CN106846349B - A kind of prostate Magnetic Resonance Image Segmentation method based on level set - Google Patents

A kind of prostate Magnetic Resonance Image Segmentation method based on level set Download PDF

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CN106846349B
CN106846349B CN201710105349.5A CN201710105349A CN106846349B CN 106846349 B CN106846349 B CN 106846349B CN 201710105349 A CN201710105349 A CN 201710105349A CN 106846349 B CN106846349 B CN 106846349B
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CN106846349A (en
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姜金刚
彭景春
张永德
韩英帅
郭晓伟
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FOSHAN BAIKANG ROBOT TECHNOLOGY Co.,Ltd.
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Harbin University of Science and Technology
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    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/10—Image acquisition modality
    • G06T2207/10072—Tomographic images
    • G06T2207/10081—Computed x-ray tomography [CT]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
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    • G06T2207/30081—Prostate

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Abstract

A kind of prostate Magnetic Resonance Image Segmentation method based on level set, it is related to Magnetic Resonance Image Segmentation technical field, the present invention is based on prostate magnetic resonance image, for the full segmentation problem of prostate inside and outside contour, it is proposed the prostate Magnetic Resonance Image Segmentation method based on Edge Distance adjustment level set movements, on the basis of constructing level set movements equation, realize that its outer profile is divided based on prostate magnetic resonance longitudinal relaxation time image, under the conditions of outer profile constraint qualification, the in-profile segmentation of prostate is realized based on prostate magnetic resonance lateral relaxation time image, and then complete comprehensive effective segmentation of prostate inside and outside contour.This method can effectively realize comprehensive segmentation of prostate inside and outside contour, be in close proximity to the desired result of clinical expert manual segmentation, and the clinical diagnosis and treatment to prostatic disorders have preferable reference value.

Description

A kind of prostate Magnetic Resonance Image Segmentation method based on level set
Technical field
The prostate Magnetic Resonance Image Segmentation method based on level set that the present invention relates to a kind of, belongs to Magnetic Resonance Image Segmentation Technical field.
Background technique
As population increases the change with living habit, the morbidity and mortality of prostate cancer are in obvious rising in recent years Trend.If clinical experience shows that prostate cancer can be found as early as possible, get timely medical treatment, there is very high survival rate, it is therefore, right It is of great significance in the correlative study of prostate cancer diagnosis and treatment.Weight of the medical image as prostate cancer diagnosis and treatment One of means are wanted, increasingly important role is played.Magnetic resonance image, can multi-parameter because it has to soft tissue resolution height Imaging, the characteristics of capable of being scanned to any tomography, it is considered to be the best medicine of prostate cancer diagnosis and adjuvant treatment at present Image.
Image segmentation is the basis based on image early diagnosis and therapy, is the critical issue primarily solved.Currently, forefront The segmentation research of gland magnetic resonance image has focused largely on the segmentation of prostate outer profile, and dividing method mainly has graph theory, deformation mould Four major class such as type, specific theory and mixed image partition method.It is complete to the prostate inside and outside contour based on magnetic resonance image Segmentation research just starts to spread out in recent years.2011, French Makni et al. was realized earliest using the method for C- mean value and is based on The prostate inside and outside contour of magnetic resonance image is divided entirely.2012, the method benefit that Dutch Litjens et al. passes through pattern-recognition Classified with dissection, sum of the grayscale values textural characteristics to prostate voxel of object, realizes inside and outside contour and divide entirely.Both sides Method is all that the manually mode that first passes through realizes that outer profile is divided, and as the initialization of inside division, makes the complete of prostate Divide time-consuming and laborious.2013, the Toth in the U.S. et al. was carried out using the method for multiple coupling level set movable contour model Inside and outside contour is divided entirely, and the segmentation effect of this method more depends on the quality of institute's segmented image, and dividing an image need to A large amount of atlas are trained, elapsed time is longer.2014, Canadian Qiu et al. utilized the side for optimizing continuous maximum flow model Method has carried out the inside and outside full segmentation of prostate, improves segmentation effect and improves segmentation efficiency.Due to prostate interior zone For magnetic resonance image there are noise, gray scale shows that unevenly zone boundary is smudgy, makes in the prostate based on magnetic resonance image It is always a challenge that outer profile divides research entirely.
Summary of the invention
In view of the above-mentioned problems, the technical problem to be solved in the present invention is to provide a kind of prostate magnetic resonance based on level set Image partition method is primarily based on longitudinal relaxation time image, by forefront on the basis of constructing uniform level collection energy function Gland is split from its surrounding tissue, i.e. the outer profile segmentation of realization prostate will secondly based on lateral relaxation time image Outer profile realizes the interior zone segmentation of prostate as constraint condition, and then realizes that the inside and outside contour of prostate is divided entirely.
Above-mentioned purpose is mainly realized by following scheme:
A kind of prostate Magnetic Resonance Image Segmentation method based on level set of the invention, it is characterised in that: the method Specific implementation process are as follows:
Step 1: level set movements equation is defined
A level set function is defined in the domain ΩEnergy function ε (φ) is defined as:
ε (φ)=μ Rp(φ)+αεdrive(φ) (1)
Wherein, Rp(φ) is the distance adjustment item of level set, εdrive(φ) is profile driving energy item, μ > 0, α < 0, all For constant；
The distance of level set adjusts item Rp(φ) is defined as:
Wherein, p is energy density function,
Energy density function construction are as follows:
Energy density function p (s) tool is s=0 and s=1 respectively there are two extreme point, first derivative and second dervative Are as follows:
Function R in formula (2)pThe gateaux derivative of (φ) are as follows:
Wherein, function dpIs defined as:
Profile driving energy item εdrive(φ) is defined as:
Wherein, g is boundary constraint function, and H is unit-step function, and unit-step function H is approximatively usually used function HεIt replaces, and is defined as:
HεDerivative δεAre as follows:
Profile driving energy function of εdriveThe gateaux derivative of (φ) are as follows:
The steady state solution of gradient flow equation is solved,
Wherein,It is the gateaux derivative of function of ε (φ)；
Formula (6) and formula (11) are substituted into (12), the gradient current expression formula of available energy function ε (φ) are as follows:
Partial differential equation shown in formula (13) are namely based on the level set movements side of the prostate inside and outside contour segmentation of formula (1) Journey；
Transient state partial derivativeIt approximate can be solved using positive finite difference equations, time-varying function φ (x, y, t) Discrete form useIt indicates, then level set movements equation discrete can be as follows finite difference equations:
Step 2: outer profile segmentation
Original longitudinal relaxation time image is read, outer segmentation initial method-indicatrix ellipse method is selected:
Shown in basic elliptic parametric equation such as formula (15):
Wherein, axIt is half axial length in the direction x, ayIt is half axial length in the direction y；
Parametric equation ψ (the x of indicatrix ellipse is obtained by converting basic elliptic equation along y-axisd,yd), such as formula (16) institute Show:
Wherein,
Region determined by fixed prostate indicatrix ellipse is set as Se, then initial level set function are as follows:
Wherein, c0For normal number；
In formula (16) and formula (17), (xc,yc) be indicatrix ellipse centre coordinate, ty∈ [- 1,1] is on description ellipse The parameter that portion linearly comes to a point along the y-axis direction, by∈ [- 1,0) and ∪ (0,1] it is to describe oval lower part inner concave bending along the y-axis direction Bent parameter, adjustment type (16) and formula (17) corresponding parameter, so that deformable ellipse approaches the foreign steamer of prostate to greatest extent Profile shape；
Then, it is determined that outer profile boundary constraint function:
In longitudinal relaxation time image, it is assumed that I is prostate image, defines the boundary indicator of image I are as follows:
Wherein, GσBe variance be σ Gaussian kernel, the boundary constraint function that formula (19) is divided as prostate outer profile, And given parameters value.
Solution finally is iterated to level set movements equation (14), realizes the outer profile segmentation of prostate；
Step 3: interior zone segmentation
Original lateral relaxation time image is read, interior segmentation initial method-multi-line section fitting process is selected:
N number of point is successively chosen in central gland, is made this N number of point join end to end to form a closed area, is set as SN, then initially Level set function are as follows:
Wherein, c0For normal number；
Then, it is determined that Internal periphery boundary constraint function:
The boundary characteristic of prostate center gland image is described using omnidirectional's boundary gradient as boundary indicator, it is assumed that I For prostate image, Ii,jFor a certain element of I, it is set as central element, 8 adjacent elements are respectively Ii-1,j-1, Ii-1,j, Ii-1,j+1, Ii,j-1, Ii,j+1, Ii+1,j-1, Ii+1,j, Ii+1j+1, for the difference for seeking this 8 element and central element, it is defined as follows correspondence 8 convolution masks,
The difference of central element and adjacent 8 element calculates are as follows:
Dif_lu=conv2 (I, Temp_lu, ' same') (29)
Dif_u=conv2 (I, Temp_u, ' same') (30)
Dif_ru=conv2 (I, Temp_ru, ' same') (31)
Dif_l=conv2 (I, Temp_l, ' same') (32)
Dif_r=conv2 (I, Temp_r, ' same') 33)
Dif_ld=conv2 (I, Temp_ld, ' same') (34)
Dif_d=conv2 (I, Temp_d, ' same') (35)
Dif_rd=conv2 (I, Temp_rd, ' same') (36)
Conv2 is convolution operator, omnidirectional's boundary gradient function of image I is defined as:
Grad_I=[Grad_Ix Grad_Iy Grad_Ixy- Grad_Ixy+] (37)
Wherein, items are respectively defined as:
Omnidirectional's boundary gradient mould of image I is defined as:
| Grad_I |=sqrt (Grad_Ix 2+Grad_Iy 2+Grad_Ixy- 2+Grad_Ixy+ 2) (42)
Boundary constraint function in formula (12) are as follows:
Formula (43) is known as the boundary constraint function of prostate Internal periphery segmentation, and given parameters value；
Solution finally is iterated to level set movements equation (14), obtains the profile of prostate center of inside gland；By The outer profile that two steps obtain carries out region with the obtained central gland profile of third step and subtracts each other, and just obtains prostatic peripheral zone area Domain, and then realize comprehensive segmentation of prostate.
The invention has the benefit that
1, two step of the prostate segmentation combined based on longitudinal relaxation time image with lateral relaxation time image is proposed It is with distinct contrast, it can be achieved that outer profile segmentation and lateral relaxation time image to combine longitudinal relaxation time image internal/external signal for method Internal structure shows clearly, and peripheral zone and central gland signal form obvious comparison, it can be achieved that the advantages of the segmentation of inner region, overcomes Longitudinal relaxation time image is difficult to differentiate between inside internal structure and lateral relaxation time image clearly multizone signal gray scale The shortcomings that value is by the extraction and segmentation of interfering outer profile.
2, distance adjustment item has been incorporated in the energy function established, and can be constantly adjusted in evolutionary process, Caused surrounding diffusion effect can maintain desired shape near desired profile at a distance from, it is same what need not be reinitialized When avoid general level set method due to numerical fault caused by constantly initializing.
3, using initial profile close to outer segmentation initialization-indicatrix ellipse method of inside and outside contour and interior segmentation initialization- Multi-line section fitting process initializes level set function respectively, and segmentation effect can be improved.
Detailed description of the invention
Detailed description will be given by the following detailed implementation and drawings by the present invention for ease of explanation,.
Fig. 1 is the flow chart of the method for the present invention；
Fig. 2 is difference a in the outer segmentation initialization-indicatrix ellipse method of the present inventionxThe outline drawing of parameter；
Fig. 3 is difference b in the outer segmentation initialization-indicatrix ellipse method of the present inventionyThe outline drawing of parameter；
Fig. 4 is human-computer interaction interface of the invention.
Specific embodiment
In order to make the objectives, technical solutions and advantages of the present invention clearer, below by shown in the accompanying drawings specific Embodiment describes the present invention.However, it should be understood that these descriptions are merely illustrative, and it is not intended to limit model of the invention It encloses.In addition, in the following description, descriptions of well-known structures and technologies are omitted, it is of the invention to avoid unnecessarily obscuring Concept.
As shown in Figure 1, Figure 2, Figure 3, Figure 4, present embodiment uses following technical scheme: a kind of based on level set Prostate Magnetic Resonance Image Segmentation method, it is characterised in that: the specific implementation process of the method are as follows:
Step 1: level set movements equation is defined
A level set function is defined in the domain ΩEnergy function ε (φ) is defined as:
ε (φ)=μ Rp(φ)+αεdrive(φ) (1)
Wherein, Rp(φ) is the distance adjustment item of level set, εdrive(φ) is profile driving energy item, drives level set letter Number curve is moved to prostate profile and border, μ > 0, α < 0, is all constant；
The distance of level set adjusts item Rp(φ) is defined as:
Wherein, p is energy density function,
In order to avoid boundary effect, energy density function construction are as follows:
Energy density function p (s) tool is s=0 and s=1 respectively there are two extreme point, first derivative and second dervative Are as follows:
Function R in formula (2)pThe gateaux derivative of (φ) are as follows:
Wherein function dpIs defined as:
Profile driving energy item εdrive(φ) is defined as:
Wherein, g is boundary constraint function, and H is unit-step function, and unit-step function H is approximatively usually used function HεIt replaces, and is defined as:
HεDerivative δεAre as follows:
Profile driving energy function of εdriveThe gateaux derivative of (φ) are as follows:
In order to seek the minimum value of energy function ε (φ), conventional method is just to solve for the steady state solution of gradient current equation:
Wherein,It is the gateaux derivative of function of ε (φ)；
Formula (6) and formula (11) are substituted into (12), the gradient current expression formula of available energy function ε (φ) are as follows:
Partial differential equation shown in formula (13) are namely based on the level set movements side of the prostate inside and outside contour segmentation of formula (1) Journey；
Transient state partial derivativeIt approximate can be solved using positive finite difference equations, time-varying function φ (x, y, t) Discrete form useIt indicates, finite difference equations that such level set movements equation discrete can be as follows:
Step 2: outer profile segmentation
Original longitudinal relaxation time image is read, outer segmentation initial method-indicatrix ellipse method is selected:
Shown in basic elliptic parametric equation such as formula (15):
Wherein, axIt is half axial length in the direction x, ayIt is half axial length in the direction y；
Since the outer contour shape of each layer of the cross-section axle position of prostate is changed along y-axis, pass through conversion along y-axis Basic elliptic equation can obtain the parametric equation ψ (x of indicatrix ellipsed,yd), as shown in formula (16):
Wherein,
Region determined by fixed prostate indicatrix ellipse is set as Se, then initial level set function are as follows:
Wherein, c0For normal number.
In formula (16) and formula (17), (xc,yc) be indicatrix ellipse centre coordinate, ty∈ [- 1,1] is on description ellipse The parameter that portion linearly comes to a point along the y-axis direction, by∈ [- 1,0) and ∪ (0,1] it is to describe oval lower part inner concave bending along the y-axis direction Bent parameter.By adjusting formula (19) and formula (20) corresponding parameter, so that deformable ellipse approaches prostate to greatest extent Outer contour shape；
Then, it is determined that outer profile boundary constraint function:
In longitudinal relaxation time image, it is assumed that I is prostate image, defines the boundary indicator of image I are as follows:
Wherein, GσIt is the Gaussian kernel that variance is σ, convolution is used to smooth prostate image in formula, reduces the influence of noise, will The boundary constraint function that formula (19) is divided as prostate outer profile, and given parameters value.
Solution finally is iterated to level set movements equation (14), realizes the outer profile segmentation of prostate；
Step 3: interior zone segmentation
Original lateral relaxation time image is read, interior segmentation initial method-multi-line section fitting process is selected:
N number of point is successively chosen in central gland, is made this N number of point join end to end to form a closed area, is set as SN, then initially Level set function are as follows:
Wherein, c0For normal number；
Then, it is determined that Internal periphery boundary constraint function:
The boundary characteristic of prostate center gland image is described using omnidirectional's boundary gradient as boundary indicator,
It is assumed that I is prostate image, Ii,jFor a certain element of I, it is set as central element.Its 8 adjacent element is respectively Ii-1,j-1, Ii-1,j, Ii-1,j+1, Ii,j-1, Ii,j+1, Ii+1,j-1, Ii+1,j, Ii+1,j+1.For the difference for seeking this 8 element and central element Value, is defined as follows corresponding 8 convolution masks,
The difference of central element and adjacent 8 element calculates are as follows:
Dif_lu=conv2 (I, Temp_lu, ' same') (29)
Dif_u=conv2 (I, Temp_u, ' same') (30)
Dif_ru=conv2 (I, Temp_ru, ' same') (31)
Dif_l=conv2 (I, Temp_l, ' same') (32)
Dif_r=conv2 (I, Temp_r, ' same') 33)
Dif_ld=conv2 (I, Temp_ld, ' same') (34)
Dif_d=conv2 (I, Temp_d, ' same') (35)
Dif_rd=conv2 (I, Temp_rd, ' same') (36)
Conv2 is convolution operator, omnidirectional's boundary gradient function of image I is defined as:
Grad_I=[Grad_Ix Grad_Iy Grad_Ixy- Grad_Ixy+] (37)
Wherein, items are respectively defined as:
Omnidirectional's boundary gradient mould of image I is defined as:
| Grad_I |=sqrt (Grad_Ix 2+Grad_Iy 2+Grad_Ixy- 2+Grad_Ixy+ 2) (42)
Boundary constraint function in formula (12) are as follows:
Formula (43) is known as the boundary constraint function of prostate Internal periphery segmentation, and given parameters value；
Solution finally is iterated to level set movements equation (14), obtains the profile of prostate center of inside gland；By The outer profile that two steps obtain carries out region with the obtained central gland profile of third step and subtracts each other, and just obtains prostatic peripheral zone area Domain, and then realize comprehensive segmentation of prostate.
The above shows and describes the basic principles and main features of the present invention and the advantages of the present invention.The technology of the industry Personnel are it should be appreciated that the present invention is not limited to the above embodiments, and the above embodiments and description only describe this The principle of invention, without departing from the spirit and scope of the present invention, various changes and improvements may be made to the invention, these changes Change and improvement all fall within the protetion scope of the claimed invention.The claimed scope of the invention by appended claims and its Equivalent thereof.

Claims (1)

1. a kind of prostate Magnetic Resonance Image Segmentation method based on level set, it is characterised in that: the specific implementation of the method Process are as follows:
Step 1: level set movements equation is defined
A level set function is defined in the domain ΩEnergy function ε (φ) is defined as:
ε (φ)=μ Rp(φ)+αεdrive(φ) (1)
Wherein, Rp(φ) is the distance adjustment item of level set, εdrive(φ) is profile driving energy item, and μ > 0, α < 0 are normal Number；
The distance of level set adjusts item Rp(φ) is defined as:
Wherein, p is energy density function,
Energy density function construction are as follows:
Energy density function p (s) tool is s=0 and s=1 respectively there are two extreme point, first derivative and second dervative are as follows:
Function R in formula (2)pThe gateaux derivative of (φ) are as follows:
Wherein function dpIs defined as:
Profile driving energy item εdrive(φ) is defined as:
Wherein, g is boundary constraint function, and H is unit-step function, and unit-step function H is approximatively usually used function HεCarry out generation It replaces, and is defined as:
HεDerivative δεAre as follows:
Profile driving energy function of εdriveThe gateaux derivative of (φ) are as follows:
Solve the steady state solution of gradient flow equation:
Wherein,It is the gateaux derivative of function of ε (φ)；
Formula (6) and formula (11) are substituted into (12), the gradient current expression formula of available energy function ε (φ) are as follows:
Partial differential equation shown in formula (13) are namely based on the level set movements equation of the prostate inside and outside contour segmentation of formula (1)；
Transient state partial derivativeApproximate can be solved using positive finite difference equations, time-varying function φ (x, y, t) from The form of dissipating is usedIt indicates, then level set movements equation discrete can be as follows finite difference equations:
Step 2: outer profile segmentation
Original longitudinal relaxation time image is read, outer segmentation initial method-indicatrix ellipse method is selected:
Shown in basic elliptic parametric equation such as formula (15):
Wherein, axIt is half axial length in the direction x, ayIt is half axial length in the direction y；
Parametric equation ψ (the x of indicatrix ellipse is obtained by converting basic elliptic equation along y-axisd,yd), as shown in formula (16):
Wherein,
Region determined by fixed prostate indicatrix ellipse is set as Se, then initial level set function are as follows:
Wherein, c0For normal number；
In formula (16) and formula (17), (xc,yc) be indicatrix ellipse centre coordinate, ty∈ [- 1,1] is to describe oval top edge The parameter that comes to a point of y-axis dimension linear, by∈ [- 1,0) ∪ (0,1] describes oval lower part and is curved concave inward along the y-axis direction Parameter, adjustment type (16) and formula (17) corresponding parameter, so that deformable ellipse approaches the foreign steamer profile of prostate to greatest extent Shape；
Then, it is determined that outer profile boundary constraint function:
In longitudinal relaxation time image, it is assumed that I is prostate image, defines the boundary indicator of image I are as follows:
Wherein, GσIt is the Gaussian kernel that variance is σ, the boundary constraint function that formula (19) is divided as prostate outer profile, and giving Parameter value；
Solution finally is iterated to level set movements equation (14), realizes the outer profile segmentation of prostate；
Step 3: interior zone segmentation
Original lateral relaxation time image is read, interior segmentation initial method-multi-line section fitting process is selected:
N number of point is successively chosen in central gland, is made this N number of point join end to end to form a closed area, is set as SN, then initial level Set function are as follows:
Wherein, c0For normal number；
Then, it is determined that Internal periphery boundary constraint function:
The boundary characteristic of prostate center gland image is described using omnidirectional's boundary gradient as boundary indicator, it is assumed that before I is Column gland image, Ii,jFor a certain element of I, it is set as central element, 8 adjacent elements are respectively Ii-1,j-1, Ii-1,j, Ii-1,j+1, Ii,j-1, Ii,j+1, Ii+1,j-1, Ii+1,j, Ii+1,j+1, for the difference for seeking this 8 element and central element, it is defined as follows pair 8 convolution masks answered,
The difference of central element and adjacent 8 element calculates are as follows:
Dif_lu=conv2 (I, Temp_lu, ' same') (29)
Dif_u=conv2 (I, Temp_u, ' same') (30)
Dif_ru=conv2 (I, Temp_ru, ' same') (31)
Dif_l=conv2 (I, Temp_l, ' same') (32)
Dif_r=conv2 (I, Temp_r, ' same') (33)
Dif_ld=conv2 (I, Temp_ld, ' same') (34)
Dif_d=conv2 (I, Temp_d, ' same') (35)
Dif_rd=conv2 (I, Temp_rd, ' same') (36)
Conv2 is convolution operator, omnidirectional's boundary gradient function of image I is defined as:
Grad_I=[Grad_Ix Grad_Iy Grad_Ixy- Grad_Ixy+] (37)
Wherein, items are respectively defined as:
Omnidirectional's boundary gradient mould of image I is defined as:
| Grad_I |=sqrt (Grad_Ix 2+Grad_Iy 2+Grad_Ixy- 2+Grad_Ixy+ 2) (42)
Boundary constraint function in formula (12) are as follows:
Formula (43) is known as the boundary constraint function of prostate Internal periphery segmentation, and given parameters value；
Solution finally is iterated to level set movements equation (14), obtains the profile of prostate center of inside gland；By second step Obtained outer profile carries out region with the obtained central gland profile of third step and subtracts each other, and just obtains prostatic peripheral zone region, into And realize comprehensive segmentation of prostate.
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