CN104268895B - 4D-CT deformation registration method for combining spatial information and temporal information - Google Patents
4D-CT deformation registration method for combining spatial information and temporal information Download PDFInfo
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- 238000011524 similarity measure Methods 0.000 claims description 25
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- G—PHYSICS
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- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
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- G06T2207/10—Image acquisition modality
- G06T2207/10072—Tomographic images
- G06T2207/10081—Computed x-ray tomography [CT]
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- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2207/00—Indexing scheme for image analysis or image enhancement
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- G06T2207/20048—Transform domain processing
- G06T2207/20064—Wavelet transform [DWT]
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- G—PHYSICS
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- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2207/00—Indexing scheme for image analysis or image enhancement
- G06T2207/30—Subject of image; Context of image processing
- G06T2207/30004—Biomedical image processing
- G06T2207/30096—Tumor; Lesion
Abstract
The invention discloses a 4D-CT (four-dimensional computed tomography) deformation registration method for combining spatial information and temporal information. The 4D-CT deformation registration method comprises the following steps: establishing a deformation model through dual-tree complex wavelet transform; quantitatively describing deformation of 4D-CT in different time phase space domains; establishing a deformation energy function and an external force constraint function through a Navier partial differential equation; estimating a wavelet coefficient representing deformation characteristics in a spatial domain from roughly and finely; describing the periodicity and continuity of a sequence image in a time domain by using a B spline-based cycle time domain model; ensuring the accuracy of a respiratory motion model by using a piecewise smooth constraint function so as to accurately describe motion rules of tumor target areas and endangered organs in the 4D-CT sequence image. The 4D-CT deformation registration method has an important significance for quantitative analysis on the motion rules of tumors and the endangered organs in the chest and abdomen.
Description
Technical field
The present invention relates to image processing field, the 4D-CT deformable registration of more particularly, to a kind of joint spatially and temporally information
Method.
Background technology
At present, thorax and abdomen malignant mortality rate is higher, and wherein pulmonary carcinoma and hepatocarcinoma occupy mortality of malignant tumors prostatitis.Thorax abdomen
Tumor implement radiotherapy when, the tumor being caused by respiratory movement and jeopardize organ move degree larger, increased the not true of Patients During Radiotherapy
Qualitative, the radiation injury of normal structure may be increased and increase relapse rate.
The review formula 4D-CT technology growing up in recent years is one group of Dynamic CT image with time correlation connection, can retouch
State tumor and jeopardize the characteristics of motion with respiratory variations for the organ.The most frequently used 4D-CT technology is passed through in clinical implementation and research
In the same breathing cycle, the CT image of different phases carries out registration to obtain the characteristics of motion.This kind of method only accounts for 4D-CT not
Simultaneously the dependency between phase images spatial domain it is believed that in the same breathing cycle CT image of each phase be separate, but neglect
Inherent relativity of time domain depending on respiratory phase images different in the same breathing cycle.
Using the free deformation model based on B-spline, respectively can be to two-dimentional time correlation sequence image and three-dimensional
Time correlation sequence image carries out registration.However, experimentation have shown that, relate to due to there are motion artifacts and global optimization process in 4D-CT
And parameter excessive, when said method is used for thorax abdomen 4D-CT image registration, take that long and robustness is weaker, easily fall into
Enter to mismatch.
Content of the invention
The purpose of the present invention is exactly to solve the above problems it is proposed that a kind of 4D-CT of joint spatially and temporally information
Deformable registration method, the method can accurately describe the characteristics of motion of tumor image, to quantitative analyses thorax and abdomen malignant and jeopardizing
The characteristics of motion of organ is significant.
To achieve these goals, the present invention adopts the following technical scheme that：
A kind of 4D-CT deformable registration method of joint spatially and temporally information, comprises the following steps：
The first step：Obtain N number of phase view data from clinical data, appoint from the N number of phase obtaining and take two phases
Image, is respectively defined as reference picture and target image, and removes artifact, noise contribution；
Second step：Reference picture and target image are carried out multi-scale wavelet decomposition, to N number of when phase images carry out deformation and join
Standard, the Deformation Law between phase images, i.e. deformation domain when obtaining different；
3rd step：3 D wavelet decomposition is carried out to described deformation domain, by wavelet coefficient according to different scale and different directions
Classified, and assumed that these different types of wavelet coefficients express different deformation characteristics, respectively using Marquardt-
Levenberg optimized algorithm is estimated to above-mentioned wavelet coefficient；Wavelet coefficient is controlled at certain according to required registration accuracy
Restrain on yardstick；
4th step：4D-CT sequence image to be represented with intensity function F (i, k), wherein, i and k is N number of exhaling respectively
Inhale the spatially and temporally sample of phase；Deformation model is set up using dual-tree complex wavelet transform and represents during difference between phase images spatial domain
Deformation domain, using the dependency being described based on the cycle Model in Time Domain of B-spline between sequence image time domain；
5th step：Set up target image transformation model, selection wavelet coefficient is transformation parameter, and target image is become
Change；Through interpolation algorithm, calculate the similarity between target image and reference picture after conversion using similarity measure function
Estimate, judge whether gained similarity measure value has reached global optimum；
6th step：Without searching out global optimum, then circulation carries out the 5th step, is that target image transformation model carries
Enter line translation for next wavelet conversion coefficient, continue to calculate similarity measure value；When optimized algorithm judges similarity measure value
When reaching global optimum, registration process terminates, and exports final wavelet conversion coefficient；
7th step：The wavelet coefficient of output is substituted into target image transformation model deformation conversion is carried out to target image.
The concrete grammar of described 4th step is：
Using the dependency being described based on the cycle Model in Time Domain of B-spline in sequence image time domain, by the motion of tumor
Track is modeled as the time domain smooth function based on B-spline；Consider that in respiratory movement, air-breathing end is to beginning moment organ fortune of exhaling simultaneously
The snap back conversion in dynamic direction, sets up segmentation constraint function it is ensured that while whole respiratory movement smooth trajectory, keeping breathing
Track is in the accuracy of air-breathing end movement locus；
To express the deformation domain of the respiratory movement correlated serieses image of 4D-CT difference phase using dual-tree complex wavelet transform,
Deformation domain is modeled as the function of wavelet coefficient；Set up deformation energy function by Navier partial differential equation, by coarse and fine
The wavelet coefficient of representation space domain deformation characteristics is estimated on ground.
Described the movement locus of tumor are modeled as being specially based on the time domain smooth function of B-spline：
Wherein, Τt(x, t) represents tyMoment when phase images in reference time tyAnd the movement locus at the x of position, it is to close
In the continuously smooth function of time t, tyRepresent the y moment of t, ψl(t)=βm(t/s-l), s ∈ R is the control point interval of time；
bl∈R3Coefficient for m rank B-spline basic function；βmFor m rank B-spline basic function, β is B-spline basic function node, and l is B-spline base
Function counting variable；
The overall smooth track model of B-spline cycle Model in Time Domain is：
Wherein, TtMovement locus at x for phase images when (x, 0) represented for 0 moment；Tt(x,te) represent t the e moment when
Movement locus at x for the phase images.
The segmentation constraint function of described foundation is specially：
Wherein,Represent sectionally smooth track at x for phase images during 0 moment,Represent the e moment of t
When sectionally smooth track at x for the phase images；
For sectionally smooth track it is assumed that air-breathing foot couple answers t=0, single constraints can be set and apply at air-breathing end.
The described function that deformation domain is modeled as wavelet coefficient is specially：
X'=x+u1(x,y,z；c)
Y'=y+u2(x,y,z；c)
Z'=z+u3(x,y,z；c)
Wherein, (x, y, z) represents the space coordinates of reference picture, and (x ', y ', z ') represents the space coordinatess of target image
System, deformation domain u=(u1,u2,u3), c is wavelet coefficient, and deformation domain u is the function of wavelet coefficient c.
Described deformation energy function of being set up by Navier partial differential equation is specially：
E (c)=inter (c)+w exter (c)
Wherein, w is weighting constant, adopts w to be constant 1, inter (c) represents internal force constraint function, exter (c) in experiment
Represent external force constraint function.
Judge in described 5th step that the concrete grammar whether gained similarity measure value has reached global optimum is：
Obtain a series of corresponding similarity measure values by a series of wavelet coefficients, similarity measure function is asked extreme value with
Measure value compares, and judges whether gained similarity measure value has reached maximum, and described maximum is optimal value.
The invention has the beneficial effects as follows：
Multi-scale wavelet basic function as deformation model, and is introduced the cycle time-domain constraints mould based on B-spline by this method
Type makes movement locus meet periodically and seriality, can preferably realize 4D-CT image different when phase images spatially and temporally
Global and local deformation recovers, and tumor is passed through joint deformable registration algorithm spatially and temporally with the characteristics of motion jeopardizing organ
Carry out the global optimization in deformation domain, thus tumor target and jeopardize organ in accurate description 4D-CT difference phase sequence image
The characteristics of motion, significant with the characteristics of motion jeopardizing organ to quantitative analyses thorax and abdomen malignant.
Brief description
Fig. 1 is deformable registration method flow diagram of the present invention；
Fig. 2 (a) is the overall smooth track model schematic based on B-spline for the present invention；
Fig. 2 (b) is the piecewise function smoothing model schematic diagram based on B-spline for the present invention；
Specific embodiment：
The present invention will be further described with embodiment below in conjunction with the accompanying drawings：
Propose a kind of 4D-CT deformable registration scheme of jointly time domain and spatial information (si) in the present invention to realize in 4D-CT not
Facies-suite image registration simultaneously, thus obtaining the clinically characteristics of motion of tumor target adjuvant radiotherapy positioning, concrete steps are such as
Shown in lower：
The first step：Obtain 10 phase image definition data reference pictures and target (floating) 4D-CT technology from clinical
Image, and remove its bed artifact, noise contribution.
Second step：Reference picture and target (floating) Image Multiscale are decomposed and deformation domain 3 D wavelet is decomposed
Afterwards, the initial value of wavelet coefficient is set to 0, first estimates the wavelet coefficient of low yardstick using optimized algorithm, then estimate high yardstick
Wavelet coefficient, according to the required corresponding yardstick of accuracy selection, till required precision, according to required precision control
System restrains on certain yardstick.
3rd step：4D-CT sequence image to be represented with intensity function F (i, k), wherein, i and k is N number of exhaling respectively
Inhale the spatially and temporally sample of phase.
When tumor motion rule in 4D-CT is obtained by deformable registration algorithm, the dependency spatially and temporally gone up need to be combined,
Should realize while spatial domain registration it is ensured that the seriality of time domain tumor motion track and periodically.Exhale for patient
Inhale seriality and the periodicity that law characteristic has inherence, and the registering target sample with respect to spatial domain, the sample of time domain is relatively
Few, that is, the resolution in time domain is relatively low.
Therefore, this patent is using a kind of correlation being described based on the cycle Model in Time Domain of B-spline in sequence image time domain
Property, the movement locus of tumor are modeled as the time domain smooth function based on B-spline.Simultaneously it is considered in respiratory movement air-breathing end is extremely
The snap back conversion in expiration beginning moment organ movement direction, sets up segmentation constraint function, can ensure whole respiratory movement
While smooth trajectory, keep breathing track in the accuracy of air-breathing end movement locus.Finally, tumor and the fortune jeopardizing organ
Dynamic rail mark carries out the global optimization in deformation domain by the registration Algorithm combined spatially and temporally, thus realizing respiratory movement correlation sequence
The time-space domain registration of row, accurately follows the tracks of tumor target and the motion jeopardizing organ in 4D-CT difference phase sequence image.
Deformation model, the deformation in quantitative description 4D-CT difference phase spatial domain are set up using dual-tree complex wavelet transform, leads to
Cross Navier partial differential equation to set up deformation energy function and external force constraint function, estimate representation space domain shape by coarse and fine
Become the wavelet coefficient of feature；Using based on the cycle Model in Time Domain of B-spline, described the cycle in time domain for the sequence image simultaneously
Property and seriality, and the accuracy of the motion model that ensured respiration using piecewise-smooth constraints function, thus accurate description 4D-CT sequence
Tumor target in row image and jeopardize organ movement.
This patent to express the shape of the respiratory movement correlated serieses image of 4D-CT difference phase using dual-tree complex wavelet transform
Variable domain.Dual-tree complex wavelet not only has the multiple dimensioned property of wavelet transformation, has good directivity and abundant space simultaneously
Phase information, and keep translation invariance, tumor and the motion change jeopardizing organ in phase images when can effectively describe difference.
For deformable registration problem, deformation domain can be modeled as the function of wavelet coefficient, then reference picture, target image,
, there is following mathematical expression in deformation domain between wavelet coefficient：
X'=x+u1(x,y,z；c)
Y'=y+u2(x,y,z；c) (1)
Z'=z+u3(x,y,z；c)
Wherein (1) formula, (x, y, z) represents the space coordinates of reference picture, and (x ', y ', z ') represents the sky of target image
Between coordinate system, deformation domain u=(u1,u2,u3) for wavelet coefficient c function.As target component, it can pass through minimization energy
Flow function obtains.For deformation domain u, in three n-dimensional subspace ns, available dual-tree complex wavelet exploded representation, different scale and non-Tongfang
Wavelet coefficient upwards is by the thick space deformation domain representing different respiratory phase to essence.
In order to reduce a large amount of wavelet coefficients that optimized algorithm in deformable registration framework once needs to estimate, can be by wavelet coefficient
Different scale and different directions are classified, and is assumed that these different types of wavelet coefficients represent different deformation domains
Feature.In deformable registration algorithm, can first estimate the wavelet coefficient on low yardstick, then estimate the wavelet systems in high yardstick again
Number, till required precision.Different scale and different sub-band wavelet coefficient estimate that order is：1-2-3-4-22-33-44, specifically
As shown in the table：
Set up deformation energy cost function in order to estimation is carried out to multi-scale wavelet coefficient, cost function is by two parts group
Become, one of which is internal force deformation energy function, and in addition one is external force cost function.Deformable registration theory in, for send out
The isotropism tissue of raw deformation, its poised state can be described by isotropic Navier partial differential equation：
Wherein (2) formula, θ is three-dimensional expansion coefficient, is expressed as follows：
X=(x1,x2,x3)TIt is the three-dimensional coordinate system of deformed microstructure, F=(F1,F2,F3)TIt is to act on deformed microstructure
External force everywhere, μ and λ is deformation constant, and its value depends on the self property of deformed microstructure.U=(u1,u2,u3)TIt is to join
The required deformation domain recovered between references object and destination object of quasi- algorithm.In the organization edge deforming upon, external force is approximately
Zero, the organization edge of corresponding medical image；And for the other positions deforming upon, it is required to external force and the balance of internal force.Right
In method for expressing and the stress in given deformation domain, the deformation domain of object to be determined by external force and deformation constant completely.
Front two parts of partial differential equation be internal force deformation energy function, by multi-scale wavelet basic function characterize deformation domain with
Afterwards, this part can obtain the linear algebra structure with numerical solution in conjunction with Wavelet Galerkin discretization method.
And last of partial differential equation can build external force cost function, produced using similarity measure constraint function
Raw, that is, adopt the similarity measure function between reference picture subject to registration and target image.
The registering target of this patent is the breathing correlated serieses of different phases in 4D-CT image, is same modality images, adopts
Gray scale mean square deviation is as similarity measure function it is ensured that full-automatic rapid registering.Similarity measure function is specially：
We have obtained for constituting Navier partial differential equation to solve the problems, such as internal force and the external force part of elastic deformation,
Wherein deformation domain is represented with orthogonal wavelet basic function, and the balance of internal force and external force ultimately forms the energy letter with regard to deformation domain
Number, final energy function can be expressed as：
E (c)=inter (c)+w exter (c) (3)
Wherein in (3) formula, w is weighting constant, adopts w to be constant 1 in experiment.Therefore, the deformation domain that we obtain is to close
In the function of wavelet coefficient, that is, energy function is also the function with regard to wavelet coefficient.Therefore minimization deformation energy function can be passed through
To estimate to represent the wavelet coefficient in deformation domain.
There is periodicity and the flatness of inherence for patient respiratory law characteristic, and the registering sample with respect to spatial domain
This, the registering sample of time domain is less, and that is, the image resolution ratio in time domain is relatively low.Therefore, this patent adopt a kind of based on B-spline
Cycle Model in Time Domain describes dependency in time domain for the sequence image, by the movement locus of tumor be modeled as based on B-spline when
Domain smooth function.Mathematic(al) representation is as follows：
In formula, Τt(x, t) represents in reference time tyAnd the movement locus at the x of position, it is the continuously smooth with regard to time t
Function, can use a suitable basic function collection { ψl}l∈LLinearly to express.Have good near in view of B-spline basic function
Like property, implicit flatness and calculating simply.We use m rank B-spline function ψl(t)=βm(t/s-l), wherein, s ∈ R is the time
Control point interval；bl∈R3Coefficient for B-spline basic function.In view of respiratory movement track, should be met on time domain smooth company
Continuous property, therefore motion trajectory model need to constrain further in conjunction with the prior information of motion.
This movement locus can be used as the smooth function curve of time, and this patent sets the smooth of identical exponent number at control point
Degree, so that movement locus hold period and flatness in whole breath cycle, as following formula represents：
Meet shown in above formula track such as Fig. 2 (a) and Fig. 2 (b).By analyzing the respiratory movement feature of clinical individual, easily
Find when air-breathing end phase goes to expiration beginning phase, tumor and jeopardize organ and snap back can be occurred to turn with respiratory movement direction
Change, still meet continuous feature in this turning point breathing lopcus function, but be unsatisfactory for smooth features, that is, track derived function is at this
It is discontinuous at turning point.Therefore, segmentation constraint function should be set up, make to keep, except the whole breathing track at air-breathing end, the company of smoothing
While continuous, should ensure that the accuracy (continuous but rough) in air-breathing end for the breathing track.By changing in air-breathing end
Smoothness constraint condition, proposes sectionally smooth track.Assume that air-breathing foot couple answers t=0, single constraints can be set and apply and inhale
In the respiratory phase of gas end, it is shown below：
Tt(x, 0)=Tt·(x,te) (6)
It is ensured that the seriality of whole movement locus and periodically, air-breathing end Temporal variation rail under this constraints
Mark is continuous, but pace of change is discontinuous, and remaining keeps speed continuous everywhere.
4th step：The wavelet conversion coefficient that target image gives in transformation model carries out deformation conversion, is then passed through
Interpolation algorithm, calculates the similarity measure between target image and reference picture two width image after conversion, and through certain
Optimisation strategy analyzing whether similarity measure value has reached global optimum.
5th step：Without searching out global optimum, then circulation carries out the 4th step, and transformation model provides next little
Wave conversion coefficient enters line translation, then proceedes to calculate similarity measure value；When optimized algorithm judges that similarity measure value reaches entirely
During office's optimal value, registration process terminates, and exports final wavelet conversion coefficient or deformation domain.
6th step：The result of output acts on target (floating) image, is ensuing acquisition tumor target and jeopardize device
The characteristics of motion of official adjuvant radiotherapy positioning offer foundation.
Although the above-mentioned accompanying drawing that combines is described to the specific embodiment of the present invention, not model is protected to the present invention
The restriction enclosed, one of ordinary skill in the art should be understood that on the basis of technical scheme, and those skilled in the art are not
Need to pay the various modifications that creative work can make or deformation still within protection scope of the present invention.
Claims (6)
1. a kind of 4D-CT deformable registration method of joint spatially and temporally information, is characterized in that, comprise the following steps：
The first step：Obtain N number of phase view data from clinical data, from the N number of phase obtaining, appoint phase images when taking two,
It is respectively defined as reference picture and target image, and remove artifact, noise contribution；
Second step：Reference picture and target image are carried out multi-scale wavelet decomposition, to N number of when phase images carry out deformable registration,
Deformation Law between phase images, i.e. deformation domain when obtaining different；
3rd step：3 D wavelet decomposition is carried out to described deformation domain, wavelet coefficient is carried out according to different scale and different directions
Classification, and assume that these different types of wavelet coefficients express different deformation characteristics, respectively using Marquardt-
Levenberg optimized algorithm is estimated to above-mentioned wavelet coefficient；Wavelet coefficient is controlled at certain according to required registration accuracy
Restrain on yardstick；
4th step：4D-CT sequence image to be represented with intensity function F (i, k), wherein, when i and k is N number of breathing respectively
The spatially and temporally sample of phase；Deformation model is set up using dual-tree complex wavelet transform and represents the deformation between phase images spatial domain during difference
Domain, using the dependency being described based on the cycle Model in Time Domain of B-spline between sequence image time domain；
5th step：Set up target image transformation model, selection wavelet coefficient is transformation parameter, enters line translation to target image；Warp
Cross interpolation algorithm, calculate the similarity measure between target image and reference picture after conversion using similarity measure function,
Judge whether gained similarity measure value has reached global optimum；
6th step：Without searching out global optimum, then circulation carries out the 5th step, under providing for target image transformation model
One wavelet conversion coefficient enters line translation, continues to calculate similarity measure value；When optimized algorithm judges that similarity measure value reaches
During global optimum, registration process terminates, and exports final wavelet conversion coefficient；
7th step：The wavelet coefficient of output is substituted into target image transformation model deformation conversion is carried out to target image；
The concrete grammar of described 4th step is：
Using the dependency being described based on the cycle Model in Time Domain of B-spline in sequence image time domain, by the movement locus of tumor
It is modeled as the time domain smooth function based on B-spline；Consider that in respiratory movement, air-breathing end is to the moment organ movement side of beginning that exhales simultaneously
To snap back conversion, set up segmentation constraint function it is ensured that while whole respiratory movement smooth trajectory, keeping breathing track
Accuracy in air-breathing end movement locus；
To express the deformation domain of the respiratory movement correlated serieses image of 4D-CT difference phase using dual-tree complex wavelet transform, by shape
Variable domain is modeled as the function of wavelet coefficient；Set up deformation energy function by Navier partial differential equation, estimated by coarse and fine
The wavelet coefficient of meter representation space domain deformation characteristics.
2. a kind of 4D-CT deformable registration method of joint spatially and temporally information as claimed in claim 1, is characterized in that, institute
State and be modeled as being specially based on the time domain smooth function of B-spline by the movement locus of tumor：
Wherein, Tt(x, t) represents tyMoment when phase images in reference time tyAnd the movement locus at the x of position, it is with regard to the time
The continuously smooth function of t, tyRepresent the y moment of t, ψl(t)=βm(t/s-l), s ∈ R is the control point interval of time；bl∈R3For
The coefficient of m rank B-spline basic function；βmFor m rank B-spline basic function, β is B-spline basic function node, and l counts for B-spline basic function
Variable；
The overall smooth track model of B-spline cycle Model in Time Domain is：
Wherein, TtMovement locus at x for phase images when (x, 0) represented for 0 moment；Tt(x,te) represent t the e moment when phasor
As the movement locus at x.
3. a kind of 4D-CT deformable registration method of joint spatially and temporally information as claimed in claim 1, is characterized in that, institute
The segmentation constraint function of setting up stated is specially：
Tt *(x, 0)=Tt *(x, te)
Wherein, Tt *Sectionally smooth track at x for phase images when (x, 0) represented for 0 moment, Tt *(x,te) represent t the e moment when
Sectionally smooth track at x for the phase images；
Tt *For sectionally smooth track it is assumed that air-breathing foot couple answers t=0, single constraints can be set and apply at air-breathing end.
4. a kind of 4D-CT deformable registration method of joint spatially and temporally information as claimed in claim 1, is characterized in that, institute
State the function that deformation domain is modeled as wavelet coefficient to be specially：
X'=x+u1(x,y,z；c)
Y'=y+u2(x,y,z；c)
Z'=z+u3(x,y,z；c)
Wherein, (x, y, z) represents the space coordinates of reference picture, and (x ', y ', z ') represents the space coordinates of target image,
Deformation domain u=(u1,u2,u3), c is wavelet coefficient, and deformation domain u is the function of wavelet coefficient c.
5. a kind of 4D-CT deformable registration method of joint spatially and temporally information as claimed in claim 1, is characterized in that, institute
State and set up deformation energy function by Navier partial differential equation and be specially：
E (c)=inter (c)+w exter (c)
Wherein, w is weighting constant, adopts w to be constant 1, inter (c) represents internal force constraint function, and exter (c) represents in experiment
External force constraint function.
6. a kind of 4D-CT deformable registration method of joint spatially and temporally information as claimed in claim 1, is characterized in that, institute
State and in the 5th step, judge that the concrete grammar whether gained similarity measure value has reached global optimum is：
Obtain a series of corresponding similarity measure values by a series of wavelet coefficients, similarity measure function is asked by extreme value and estimated
Value compares, and judges whether gained similarity measure value has reached maximum, and described maximum is optimal value.
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