Step 2, the active contour model of use based on region carry out iteration evolution to the target in the inhomogeneous nuclear magnetic resonance image of gray scale, obtain the contour curve of target.

The described active contour model based on region is specially:

image area,

be a nuclear magnetic resonance image that the gray scale collecting is inhomogeneous, the x in I (x) represents gray-scale value, is a constant in image area Ω; J is true picture; B represents the gray scale unevenness of nuclear magnetic resonance image, is a kind of deviation territory, is a matrix;

be the subdomain of image area Ω, have J (x) ≈ c _i, N is positive integer, c _irepresent the gray-scale value in i region in true picture J.

The energy functional of the active contour model based on region is as shown in formula (13):

$E=E(\mathrm{\φ},c_1^{\mathrm{cv}},c_2^{\mathrm{cv}},b,c)+P\left(\mathrm{\φ}\right)---\left(13\right)$

Wherein, E is energy functional;

for Part I energy functional, be expressed as formula (14); φ is level set function;

the gray-scale value of target in presentation video;

the gray-scale value of background in presentation video; C is the local gray-value in true picture; P (φ) is Part II energy functional, is expressed as formula (15).

$E(\mathrm{\φ},c_1^{\mathrm{cv}},c_2^{\mathrm{cv}},b,c)=\mathrm{\μ}{E}^{\mathrm{local}}(\mathrm{\φ},b,c)+(1-\mathrm{\μ})E^{\mathrm{global}}(\mathrm{\φ},c_1^{\mathrm{cv}},c_2^{\mathrm{cv}})---\left(14\right)$

Wherein, μ is coefficient, the inhomogeneous degree of gray scale of the big or small presentation video of its value, and its value is larger, and the inhomogeneous degree of the gray scale of presentation video is higher; Its value is less, and the inhomogeneous degree of the gray scale of presentation video is lower;

e is natural logarithm; b _εit is the normalization item of deviation territory b; E ^local(φ, b, c) is local energy item, as shown in formula (16);

global energy item, as shown in formula (17).

$P\left(\mathrm{\φ}\right)=\mathrm{\η}\underset{\mathrm{\Ω}}{\∫}\frac{1}{2}{\left(\right|\▿\mathrm{\φ}\left(x\right)|-1)}^2\mathrm{dx}+\mathrm{\γ}\underset{\mathrm{\Ω}}{\∫}|\▿H\left(\mathrm{\φ}\left(x\right)\right)|\mathrm{dx}---\left(15\right)$

Wherein, η and γ are constants, get arithmetic number; for gradient symbol; H (φ (x)) is Heaviside function.

$E^{\mathrm{local}}(\mathrm{\φ},b,c)=\∫(\underset{i=1}{\overset{2}{\mathrm{\Σ}}}\∫K(x-y){|I\left(y\right)-b\left(x\right)c_i|}^2{M}_i\left(\mathrm{\φ}\left(y\right)\right)\mathrm{dy})\mathrm{dx}---\left(16\right)$

Wherein, certain in x presentation graphs image field Ω a bit; K is a non-negative gauss kernel function, and it defines as shown in formula (18); B (x) c _iit is the cluster centre that will predict; M ₁(φ (y))=H (φ (y)), M ₂(φ (y))=1-H (φ (y)).

$E^{\mathrm{global}}(\mathrm{\φ},c_1^{\mathrm{cv}},c_2^{\mathrm{cv}})={\mathrm{\λ}}_1\∫{|I\left(x\right)-c_1^{\mathrm{cv}}|}^{2}H\left(\mathrm{\φ}\left(x\right)\right)\mathrm{dx}+{\mathrm{\λ}}_2\∫{|I\left(x\right)-c_2^{\mathrm{cv}}|}^2(1-H\left(\mathrm{\φ}\left(x\right)\right))\mathrm{dx}---\left(17\right)$

$K\left(\mathrm{\ω}\right)=\left\{\begin{array}{cc}\frac{1}{a}{e}^{-{\left|\mathrm{\ω}\right|}^2/2{\mathrm{\σ}}^2}& \mathrm{for}\left|\mathrm{\ω}\right|\≤\mathrm{\ρ}\\ 0& \mathrm{otherwise}\end{array}\right.---\left(18\right)$

Wherein, a is a constant, and ω is the average of gaussian kernel function, and σ is variance.

Beneficial effect

Dividing method for the inhomogeneous nuclear magnetic resonance image of gray scale of the present invention, compared with the prior art, has fast operation, strong, the segmentation result advantage accurately of profile initialization robust, anti-noise ability initiatively.

Brief description of the drawings

Fig. 1 is the result design sketch that the method that adopts CV model, active contour model based on cluster and the present invention to propose in the specific embodiment of the invention 1 is cut apart the inhomogeneous brain nuclear magnetic resonance image of identical gray scale; Wherein, if Fig. 1 (a) is the segmentation result of CV model; Fig. 1 (b) is the segmentation result of the active contour model based on cluster; Fig. 1 (c) is the segmentation result of the method that proposes of the present invention;

Fig. 2 verifies in the specific embodiment of the invention 2 that initialization has the experiment effect figure of robustness to active profile for the dividing method for the inhomogeneous nuclear magnetic resonance image of gray scale that the present invention proposes; Wherein, 2 (a) are width composite noise figure (128x128); Fig. 2 (b) is that the initial profile figure of initiatively profile is foursquare segmentation effect figure, and this initial profile graphics package has contained whole target; Fig. 2 (c) is that the initial profile figure of initiatively profile is leg-of-mutton segmentation effect figure, and this initial profile graphics package has contained part target; Fig. 2 (d) is that the initial profile figure of initiatively profile is leg-of-mutton segmentation effect figure, and this initial profile figure is positioned in the middle of target.

Fig. 3 is the segmentation effect figure by the inhomogeneous composite noise figure of same gray scale method that relatively CV model, active contour model based on cluster and the present invention propose in the specific embodiment of the invention 3; Wherein, Fig. 3 (a) is a width composite noise figure; Fig. 3 (b) is the segmentation effect figure of CV model; Fig. 3 (c) is the segmentation effect figure of the active contour model based on cluster; Fig. 3 (d) is the segmentation effect figure of the method that proposes of the present invention.

Fig. 4 is the segmentation effect figure by the inhomogeneous composite noise figure of same gray scale method that relatively CV model, active contour model based on cluster and the present invention propose in the specific embodiment of the invention 4; Wherein, Fig. 4 (a) is a width composite noise figure; Fig. 4 (b) is the segmentation effect figure of CV model; Fig. 4 (c) is the segmentation effect figure of the active contour model based on cluster; Fig. 4 (d) is the segmentation effect figure of the method that proposes of the present invention.

Fig. 5 is the segmentation effect figure by the inhomogeneous composite noise figure of same gray scale method that relatively CV model, active contour model based on cluster and the present invention propose in the specific embodiment of the invention 5; Wherein, Fig. 5 (a) is a width composite noise figure; Fig. 5 (b) is the segmentation effect figure of CV model; Fig. 5 (c) is the segmentation effect figure of the active contour model based on cluster; Fig. 5 (d) is the segmentation effect figure of the method that proposes of the present invention.

Fig. 6 is the segmentation effect figure by the inhomogeneous composite noise figure of same gray scale method that relatively CV model, active contour model based on cluster and the present invention propose in the specific embodiment of the invention 6; Wherein, Fig. 6 (a) is a width composite noise figure; Fig. 6 (b) is the segmentation effect figure of CV model; Fig. 6 (c) is the segmentation effect figure of the active contour model based on cluster; Fig. 6 (d) is the segmentation effect figure of the method that proposes of the present invention.

Embodiment

Below in conjunction with the drawings and specific embodiments, the embodiment of the inventive method is elaborated.

For a dividing method for the inhomogeneous nuclear magnetic resonance image of gray scale, its concrete implementation step is as follows:

Step 1, the inhomogeneous nuclear magnetic resonance image of gray scale is carried out to initialization operation, on the inhomogeneous nuclear magnetic resonance image of gray scale, sketch out a closed curve.

Step 2, the active contour model of use based on region carry out iteration evolution to the target in the inhomogeneous nuclear magnetic resonance image of gray scale, obtain the contour curve of target.The described active contour model based on region is specially:

image area,

be a nuclear magnetic resonance image that the gray scale collecting is inhomogeneous, the x in I (x) represents gray-scale value, is a constant in image area Ω; J is true picture; B represents the gray scale unevenness of nuclear magnetic resonance image, is a kind of deviation territory, is a matrix;

be the subdomain of image area Ω, have J (x) ≈ c _i, N is positive integer, c _irepresent the gray-scale value in i region in true picture J.

The energy functional of the active contour model based on region is

wherein, Part I energy functional

be expressed as formula (19), Part II energy functional P (φ) is expressed as formula (20)

$E(\mathrm{\φ},c_1^{\mathrm{cv}},c_2^{\mathrm{cv}},b,c)=\mathrm{\μ}{E}^{\mathrm{local}}(\mathrm{\φ},b,c)+(1-\mathrm{\μ})E^{\mathrm{global}}(\mathrm{\φ},c_1^{\mathrm{cv}},c_2^{\mathrm{cv}})---\left(19\right)$

Wherein,

e is natural logarithm; b _εbe the normalization item of deviation territory b, initial value ε=1 is set in the middle of experiment; Local energy item E ^local(φ, b, c) is as shown in formula (21); Global energy item

as shown in formula (22).

$P\left(\mathrm{\φ}\right)=\mathrm{\η}\underset{\mathrm{\Ω}}{\∫}\frac{1}{2}{\left(\right|\▿\mathrm{\φ}\left(x\right)|-1)}^2\mathrm{dx}+\mathrm{\γ}\underset{\mathrm{\Ω}}{\∫}|\▿H\left(\mathrm{\φ}\left(x\right)\right)|\mathrm{dx}---\left(20\right)$

Initial value is set: η=1.0, γ=0.001 × 255 × 255 in the middle of experiment.

$E^{\mathrm{local}}(\mathrm{\φ},b,c)=\∫(\underset{i=1}{\overset{2}{\mathrm{\Σ}}}\∫K(x-y){|I\left(y\right)-b\left(x\right)c_i|}^2{M}_i\left(\mathrm{\φ}\left(y\right)\right)\mathrm{dy})\mathrm{dx}---\left(21\right)$

Wherein, non-negative gauss kernel function K is as shown in formula (23); M ₁(φ (y))=H (φ (y)), M ₂(φ (y))=1-H (φ (y)).

$E^{\mathrm{global}}(\mathrm{\φ},c_1^{\mathrm{cv}},c_2^{\mathrm{cv}})={\mathrm{\λ}}_1\∫{|I\left(x\right)-c_1^{\mathrm{cv}}|}^{2}H\left(\mathrm{\φ}\left(x\right)\right)\mathrm{dx}+{\mathrm{\λ}}_2\∫{|I\left(x\right)-c_2^{\mathrm{cv}}|}^2(1-H\left(\mathrm{\φ}\left(x\right)\right))\mathrm{dx}---\left(22\right)$

Initial value: λ is set in the middle of experiment ₁=λ ₂=1.0.

$K\left(\mathrm{\ω}\right)=\left\{\begin{array}{cc}\frac{1}{a}{e}^{-{\left|\mathrm{\ω}\right|}^2/2{\mathrm{\σ}}^2}& \mathrm{for}\left|\mathrm{\ω}\right|\≤\mathrm{\ρ}\\ 0& \mathrm{otherwise}\end{array}\right.---\left(23\right)$

Initial value is set in the middle of experiment is: a=1.0, σ=4.0.

In the middle of experiment, setup times step-length is 0.1 second.

Embodiment 1:

Cut apart the accuracy of the inhomogeneous nuclear magnetic resonance image of gray scale in order to verify the active contour model based on region, adopt respectively put forward the methods of the present invention, CV model and the active contour model based on cluster to carry out contrast experiment to the inhomogeneous brain nuclear magnetic resonance image of identical gray scale, result as shown in Figure 1.Wherein, if Fig. 1 (a) is the segmentation result of CV model; Fig. 1 (b) is the segmentation result of the active contour model based on cluster; Fig. 1 (c) is the segmentation result of the dividing method for the inhomogeneous nuclear magnetic resonance image of gray scale that proposes of the present invention.Square frame in Fig. 1 (a), Fig. 1 (b), Fig. 1 (c) is the initial profile figure of active profile, and active profile initialization figure and the position of these three figure are duplicate.Experimental result shows, the automatic Segmentation better effects if for the inhomogeneous nuclear magnetic resonance image of gray scale that the present invention proposes.

Embodiment 2:

In order to verify that method that the present invention proposes is to the initialized robustness of active profile, for a width composite noise figure (128x128), as shown in Fig. 2 (a), respectively active profile is defined as to state in 3, be respectively: 1. the square in Fig. 2 (b) is the initial profile figure of active profile, and it has comprised whole target; 2. the triangle in Fig. 2 (c) is the initial profile figure of active profile, and it has comprised part target; 3. the triangle in Fig. 2 (d) is the initial profile figure of active profile, and it is positioned in the middle of target.Experimental result shows, to active profile, initialization has good robustness to the dividing method for the inhomogeneous nuclear magnetic resonance image of gray scale that the present invention proposes.

In order to verify the noise immunity of the dividing method for the inhomogeneous nuclear magnetic resonance image of gray scale that the present invention proposes and the accuracy of cutting apart for the different inhomogeneous images of gray scale, in experiment, adopt respectively the dividing method for the inhomogeneous nuclear magnetic resonance image of gray scale, CV model and the active contour model based on cluster that the present invention proposes to carry out 4 experiments to 4 width composite noise figure (128x128).

Embodiment 3:

The composite noise figure using in experiment is as shown in Fig. 3 (a), and the circle in Fig. 3 (a) is the initial profile figure of active profile; Fig. 3 (b) is the segmentation effect figure of CV model; Fig. 3 (c) is the segmentation effect figure of the active contour model based on cluster; Fig. 3 (d) is the segmentation effect figure of the method that proposes of the present invention.Experimental result shows, the dividing method for the inhomogeneous composite noise figure of gray scale that the present invention proposes is identical with the active contour model segmentation effect based on cluster.

Embodiment 4:

The composite noise figure using in experiment is as shown in Fig. 4 (a), and the circle in Fig. 4 (a) is the initial profile figure of active profile; Fig. 4 (b) is the segmentation effect figure of CV model; Fig. 4 (c) is the segmentation effect figure of the active contour model based on cluster; Fig. 4 (d) is the segmentation effect figure of the method that proposes of the present invention.Experimental result shows, the automatic Segmentation better effects if for the inhomogeneous composite noise figure of gray scale that the present invention proposes.

Embodiment 5:

The composite noise figure using in experiment is as shown in Fig. 5 (a), and the circle in Fig. 5 (a) is the initial profile figure of active profile; Fig. 5 (b) is the segmentation effect figure of CV model; Fig. 5 (c) is the segmentation effect figure of the active contour model based on cluster; Fig. 5 (d) is the segmentation effect figure of the method that proposes of the present invention.Experimental result shows, the automatic Segmentation better effects if for the inhomogeneous composite noise figure of gray scale that the present invention proposes.

Embodiment 6:

The composite noise figure using in experiment is as shown in Fig. 6 (a), and the circle in Fig. 6 (a) is the initial profile figure of active profile; Fig. 6 (b) is the segmentation effect figure of CV model; Fig. 6 (c) is the segmentation effect figure of the active contour model based on cluster; Fig. 6 (d) is the segmentation effect figure of the method that proposes of the present invention.Experimental result shows, the automatic Segmentation better effects if for the inhomogeneous composite noise figure of gray scale that the present invention proposes.

Below in conjunction with specific embodiments technical scheme of the present invention is described; but these explanations can not be understood to limit scope of the present invention; protection scope of the present invention is limited by the claims of enclosing, and any change on the claims in the present invention basis is all protection scope of the present invention.

Claims (1)

1. for a dividing method for the inhomogeneous nuclear magnetic resonance image of gray scale, it is characterized in that: its concrete implementation step is as follows:

Step 1, the inhomogeneous nuclear magnetic resonance image of gray scale is carried out to initialization operation, on the inhomogeneous nuclear magnetic resonance image of gray scale, sketch out a closed curve;

Step 2, the active contour model of use based on region carry out iteration evolution to the target in the inhomogeneous nuclear magnetic resonance image of gray scale, obtain the contour curve of target; Be specially:

image area,

be a nuclear magnetic resonance image that the gray scale collecting is inhomogeneous, the x in I (x) represents gray-scale value, is a constant in image area Ω; J is true picture; B represents the gray scale unevenness of nuclear magnetic resonance image, is a kind of deviation territory, is a matrix; True picture J is approximately constant in every zonule, that is: for x ∈ Ω _i,

be the subdomain of image area Ω, have J (x) ≈ c _i, N is positive integer, c _irepresent the gray-scale value in i region in true picture J;

The energy functional of the active contour model based on region is as shown in Equation (13):

$E=E(\mathrm{\φ},c_1^{\mathrm{cv}},c_2^{\mathrm{cv}},b,c)+P\left(\mathrm{\φ}\right)---\left(13\right)$

Wherein, E is energy functional;

for Part I energy functional, be expressed as formula (14); φ is level set function; the gray-scale value of target in presentation video; the gray-scale value of background in presentation video; C is the local gray-value in true picture; P (φ) is Part II energy functional, is expressed as formula (15);

$E(\mathrm{\φ},c_1^{\mathrm{cv}},c_2^{\mathrm{cv}},b,c)=\mathrm{\μ}{E}^{\mathrm{local}}(\mathrm{\φ},b,c)+(1-\mathrm{\μ})E^{\mathrm{global}}(\mathrm{\φ},c_1^{\mathrm{cv}},c_2^{\mathrm{cv}})---\left(14\right)$

Wherein, μ is coefficient, the inhomogeneous degree of gray scale of the big or small presentation video of its value, and its value is larger, and the inhomogeneous degree of the gray scale of presentation video is higher; Its value is less, and the inhomogeneous degree of the gray scale of presentation video is lower;

e is natural logarithm; b _εit is the normalization item of deviation territory b; E ^local(φ, b, c) is local energy item, as shown in Equation (16);

global energy item, as shown in Equation (17);

$P\left(\mathrm{\φ}\right)=\mathrm{\η}\underset{\mathrm{\Ω}}{\∫}\frac{1}{2}{\left(\right|\▿\mathrm{\φ}\left(x\right)|-1)}^2\mathrm{dx}+\mathrm{\γ}\underset{\mathrm{\Ω}}{\∫}|\▿H\left(\mathrm{\φ}\left(x\right)\right)|\mathrm{dx}---\left(15\right)$

Wherein, η and γ are constants, get arithmetic number;

for gradient symbol; H (φ (x)) is Heaviside function;

$E^{\mathrm{local}}(\mathrm{\φ},b,c)=\∫(\underset{i=1}{\overset{2}{\mathrm{\Σ}}}\∫K(x-y){|I\left(y\right)-b\left(x\right)c_i|}^2{M}_i\left(\mathrm{\φ}\left(y\right)\right)\mathrm{dy})\mathrm{dx}---\left(16\right)$

Wherein, certain in x presentation graphs image field Ω a bit; K is a non-negative gauss kernel function, and it defines as shown in Equation (18); B (x) c _iit is the cluster centre that will predict; M ₁(φ (y))=H (φ (y)), M ₂(φ (y))=1-H (φ (y)); The span of y is determined by the following method: in image area Ω, centered by each some x, defined a circular neighborhood O in the radius ρ relatively little with _x:

$E^{\mathrm{global}}(\mathrm{\φ},c_1^{\mathrm{cv}},c_2^{\mathrm{cv}})={\mathrm{\λ}}_1\∫{|I\left(x\right)-c_1^{\mathrm{cv}}|}^{2}H\left(\mathrm{\φ}\left(x\right)\right)\mathrm{dx}+{\mathrm{\λ}}_2\∫{|I\left(x\right)-c_2^{\mathrm{cv}}|}^2(1-H\left(\mathrm{\φ}\left(x\right)\right))\mathrm{dx}---\left(17\right)$

Wherein, λ ₁, λ ₂, ν is constant;

$K\left(\mathrm{\ω}\right)=\left\{\begin{array}{cc}\frac{1}{a}{e}^{{-\left|\mathrm{\ω}\right|}^2/{2\mathrm{\σ}}^2}& \mathrm{for}\left|\mathrm{\ω}\right|\≤\mathrm{\ρ}\\ 0& \mathrm{otherwise}\end{array}\right.---\left(18\right)$

Wherein, a is a constant, and ω is the average of gaussian kernel function, and σ is variance.

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