CN107689046A - A kind of brain MRI image dividing method based on D S evidence theories - Google Patents
A kind of brain MRI image dividing method based on D S evidence theories Download PDFInfo
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- CN107689046A CN107689046A CN201710612862.3A CN201710612862A CN107689046A CN 107689046 A CN107689046 A CN 107689046A CN 201710612862 A CN201710612862 A CN 201710612862A CN 107689046 A CN107689046 A CN 107689046A
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- G—PHYSICS
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- G06T7/10—Segmentation; Edge detection
- G06T7/11—Region-based segmentation
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- G06F18/25—Fusion techniques
- G06F18/251—Fusion techniques of input or preprocessed data
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Abstract
The invention provides a kind of brain MRI image dividing method based on D S evidence theories, it is related to field of medical image processing, this method is merged the neighborhood information between the half-tone information and pixel of a width brain MRI image, information carries out the segmentation of image of both comprehensive, this method eliminates redundancy and contradiction that may be present between information by the fusion between different information, it is subject to complementation, it is uncertain to reduce it, the accuracy and noise immunity of image after splitting are improved, reduces the erroneous segmentation rate of image slices vegetarian refreshments.
Description
Technical field
The present invention relates to field of medical image processing, and in particular to a kind of brain MRI image point based on D-S evidence theory
Segmentation method.
Background technology
As the fast development of science and technology, Magnetic resonance imaging (MRI, magnetic resonance imaging) are extensive
, can be by different tissue segmentations, so as to aid in doctor to find by brain MRI image applied to the diagnosis and treatment of the disease to brain
Brain lesionses.But low contrast due to MRI image and the interference for being vulnerable to noise in imaging process so that different tissues it
Between easily there is aliasing, so as to cause segmentation difficult.
D-S evidence theory algorithm is one of algorithm maximally efficient in information fusion, and its collaboration utilizes multi-source information, to obtain
Obtain more objective to things or target, more essential understanding.Evidence theory widens the space of elementary events in probability theory for basic thing
The power set of part, also known as framework of identification, Basic probability assignment function (Basic Probability are established on framework of identification
Assignment, BPA).In addition, evidence theory additionally provides a Dempster rule of combination, the rule can be in no elder generation
The fusion of evidence is realized in the case of testing information.Just because of DS evidence theories in terms of uncertain knowledge expression have it is excellent
Performance, so its theoretical and application development was very fast in recent years, the theory refers in multi-sensor information fusion, medical diagnosis, military affairs
Wave, played important function in terms of target identification.
Traditional segmentation to brain MRI image only passes through the feature in terms of certain, such as texture information, half-tone information, sky
Between information etc., therefore obtained result has significant limitation, for containing noise, obscurity boundary image for, obtain
The MRI image segmentation effect arrived is also not usually fine.
The content of the invention
For overcome the deficiencies in the prior art, the present invention provides a kind of brain MRI image segmentation based on D-S evidence theory
Method, this method integrate the different characteristic of same image, then carry out the segmentation of image, and the dividing method has good anti-noise
Property, and the image segmentation error rate after segmentation is small.
The technical solution adopted for the present invention to solve the technical problems comprises the following steps：
Step 1：Artwork F to be split is subjected to medium filtering and generates a filtered image Fm, described medium filtering
It is：Equation below X=Med (X are used to the gray value of artwork F each pixel using 3 × 3 square templates1,X2,…,
Xn) evaluation is carried out, wherein because template size is 3 × 3, therefore n=9, XiIt is one of 3 × 3 template pixels；
Step 2：By artwork F and filtered figure FmClustered using FCM algorithms, c × n sizes corresponding to generation
Subordinated-degree matrix：Uc×nAnd U'c×n, wherein c represents that the image is divided into c classes, respectively A1,A2,...,Ac, n represents the image
Share n pixel, respectively P1,P2,...,Pn, each pixel PiBelong to AjThe probability of class (1 ＜ j ＜ c) is expressed as
uij, Uc×n=(uij)c×n；
Step 3：The subordinated-degree matrix U and U' that are generated in step 2 the n group probability being respectively converted into evidence theory are referred to
Send function (BPA), respectively m1,m2,...,mn、m'1,m'2,...,m'nSpecific transformation rule is as follows：
Subordinated-degree matrix U is converted to the BPA, i.e. m of the burnt member of only list collection firstj(Ai)=uij(0 ＜ i ＜ c, 0 ＜ j
＜ n)；Secondly each pixel P is determinedjCorresponding this group of mjMaximum, be represented by M (j)=max (mj(Ai)), note makes mj
Obtain the A of maximumiFor Am；Then given threshold α, for any Ai(0 ＜ i ＜ c), if making M (j)-mj(Ai) ＜ α, then by Ai
And AmAdd set DjIn；Next by DjIn the burnt member of the more subsets of Element generation and add corresponding mj, create-rule isIf set DjFor sky, then corresponding mjIn the only burnt member of list collection；
Step 4：By the m that subordinated-degree matrix U and U' are generated respectively in step 31,m2,...,mnAnd m'1,m'2,...,m'n
Merged using Dempster rules of combination, the BPA m* after generation fusion1,m*2,…,m*n；
Step 5：BPA m* after the n groups obtained in step 4 are merged1,m*2,...,m*nBe converted to subordinated-degree matrix
U*, specific conversion method are：
Wherein 0 ＜ j ＜ n, Θ represents the complete or collected works in evidence theory, the formula
It is meant that m*jIn the quality of the burnt member of more subsets give the burnt member of list collection, due to only including the BPA of the burnt member of list collection
It is identical with the column vector in subordinated-degree matrix, therefore have above formula；
Step 6：Segmentation is generated after carrying out decision-making to classification described in each pixel according to the subordinated-degree matrix U* after fusion
Image afterwards, the decision-making technique are：If i make U* jth column vector achieve maximum, pixel PjGeneric is
Ai。
Basic theory of the invention introduced below：
Define 1 and represent a mutual exclusion and complete set, i.e. Θ={ θ with Θ in D-S evidence theory1,θ2,...,
θ1, Θ is referred to as framework of identification, wherein θiA referred to as framework of identification Θ event, the collection being made up of all subsets of framework of identification Θ
Θ power set is collectively referred to as, is denoted as 2Θ, its element number is 2|Θ|；
Define 2 and set Θ as a framework of identification, A is Θ subset, then function m meets following condition
2)0≤m(A)≤1；
Then m is referred to as the basic probability assignment (BPA, basic probability assignment) on framework of identification Θ,
ForIf m (A) ＞ 0, A are referred to as burnt member,Represent that empty set does not have any degree of belief,Table
Show that all subset trust value sums are equal to 1；
Define 3Dempster rules of combination：The rule of combination can be merged a plurality of evidence, be specifically expressed as
WhereinRepresent the conflict between evidence；
4FCM clustering algorithms are defined by sample space X={ x1,x2,…,xnSample point be divided into c (c ＞ 1) class, each sample
The degree that this i belongs to jth class (1 ＜ j ＜ c) is expressed as uij, sample space X fuzzy clustering subordinated-degree matrix U=
(uij)c×nRepresent, matrix u meets following condition：
5 object functions are defined to be defined as：
In formula：V={ v1,…,vj,…,vc, vjFor the cluster centre of jth class；d2(xi,vk) it is xiWith vjThe distance between
Metric function；M is FUZZY WEIGHTED index.In order to obtain the division of data set X optimal fuzzy c class, it is necessary to which trying to achieve makes | Jm(U(t+1),
V(t+1))-Jm(U(t),V(t)) | the solution (U, V) during ＜ ε minimums.This can be completed by following iteration：
1) initialize, input data set { xi, i=1,2 ..., n, it is cluster numbers c, Fuzzy Weighting Exponent m ∈ R ＞ 1, maximum
Iterations T and threshold epsilon, random initializtion subordinated-degree matrix U(t)(t=0, t are iterations)；
2) using following formula renewal degree of membership center and subordinated-degree matrix：
If 3) | Jm(U(t+1),V(t+1))-Jm(U(t),V(t)) | ＜ ε or t ＞ T, then cluster stopping generation subordinated-degree matrix U, no
Then go to 2.
It is proposed that a kind of characteristic information for the use of MRI image two is divided the beneficial effects of the present invention are the present invention
The method cut, i.e. original image and medium filtering image, original image represent original gradation information, and filtering image represents certain pixel
Neighborhood information, the information of comprehensive these two aspects preferably can be split to image；Present invention is alternatively directed to image to generate evidence
BPA gives rational method in theory, and the BPA generated using this method is merged, and may finally be split well
Effect；Brain MRI image dividing method based on D-S evidence theory has the features such as noise immunity is good, and segmentation error rate is small.
Brief description of the drawings
Fig. 1 is the algorithm entire block diagram of the present invention；
Fig. 2 is present invention MRI image to be split；
Fig. 3 is the MRI image after medium filtering of the present invention；
Fig. 4 is the Filtering Template figure of the present invention；
Fig. 5 is the image of present invention fusion segmentation.
Embodiment
The present invention is further described with reference to the accompanying drawings and examples.
Step 1：MRI original images F to be split is subjected to medium filtering and generates a filtered image Fm, original to be split
Image as shown in Fig. 2 filtered image as shown in figure 3, described medium filtering is：Using 3 × 3 square templates to original
The gray value for scheming F each pixel uses equation below X=Med (X1,X2,…,Xn) carry out evaluation, template as shown in figure 4,
Wherein because template size is 3 × 3, therefore n=9, XiIt is 3 × 3 template pixel P1、P2、P3、P4、P5、P6、P7、P8、P9In appoint
Meaning one；
Step 2：By artwork F and filtered figure FmClustered using FCM algorithms, c × n sizes corresponding to generation
Subordinated-degree matrix：Uc×nAnd U'c×n, wherein c represents that the image is divided into c classes, respectively A1,A2,...,Ac, n represents the image
Share n pixel, respectively P1,P2,...,Pn, each pixel PiBelong to AjThe probability of class (1 ＜ j ＜ c) is expressed as
uij, Uc×n=(uij)c×n；
In the present embodiment, artwork size is 432 × 432 totally 186624 pixels, and needed to be divided into 4 classes, point
It is not background, white matter of brain, ectocinerea and cerebrospinal fluid, therefore c=4, n=186624 are used 4 × 186624 corresponding to the generation of FCM algorithms
The subordinated-degree matrix of size：U4×186624And U'4×186624；
Step 3：186624 subordinated-degree matrix U and U' that are generated in step 2 are respectively converted into D-S evidence theory
Group probability assignment function (BPA), respectively m1,m2,...,m186624、m'1,m'2,...,m'186624Specific transformation rule is as follows：
Subordinated-degree matrix U is converted to the BPA, i.e. m of the burnt member of only list collection firstj(Ai)=uij(the ＜ j of 0 ＜ i ＜ 4,0
＜ 186624)；Secondly each pixel P is determinedjCorresponding this group of mjMaximum, be represented by M (j)=max (mj(Ai)),
Note makes mjObtain the A of maximumiFor Am；Then given threshold α=0.1, for any Ai(0 ＜ i ＜ 4), if making M (j)-mj(Ai)
＜ α, then by AiAnd AmAdd set DjIn；Next by DjIn the burnt member of the more subsets of Element generation and add corresponding mj, generation rule
It is thenIf set DjFor sky, then corresponding mjIn the only burnt member of list collection；
Step 4：By the m that subordinated-degree matrix U and U' are generated respectively in step 31,m2,...m,1866With2m'1,m'2,...,
m'186624Merged using Dempster rules of combination, the BPAm* after generation fusion1,m*2,...,m*186624；
Step 5：By the BPA m* after obtained in step 4 186624 groups of fusions1,m*2,...,m*186624Be converted to person in servitude
Category degree matrix U *, specific conversion method are：
Wherein 0 ＜ j ＜ 186624, Θ represent complete in D-S evidence theory
Collection, is Θ={ A in this specific embodiment1,A2,A3,A4}；
Step 6：After decision making segmentation being carried out according to the subordinated-degree matrix U* after fusion to classification described in each pixel
MRI image, as shown in figure 5, the decision-making technique is：If i make U* jth column vector achieve maximum, pixel
PjGeneric is Ai。
Claims (1)
1. a kind of brain MRI image dividing method based on D-S evidence theory, it is characterised in that comprise the steps：
Step 1：Artwork F to be split is subjected to medium filtering and generates a filtered image Fm, described medium filtering is：Make
Equation below is used to the gray value of artwork F each pixel with 3 × 3 square templates
X=Med (X1,X2,…,Xn) evaluation is carried out, wherein because template size is 3 × 3, therefore n=9, XiIt is 3 × 3 template pixels
One of point；
Step 2：By artwork F and filtered figure FmClustered using FCM algorithms, the degree of membership of c × n sizes corresponding to generation
Matrix：Uc×nAnd U'c×n, wherein c represents that the image is divided into c classes, respectively A1,A2,...,Ac, it is individual that n represents that the image shares n
Pixel, respectively P1,P2,...,Pn, each pixel PiBelong to AjThe probability of class (1 ＜ j ＜ c) is expressed as uij, Uc×n=
(uij)c×n；
Step 3：The n groups probability subordinated-degree matrix U and U' that are generated in step 2 being respectively converted into evidence theory assigns letter
Number (BPA), respectively m1,m2,...,mn、m'1,m'2,...,m'nSpecific transformation rule is as follows：
Subordinated-degree matrix U is converted to the BPA, i.e. m of the burnt member of only list collection firstj(Ai)=uij(0 ＜ i ＜ c, 0 ＜ j ＜ n)；
Secondly each pixel P is determinedjCorresponding this group of mjMaximum, be represented by M (j)=max (mj(Ai)), note makes mjObtain most
The A being worth greatlyiFor Am；Then given threshold α, for any Ai(0 ＜ i ＜ c), if making M (j)-mj(Ai) ＜ α, then by AiAnd AmAdd collection
Close DjIn；Next by DjIn the burnt member of the more subsets of Element generation and add corresponding mj, create-rule is
If set DjFor sky, then corresponding mjIn the only burnt member of list collection；
Step 4：By the m that subordinated-degree matrix U and U' are generated respectively in step 31,m2,...,mnAnd m'1,m'2,...,m'nUse
Dempster rules of combination are merged, the BPA m* after generation fusion1,m*2,…,m*n；
Step 5：BPA m* after the n groups obtained in step 4 are merged1,m*2,...,m*nSubordinated-degree matrix U* is converted to, is had
Body conversion method is：
Wherein 0 ＜ j ＜ n, Θ represents the complete or collected works in evidence theory, and the formula contains
Justice is by m*jIn the quality of the burnt member of more subsets give the burnt member of list collection, due to only including the BPA and person in servitude of the burnt member of list collection
Column vector in category degree matrix is identical, therefore has above formula；
Step 6：After splitting according to the subordinated-degree matrix U* after fusion to generation after classification progress decision-making described in each pixel
Image, the decision-making technique are：If i make U* jth column vector achieve maximum, pixel PjGeneric is Ai。
Step introduced below it is above-mentioned it is rapid in be related to theory：
Define 1 and represent a mutual exclusion and complete set, i.e. Θ={ θ with Θ in D-S evidence theory1,θ2,...,θ1,
Θ is referred to as framework of identification, wherein θiA referred to as framework of identification Θ event, the set being made up of all subsets of framework of identification Θ
Referred to as Θ power set, is denoted as 2Θ, its element number is 2|Θ|；
Define 2 and set Θ as a framework of identification, A is Θ subset, then function m meets following condition
1)
2)0≤m(A)≤1；
3)
Then m is referred to as the basic probability assignment (BPA, basic probability assignment) on framework of identification Θ, forIf m (A) ＞ 0, A are referred to as burnt member,Represent that empty set does not have any degree of belief,Represent institute
There is subset trust value sum to be equal to 1；
Define 3 Dempster rules of combination：The rule of combination can be merged a plurality of evidence, be specifically expressed as
WhereinRepresent the conflict between evidence；
4 FCM clustering algorithms are defined by sample space X={ x1,x2,…,xnSample point be divided into c (c ＞ 1) class, each sample
The degree that point i belongs to jth class (1 ＜ j ＜ c) is expressed as uij, sample space X fuzzy clustering subordinated-degree matrix U=(uij)c×n
Represent, matrix u meets following condition：
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In formula：V={ v1,…,vj,…,vc, vjFor the cluster centre of jth class；d2(xi,vk) it is xiWith vjThe distance between measurement
Function；M is FUZZY WEIGHTED index.In order to obtain the division of data set X optimal fuzzy c class, it is necessary to which trying to achieve makes | Jm(U(t+1),V(t +1))-Jm(U(t),V(t)) | the solution (U, V) during ＜ ε minimums.This can be completed by following iteration：
1) initialize, input data set { xi, i=1,2 ..., n, cluster numbers c, Fuzzy Weighting Exponent m ∈ R ＞ 1, greatest iteration time
Number T and threshold epsilon, random initializtion subordinated-degree matrix U(t)(t=0, t are iterations)；
2) using following formula renewal degree of membership center and subordinated-degree matrix：
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Priority Applications (1)
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