CN105488754B - Image Feature Matching method and system based on local linear migration and affine transformation - Google Patents
Image Feature Matching method and system based on local linear migration and affine transformation Download PDFInfo
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Abstract
The present invention proposes a kind of Image Feature Matching method and system based on local linear migration and affine transformation, correct matching is established for the matching of the mistake by removing initial matching point centering, include establishing the corresponding model of geometric transformation between image to be matched for the affine transformation between image to be matched, and it is the correct matched corresponding model of posterior probability to establish matching double points, based on nearest-neighbors match point, least square method, optimal method solving model parameter；Initial matching point is calculated to for correct matched posterior probability, and according to threshold decision initial matching point to correcting errors.This method to be modeled for there are the case where affine transformation between image to be matched, matched error rate is significantly reduced, even if still keeping good robustness there are in the case of a large amount of erroneous matchings in preliminary matches.
Description
Technical field
The present invention relates to Image Feature Matching technical fields, specifically, the present invention relates to based on local linear migration and
The Image Feature Matching technical solution of affine transformation.
Background technology
The elementary object of images match be will use different sensors in different times with obtained under visual angle it is same
The same area of the two images of scene is corresponded to.
In in the past few decades, scholars have studied many methods to solve remote sensing images matching problem.These methods
Two classes can be substantially divided into：Matching process based on region and feature-based matching method.The former is by searching for two images
The similarity degree of original gray value finds match information in middle certain area；The latter then utilizes description of local feature similar
Property or space geometry constraint find matching double points.In the case of with a small amount of significantly details, the information ratio of gray value offer
Local shape and structure are more, more preferable to the matching effect of the method based on region.But the method calculation amount based on region
Greatly, it and in the case where image fault and luminosity change and is not suitable for.On the contrary, characterization method has better robustness, it can be with
The image for handling babble, is widely used.
Corresponding match point in two images how is found, forms matching double points, and ensure that the correctness of matching double points is
The key of image matching method.
Matching process based on region mainly has three kinds of correlation method, Fourier methods and mutual information method.Correlation method it is main
Thought is to calculate the similitude that window is corresponded in two images, then using a pair with maximum similarity degree as matching double points.
But correlation method can not be applicable in the inapparent texture-free region of similitude, and be calculated complicated.Fourier methods are utilized image and exist
The Fourier Representations of frequency domain.Compared with traditional correlation technique, this method is made an uproar in computational efficiency higher and to frequency class
Sound has good robustness.However, this method is handling the images with different spectrum structures with certain restrictions.Mutual trust
For breath method although its matching effect is good, it is unable to get the global maximum in entire search space, therefore inevitable
Meeting lower its robustness.
In feature-based matching method, a kind of strategy being divided into two steps of generally use.The first step is retouched by feature
The similarity degree for stating son determines one group of initial matching double points, and the wherein overwhelming majority is correctly to match, but inevitably contain
A large amount of erroneous matching.Second step finally can be matched correctly by removing the matching of mistake by geometrical constraint
The point pair geometric parameter converted between two images.The exemplary of this strategy includes RANSAC methods
(M.A.Fischler and R.C.Bolles,“Random sample consensus:A paradigm for model
fitting with application to image analysis and automated cartog-raphy,”
Commun.ACM, vol.24, no.6, pp.381-395, Jun.1981), ARHV methods (P.H.S.Torr and
A.Zisserman,“MLESAC:A new robust estimator with application to estimating
image geometry,”Comput.Vis.Image Under-stand.,vol.78,no.1,pp.138–156,
) etc. Apr.2000 the method and VFC methods (J.Ma, J.Zhao, J.Tian, A.L.Yuille, and of parameter model are depended on
Z.Tu,“Robust point matching via vector field consensus,”IEEE Trans.Image
Process., vol.23, no.4, pp.1706-1721, Apr.2014.), GS methods (H.Liu and S.Yan, " Common
visual pattern discovery via spatially coher-ent correspondence,”in Proc.IEEE
Conf.Comput.Vis.Pattern Recog., Jun.2010, pp.1609-1616.) and ICF methods (X.Li and
Z.Hu,“Rejecting misma tches by correspondence function,”Int.J.Comput.Vis.,
Vol.89, no.1, pp.1-17, Aug.2010) method based on nonparametric model such as.
Although these methods obtain success in many fields, contain in the picture largely caused by visual angle change
The initial matching point pair that many mistakes can be obtained when localized distortion and more complex picture material, after preliminary matches, works as error rate
When more than certain proportion, these methods cannot effectively remove mistake.Therefore have to initial matching error rate there is an urgent need for a kind of
The matching process of higher robustness.
Invention content
For prior art defect, the present invention proposes a kind of characteristics of image based on local linear migration and affine transformation
Matching technique scheme.
In order to achieve the above objectives, the technical solution adopted by the present invention is a kind of based on local linear migration and affine transformation
Image Feature Matching method, includes the following steps,
Step 1, it is that correct matched posteriority is general to establish the corresponding model of geometric transformation and matching double points between image to be matched
The corresponding model of rate, realization is as follows,
For the affine transformation between image to be matched, foundation transformation mathematical model is as follows,
Y=t (x)=Ax+o
Wherein, if two images to be matched are image a and image b, x and y are the seat of pixel on image a and image b respectively
Mark vector, t (x) indicate affine transformation relationship, and A is one 2 × 2 affine matrix, and o is one 2 × 1 matrix, and expression waits for
With the translation between image；
If known one group of initial matching point centering, point set is X={ x on image a1,…,xN}T, corresponding point set on image b
For Y={ y1,…,yN}T, it is correct matched posterior probability p to calculate wherein n-th pair of match pointnThere is following posterior probability mathematical modulo
Type,
Wherein, γ and σ is model parameter, and e is mathematics constant, and b is preset coefficient；
Step 2, according to point set X={ x1,…,xN}TWith Y={ y1,…,yN}TSolving model parameter, including following sub-step
Suddenly,
Step 2.1, it is each match point xn, n=1 ..., N search for K nearest neighbours' match point respectively, and K takes pre-
If value；
Step 2.2, according to the search result of step 2.1, least square method is used to solve dimension as the weight matrix of N × N
W；
Step 2.3, by optimal method solving model parameter s, R, o, γ, σ, including following sub-step,
Step 2.3.1, initialization, including enable γ=γ0, A=I2×2, o=0, P=IN×N, γ0For the default initial of γ
Value, enables current iteration number k=1, and σ is calculated using following model parameter formula,
Wherein, matrix T=(t (x1),…,t(xN))T, tr () indicates to seek the mark of matrix；
Step 2.3.2, updates matrix P, including using gained posterior probability mathematical model in step 1, be calculated N to
With point to being respectively correct matched posterior probability p1,…,pN, enable P=diag (p1,…,pN), diag indicates diagonal matrix；
Step 2.3.3, calculating parameter A, o is as follows,
Using following formula calculating parameter A,
Wherein, matrix
By IN×NOmission is denoted as I, matrix Q=(I-W)TP (I-W), λ are preset parameter；
Using following formula calculating parameter o,
O=μy-Aμx
Step 2.3.4, according to parameter A, o that step 2.3.3 is calculated, it is as follows to recalculate parameter γ, σ,
Using following formula calculating parameter γ,
σ is calculated using model parameter formula in step 2.3.1；
Step 2.3.5 differentiates the condition of convergence, including calculates current parameter L, when meeting k=kmaxOr (L-Lold)/
Lold≤ ε terminates iteration, kmaxFor maximum iteration, ε is convergence threshold；Otherwise, k=k+1, return to step 2.3.2；It is described
The calculation formula of parameter L is as follows,
Wherein, LoldIndicate the last L being calculated；
Step 3, initial matching point is calculated to for correct matched posterior probability, and according to threshold decision initial matching point pair
Correct errors, realize it is as follows,
The model parameter solved in the step 2.3 is substituted into posterior probability mathematical model described in step 1, is calculated
N-th pair of matching double points is correct matched posterior probability；Work as pnWhen >=threshold, then it is assumed that n-th pair of match point is correct
Match；Work as pn<When threshold, then it is assumed that n-th pair of match point is the matching of mistake, and wherein threshold is preset judgement threshold
Value.
Moreover, step 2.2 includes following sub-step,
Step 2.2.1, as match point xjIt is not the match point x searched in the step 2.1iK neighbours' match point it
For the moment, then by WijIt is set as 0, wherein match point xjWith match point xiFor the match point in point set X, and i, j=1 ..., N, WijTable
Show the element of weight matrix W the i-th row jth row；
Step 2.2.2,Constraints under, solve to obtain using least square method so that following generations
Valence function E (W) gets the weight matrix W of minimum value, and cost function E (W) is as follows,
The present invention correspondingly provides a kind of Image Feature Matching system based on local linear migration and affine transformation, including
With lower module,
Model construction module is correct for establishing the corresponding model of geometric transformation and matching double points between image to be matched
The corresponding model of posterior probability matched, realization is as follows,
For the affine transformation between image to be matched, foundation transformation mathematical model is as follows,
Y=t (x)=Ax+o
Wherein, if two images to be matched are image a and image b, x and y are the seat of pixel on image a and image b respectively
Mark vector, t (x) indicate affine transformation relationship, and A is one 2 × 2 affine matrix, and o is one 2 × 1 matrix, and expression waits for
With the translation between image；
If known one group of initial matching point centering, point set is X={ x on image a1,…,xN}T, corresponding point set on image b
For Y={ y1,…,yN}T, it is correct matched posterior probability p to calculate wherein n-th pair of match pointnThere is following posterior probability mathematical modulo
Type,
Wherein, γ and σ is model parameter, and e is mathematics constant, and b is preset coefficient；
Parametric solution module, for according to point set X={ x1,…,xN}TWith Y={ y1,…,yN}TSolving model parameter, packet
Following submodule is included,
Neighbours' match point submodule, for being each match point xn, n=1 ..., N search for K nearest neighbours respectively
Match point, K take preset value；
Weight matrix submodule is solved for the search result according to neighbours' match point submodule using least square method
Dimension is the weight matrix W of N × N；
Optimization submodule is used for by optimal method solving model parameter s, R, o, γ, σ, including to place an order
Member,
Initialization unit, for enabling γ=γ0, A=I2×2, o=0, P=IN×N, γ0For the preset initial value of γ, order is worked as
Preceding iterations k=1 calculates σ using following model parameter formula,
Wherein, matrix T=(t (x1),…,t(xN))T, tr () indicates to seek the mark of matrix；
Updating unit, for updating gained posterior probability mathematical model, meter in matrix P, including use model construction module
It is respectively correct matched posterior probability p to matching double points that calculation, which obtains N,1,…,pN, enable P=diag (p1,…,pN), diag is indicated
Diagonal matrix；
First parameter calculation unit, it is as follows for calculating parameter A, o,
Using following formula calculating parameter A,
Using following formula calculating parameter o,
O=μy-Aμx
Second parameter calculation unit, parameter A, o for being calculated according to the first parameter calculation unit recalculate ginseng
Number γ, σ is as follows,
Using following formula calculating parameter γ,
σ is calculated using model parameter formula in initialization unit；
Iteration judging unit for differentiating the condition of convergence, including calculates current parameter L, when meeting k=kmaxOr (L-
Lold)/Lold≤ ε terminates iteration, kmaxFor maximum iteration, ε is convergence threshold；Otherwise, k=k+1, order updating unit work
Make；The calculation formula of the parameter L is as follows,
Wherein, LoldIndicate the last L being calculated；
Judging result module, for calculating initial matching point to for correct matched posterior probability, and according to threshold decision
For initial matching point to correcting errors, realization is as follows,
The model parameter solved in the optimization submodule is substituted into posterior probability described in model construction module
Mathematical model, it is correct matched posterior probability that n-th pair of matching double points, which is calculated,；Work as pnWhen >=threshold, then it is assumed that the
N is correctly to match to match point；Work as pn<When threshold, then it is assumed that n-th pair of match point is the matching of mistake, wherein
Threshold is preset judgment threshold.
Moreover, weight matrix submodule includes with lower unit,
Initial assignment unit, for working as match point xjIt is not the match point x searched in neighbours' match point submodulei
K neighbours' match point for the moment, then by WijIt is set as 0, wherein match point xjWith match point xiFor the match point in point set X,
And i, j=1 ..., N, WijIndicate the element of weight matrix W the i-th row jth row；
Unit is solved, is used forConstraints under, solve to obtain using least square method so that following
Cost function E (W) gets the weight matrix W of minimum value, and cost function E (W) is as follows,
The present invention has the following advantages：
1, the present invention proposes a kind of unified maximum likelihood frame for Image Feature Matching.With the parameter generally used
Model is compared, and this frame can handle nonparametric model situation, and application range is wider.
2, the present invention constructs a kind of constraint of local geometric and is optimized to transformation model.This constraint saves adjacent spy
The case where levying the partial structurtes between point, therefore can be used to handle containing a large amount of erroneous matchings has stronger robustness.
Specific implementation mode
This method carries out mathematical modeling to image affine transformation to be matched first, then tentatively establishes a system by removal degree
Correct matching is established in the matching of mistake in the matching double points of row.This method utilizes Bayes's maximum likelihood with hidden variable
Estimation carries out mathematical modeling.Meanwhile have also been constructed it is a kind of reservation adjacent feature point between partial structurtes geometrical constraint, even if first
Step matching in there are a large amount of erroneous matchings in the case of, still keep good robustness.
Technical solution of the present invention is further described below by embodiment.
The flow of institute of embodiment of the present invention providing method includes mainly 3 steps：
Step 1, it is that correct matched posteriority is general to establish the corresponding model of geometric transformation and matching double points between image to be matched
The corresponding model of rate；
For the affine transformation between image to be matched, it is as follows to establish transformation mathematical model：
Y=t (x)=Ax+o
Wherein, x and y is the coordinate vector of pixel, that is, sets two images to be matched to including as image a and image b, x and y
It is the coordinate vector of pixel on image a and image b respectively, t (x) indicates affine transformation relationship, and A is one 2 × 2 affine square
Battle array, o is one 2 × 1 matrix, indicates the translation between image to be matched；
Due to inevitably wrong, the present invention using matching double points obtained by images match in the prior art progress initial matching
Purpose be to remove to wherein mistake, then for point set on known one group of initial matching point centering image a be X=
{x1,…,xN}T, corresponding point set is Y={ y on image b1,…,yN}T, midpoint x1Corresponding matching point y1, and so on, point xNIt is right
Answer match point yN, including N is to initial matching point pair, wherein n-th pair of matching double points is correct matched posterior probability pnIt can be by such as
Lower posterior probability mathematical model is calculated：
Wherein, γ and σ is model parameter, and e is mathematics constant, and coefficient b can be preassigned by those skilled in the art, or
Person uses variable element, and embodiment is using 2/5, i.e.,
Step 2, according to known initial matching point pair, i.e. point set X={ x1,…,xN, Y={ y1,…,yN, solve institute
State the parameter of two models in step 1；Including following sub-step：
Step 2.1, it is each match point xn, the search of k-d tree association search method and its is respectively adopted in n=1 ..., N
K nearest neighbours' match point, when it is implemented, those skilled in the art can voluntarily preset the value of K, K takes in the present embodiment
15；
Step 2.2, according to the search result of the step 2.1, least square method is used to solve dimension as the weight of N × N
Matrix W；
In embodiment, weight matrix W solutions are as follows,
Step 2.2.1, as match point xjIt is not the match point x searched in the step 2.1iK neighbours' match point it
For the moment, then by WijIt is set as 0, wherein match point xjWith match point xiFor the match point in point set X, and i, j=1 ..., N, WijTable
Show the element of weight matrix W the i-th row jth row；
Step 2.2.2,Constraints under, solve to obtain using least square method so that following generations
Valence function E (W) gets the weight matrix W of minimum value, and cost function E (W) is as follows：
Step 2.3, unknown mathematical model parameter is solved by optimal method：A、o、γ、σ；
The solution procedure of unknown mathematical model parameter A, o, γ, σ are as follows in embodiment：
Step 2.3.1, initiation parameter；Enable parameter γ=γ0(when it is implemented, those skilled in the art can be voluntarily
Set the initial value γ of γ0, embodiment takes γ0=0.9), matrix A=I2×2(i.e. dimension is the square of 2 × 2, element all 1
Battle array), parameter o=0, matrix P=IN×N(i.e. dimension be N × N, element all 1 matrix), current iteration number k=1, use
Following model parameter formula calculate σ：
Wherein, matrix T=(t (x1),…,t(xN))T, tr () indicates to seek the mark of matrix；
Step 2.3.2, update matrix P：
Using posterior probability mathematical model described in step 1, it is calculated the 1st ..., N is respectively correct to matching double points
Matched posterior probability p1,…,pN, enable P=diag (p1,…,pN), diag indicates diagonal matrix；
Step 2.3.3, calculating parameter A, o；
Using following formula calculating parameter A：
Wherein, each matrix IN×1I.e. dimension be N × 1, element all 1 matrix, by IN×NOmission is denoted as I, matrix Q=
(I-W)TP (I-W), λ are a preset parameter, those skilled in the art's predeterminable value when specific implementation, in the present embodiment
Take 100；
Using following formula calculating parameter o：
O=μy-Aμx
Step 2.3.4 can recalculate parameter according to parameter A, o that step 2.3.3 is calculated based on current t (x)
γ、σ；Using following formula calculating parameter γ：
σ is calculated using model parameter formula described in step 2.3.1；
Step 2.3.5 differentiates the condition of convergence：
Current parameter L is calculated, when meeting k=kmaxOr (L-Lold)/Lold≤ ε terminates iteration；Otherwise, that is, work as k<
kmaxAnd (L-Lold)/Lold＞ ε, k=k+1 return to step 2.3.2, when it is implemented, those skilled in the art free can preset
Maximum iteration kmaxValue, the value of the present embodiment is 50；
Wherein, ε is convergence threshold, those skilled in the art's predeterminable value when specific implementation, such as takes 0.0001, Lold
Indicate that the last L for executing step 2.3.5 and being calculated can enable L when executing step 2.3.5 for the first timeoldIt is larger for one
Initial value, for example, 10 6 powers, execute the result of calculation that can be used that last time executes step 2.3.5 later.The calculating of L
Formula is as follows：
Step 3, initial matching point is calculated to for correct matched posterior probability, and according to threshold decision initial matching point pair
Correct errors；
The parameter solved in the step 2.3 is substituted into posterior probability mathematical model described in step 1, is calculated n-th
It is correct matched posterior probability to matching double points；Work as pnWhen >=threshold, then it is assumed that n-th pair of match point is correctly to match；
Work as pn<When threshold, then it is assumed that n-th pair of match point is the matching of mistake, and wherein threshold is judgment threshold, specific real
Shi Shi, those skilled in the art can free default judgment threshold value, take 0.5 in the present embodiment.
When it is implemented, software mode, which can be used, in the above flow realizes automatic running.It can also be carried using modular mode
For corresponding system, the embodiment of the present invention correspondingly provides a kind of Image Feature Matching based on local linear migration and affine transformation
System comprises the following modules,
Model construction module is correct for establishing the corresponding model of geometric transformation and matching double points between image to be matched
The corresponding model of posterior probability matched, realization is as follows,
For the affine transformation between image to be matched, foundation transformation mathematical model is as follows,
Y=t (x)=Ax+o
Wherein, if two images to be matched are image a and image b, x and y are the seat of pixel on image a and image b respectively
Mark vector, t (x) indicate affine transformation relationship, and A is one 2 × 2 affine matrix, and o is one 2 × 1 matrix, and expression waits for
With the translation between image；
If known one group of initial matching point centering, point set is X={ x on image a1,…,xN}T, corresponding point set on image b
For Y={ y1,…,yN}T, it is correct matched posterior probability p to calculate wherein n-th pair of match pointnThere is following posterior probability mathematical modulo
Type,
Wherein, γ and σ is model parameter, and e is mathematics constant, and b is preset coefficient；
Parametric solution module, for according to point set X={ x1,…,xN}TWith Y={ y1,…,yN}TSolving model parameter, packet
Following submodule is included,
Neighbours' match point submodule, for being each match point xn, n=1 ..., N search for K nearest neighbours respectively
Match point, K take preset value；
Weight matrix submodule is solved for the search result according to neighbours' match point submodule using least square method
Dimension is the weight matrix W of N × N；
Optimization submodule is used for by optimal method solving model parameter s, R, o, γ, σ, including to place an order
Member,
Initialization unit, for enabling γ=γ0, A=I2×2, o=0, P=IN×N, γ0For the preset initial value of γ, order is worked as
Preceding iterations k=1 calculates σ using following model parameter formula,
Wherein, matrix T=(t (x1),…,t(xN))T, tr () indicates to seek the mark of matrix；
Updating unit, for updating gained posterior probability mathematical model, meter in matrix P, including use model construction module
It is respectively correct matched posterior probability p to matching double points that calculation, which obtains N,1,…,pN, enable P=diag (p1,…,pN), diag is indicated
Diagonal matrix；
First parameter calculation unit, it is as follows for calculating parameter A, o,
Using following formula calculating parameter A,
Wherein, matrix
By IN×NOmission is denoted as I, matrix Q=(I-W)TP (I-W), λ are preset parameter；
Using following formula calculating parameter o,
O=μy-Aμx
Second parameter calculation unit, parameter A, o for being calculated according to the first parameter calculation unit recalculate ginseng
Number γ, σ is as follows,
Using following formula calculating parameter γ,
σ is calculated using model parameter formula in initialization unit；
Iteration judging unit for differentiating the condition of convergence, including calculates current parameter L, when meeting k=kmaxOr (L-
Lold)/Lold≤ ε terminates iteration, kmaxFor maximum iteration, ε is convergence threshold；Otherwise, k=k+1, order updating unit work
Make；The calculation formula of the parameter L is as follows,
Wherein, LoldIndicate the last L being calculated；
Judging result module, for calculating initial matching point to for correct matched posterior probability, and according to threshold decision
For initial matching point to correcting errors, realization is as follows,
The model parameter solved in the optimization submodule is substituted into posterior probability described in model construction module
Mathematical model, it is correct matched posterior probability that n-th pair of matching double points, which is calculated,；Work as pnWhen >=threshold, then it is assumed that the
N is correctly to match to match point；Work as pn<When threshold, then it is assumed that n-th pair of match point is the matching of mistake, wherein
Threshold is preset judgment threshold.
Further, weight matrix submodule include with lower unit,
Initial assignment unit, for working as match point xjIt is not the match point x searched in neighbours' match point submodulei
K neighbours' match point for the moment, then by WijIt is set as 0, wherein match point xjWith match point xiFor the match point in point set X,
And i, j=1 ..., N, WijIndicate the element of weight matrix W the i-th row jth row；
Unit is solved, is used forConstraints under, solve to obtain using least square method so that following
Cost function E (W) gets the weight matrix W of minimum value, and cost function E (W) is as follows,
RANSAC, ICF, GS method of selection carries out the comparison of images match with the present invention.Comparing result such as following table, wherein just
It is the ratio of correct matching double points that true rate, which refers in the matching double points that method finally provides,；Missing rate refers to method in screening process
The middle ratio for correct matching double points being judged as error matching points pair.It can be seen that this method used time is most short, accuracy rate highest is lost
Leak rate is minimum.
Method Contrast on effect table
| Method | Time | Accuracy | Missing rate |
| RANSAC | 15.36 | 75.32% | 19.54% |
| ICF | 1.66 | 46.34% | 8.66% |
| GS | 0.64 | 86.87% | 33.29% |
| The present invention | 0.34 | 99.11% | 2.92% |
Specific embodiment described herein is only an example for the spirit of the invention.Technology belonging to the present invention is led
The technical staff in domain can make various modifications or additions to the described embodiments or be substituted using similar fashion,
However, it does not deviate from the spirit of the invention or beyond the scope of the appended claims.
Claims (4)
1. a kind of Image Feature Matching method based on local linear migration and affine transformation, it is characterised in that：Including following step
Suddenly,
Step 1, it is correct matched posterior probability phase to establish the corresponding model of geometric transformation and matching double points between image to be matched
The model answered, realization is as follows,
For the rigid geometric transformation between image to be matched, foundation transformation mathematical model is as follows,
Y=t (x)=sRx+o
Wherein, if two images to be matched be image a and image b, x and y be respectively pixel on image a and image b coordinate to
Amount, t (x) indicate that rigid geometric transform relation, s indicate that the dimension scale between image to be matched, R are one 2 × 2 matrix, table
Show that the rotation between image to be matched, o are one 2 × 1 matrixes, indicates the translation between image to be matched；
If known one group of initial matching point centering, point set is X={ x on image a1,…,xN}T, corresponding point set is Y on image b
={ y1,…,yN}T, it is correct matched posterior probability p to calculate wherein n-th pair of match pointnThere is following posterior probability mathematical model,
Wherein, γ and σ is model parameter, and e is mathematics constant, and b is preset coefficient；
Step 2, according to point set X={ x1,…,xN}TWith Y={ y1,…,yN}TSolving model parameter, including following sub-step,
Step 2.1, it is each match point xn, n=1 ..., N search for K nearest neighbours' match point respectively, and K takes preset value；
Step 2.2, according to the search result of step 2.1, least square method is used to solve dimension as the weight matrix W of N × N；
Step 2.3, by optimal method solving model parameter s, R, o, γ, σ, including following sub-step,
Step 2.3.1, initialization, including enable γ=γ0, R=I2×2, o=0, P=IN×N, γ0For the preset initial value of γ, enable
Current iteration number k=1 calculates σ using following model parameter formula,
Wherein, T=(t (x1),…,t(xN))T, tr () indicates to seek the mark of matrix；
Step 2.3.2 updates matrix P, including using gained posterior probability mathematical model in step 1, N is calculated to match point
To being respectively correct matched posterior probability p1,…,pN, enable P=diag (p1,…,pN), diag indicates diagonal matrix；
Step 2.3.3, calculating parameter s, R, o are as follows,
Using following formula calculating parameter s,
Wherein, matrix
By IN×NOmission is denoted as I, matrix Q=(I-W)TP (I-W), λ are preset parameter；
Using following formula calculating parameter R,
R=UDVT
Wherein, D=diag (1, det (UVT)), the determinant of det () representing matrix, matrix U and V are obtained by singular value decomposition
；
Using following formula calculating parameter o,
O=μy-sRμx
Step 2.3.4, parameter s, R, the o being calculated according to step 2.3.3, it is as follows to recalculate parameter γ, σ,
Using following formula calculating parameter γ,
σ is calculated using model parameter formula in step 2.3.1；
Step 2.3.5 differentiates the condition of convergence, including calculates current parameter L, when meeting k=kmaxOr (L-Lold)/Lold≤
ε terminates iteration, kmaxFor maximum iteration, ε is convergence threshold；Otherwise, k=k+1, return to step 2.3.2；The parameter L
Calculation formula it is as follows,
Wherein, LoldIndicate the last L being calculated；
Step 3, initial matching point is calculated to for correct matched posterior probability, and just according to threshold decision initial matching point pair
Accidentally, realization is as follows,
The model parameter solved in the step 2.3 is substituted into posterior probability mathematical model described in step 1, is calculated n-th
It is correct matched posterior probability to matching double points；Work as pnWhen >=threshold, then it is assumed that n-th pair of match point is correctly to match；
Work as pn<When threshold, then it is assumed that n-th pair of match point is the matching of mistake, and wherein threshold is preset judgment threshold.
2. the Image Feature Matching method according to claim 1 based on local linear migration and affine transformation, feature exist
In：Step 2.2 includes following sub-step,
Step 2.2.1, as match point xjIt is not the match point x searched in the step 2.1iOne of K neighbours' match point
When, then by WijIt is set as 0, wherein match point xjWith match point xiFor the match point in point set X, and i, j=1 ..., N, WijIt indicates
The element of weight matrix W the i-th row jth row；
Step 2.2.2,Constraints under, solve to obtain using least square method so that following cost letters
Number E (W) gets the weight matrix W of minimum value, and cost function E (W) is as follows,
3. a kind of Image Feature Matching system based on local linear migration and affine transformation, it is characterised in that：Including with lower die
Block,
Model construction module is correct matched for establishing the corresponding model of geometric transformation and matching double points between image to be matched
The corresponding model of posterior probability, realization is as follows,
For the rigid geometric transformation between image to be matched, foundation transformation mathematical model is as follows,
Y=t (x)=sRx+o
Wherein, if two images to be matched be image a and image b, x and y be respectively pixel on image a and image b coordinate to
Amount, t (x) indicate that rigid geometric transform relation, s indicate that the dimension scale between image to be matched, R are one 2 × 2 matrix, table
Show that the rotation between image to be matched, o are one 2 × 1 matrixes, indicates the translation between image to be matched；
If known one group of initial matching point centering, point set is X={ x on image a1,…,xN}T, corresponding point set is Y on image b
={ y1,…,yN}T, it is correct matched posterior probability p to calculate wherein n-th pair of match pointnThere is following posterior probability mathematical model,
Wherein, γ and σ is model parameter, and e is mathematics constant, and b is preset coefficient；
Parametric solution module, for according to point set X={ x1,…,xN}TWith Y={ y1,…,yN}TSolving model parameter, including with
Lower submodule,
Neighbours' match point submodule, for being each match point xn, n=1 ..., N search for nearest K neighbours matching respectively
Point, K take preset value；
Weight matrix submodule solves dimension for the search result according to neighbours' match point submodule using least square method
For the weight matrix W of N × N；
Optimization submodule, for by optimal method solving model parameter s, R, o, γ, σ, including with lower unit,
Initialization unit, for enabling γ=γ0, R=I2×2, o=0, P=IN×N, γ0For the preset initial value of γ, current change is enabled
Generation number k=1 calculates σ using following model parameter formula,
Wherein, T=(t (x1),…,t(xN))T, tr () indicates to seek the mark of matrix；
Updating unit is calculated for updating gained posterior probability mathematical model in matrix P, including use model construction module
It is respectively correct matched posterior probability p to matching double points to N1,…,pN, enable P=diag (p1,…,pN), diag indicates diagonal
Matrix；
First parameter calculation unit, it is as follows for calculating parameter s, R, o,
Using following formula calculating parameter s,
Wherein, matrix It will
IN×NOmission is denoted as I, matrix Q=(I-W)TP (I-W), λ are preset parameter；
Using following formula calculating parameter R,
R=UDVT
Wherein, D=diag (1, det (UVT)), the determinant of det () representing matrix, matrix U and V are obtained by singular value decomposition
；Using following formula calculating parameter o,
O=μy-sRμx
Second parameter calculation unit, parameter s, R, o for being calculated according to the first parameter calculation unit, recalculates parameter
γ, σ are as follows,
Using following formula calculating parameter γ,
σ is calculated using model parameter formula in initialization unit；
Iteration judging unit for differentiating the condition of convergence, including calculates current parameter L, when meeting k=kmaxOr (L-
Lold)/Lold≤ ε terminates iteration, kmaxFor maximum iteration, ε is convergence threshold；Otherwise, k=k+1, order updating unit work
Make；The calculation formula of the parameter L is as follows,
Wherein, LoldIndicate the last L being calculated；
Judging result module, for calculating initial matching point to for correct matched posterior probability, and it is initial according to threshold decision
Matching double points are corrected errors, and realization is as follows,
The model parameter solved in the optimization submodule is substituted into posterior probability mathematics described in model construction module
Model, it is correct matched posterior probability that n-th pair of matching double points, which is calculated,；Work as pnWhen >=threshold, then it is assumed that n-th pair
Match point is correctly to match；Work as pn<When threshold, then it is assumed that n-th pair of match point is the matching of mistake, wherein threshold
For preset judgment threshold.
4. the Image Feature Matching system according to claim 3 based on local linear migration and affine transformation, feature exist
In：Weight matrix submodule include with lower unit,
Initial assignment unit, for working as match point xjIt is not the match point x searched in neighbours' match point submoduleiK
Neighbours' match point a period of time, then by WijIt is set as 0, wherein match point xjWith match point xiFor the match point in point set X, and i, j
=1 ..., N, WijIndicate the element of weight matrix W the i-th row jth row；
Unit is solved, is used forConstraints under, solve to obtain using least square method so that following costs
Function E (W) gets the weight matrix W of minimum value, and cost function E (W) is as follows,
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