CN102930502A - Consistency image transformation method and system capable of keeping control point correspondence - Google Patents

Abstract

The invention discloses a consistency image transformation method and a system capable of keeping control point correspondence. The method comprises the following steps of building a forward and reverse transformation function based on the control point correspondence, determining a displacement function of the forward and reverse transformation function, relocating the displacement function of the forward and reverse transformation function, adjusting the displacement function of the forward and reverse transformation function of an image for the first time, calculating an inverse function of the forward and reverse transformation function of the image, adjusting the displacement function of the forward and reverse transformation function of the image for the second time, determining temporary mapping positions of a source control point and a target control point, calculating a control point error and a consistency error of image transformation, and repeating the process until the control point error and the consistency error satisfy requirements. According to the method, the consistency image transformation capable of keeping the control point correspondence is achieved, the consistency transformation problem in elastic registering of the image can be realized, and the correspondence of the original control points is kept as much as possible on the premise of solving the consistency image transformation.

Description

But consistance image conversion method and the system of retentive control point correspondence

Technical field

The invention belongs to image processing field, but relate in particular to a kind of consistance transform method and image transformation system based on the retentive control point correspondence.

Background technology

H.J.Johnson and G.E.Christensen have proposed a kind of consistance conversion method for solving in 2002.By the conversion of iterative consistance, so that positive inverse transformation has minimum distortion energy and conformity error.Suppose that forward shape becomes h, the deformational displacement field is u (x); Reciprocal transformation is g, and the deformational displacement field is w (x).H (x)=x+u (x) then, g (x)=x+w (x).The inverse function of definition positive-going transition is h ^-1, its displacement field is

The inverse function of reciprocal transformation is g ^-1, its displacement field is

Then

Suppose reference mark corresponding relation (q _i, p _i) known, the algorithmic procedure that H.J.Johnson and G.E.Christensen provide is as follows:

Step 1, r _i=q _i, s _i=p _iU (x)=0; W (x)=0 sets Optimal Step Size α and β, maximum reference mark offset error ζ, iterations iter, maximum iteration time miter etc.

Step 2 is based on the corresponding relation at reference mark Utilize the thin-plate spline interpolation method to find the solution forward deformation function f ₁(x), satisfy f ₁(r _i)=p _iCorresponding relation based on the reference mark

Utilize the thin-plate spline interpolation method to find the solution the reverse strain function f ₂(x), satisfy f ₂(s _i)=q _i

Step 3, u (x)=u (x)+α [f ₁(x)-and x], w (x)=w (x)+α [f ₂(x)-x].

Step 4, r _i=q _i+ u (r _i), s _i=p _i+ w (s _i), iter=iter+1.

Step 5 is asked for the inverse function h of positive and negative conversion ^-1(x), g ^-1(x).

Step 6 is upgraded the displacement field of positive and negative conversion.U (x)=u (x)-β [u (x)-g ^-1(x)+and x], while w (x)=w (x)-β [w (x)-h ^-1(x)+x].

Step 7 checks whether satisfy stop criterion.Use avgerr _{Q → p}If expression reference mark offset error is iter〉miter, perhaps avgerr _{Q → p}＜ζ, perhaps avgerr _{P → q}During＜ζ, iteration finishes; Otherwise return Step 2.

There is following problem in the above-mentioned method of value solving that H.J.Johnson and G.E.Christensen propose:

(1) reference mark r _i, s _iAdjustment can depart from p _i, q _i

In the iterative process that array is found the solution, each adjustment u (x) of positive-going transition and reciprocal transformation=u (x)+α [f ₁(x)-and x], w (x)=w (x)+α [f ₂(x)-and x], can not guarantee to make r _i, s _iMove closer to target location p _i, q _iWe suppose reference mark q take positive-displacement field u (x) as example _iWith p _iCorrespondence through iteration, obtains current displacement field u _k(x), satisfy u _k(q _i)=r _i-q _iThe deformation function f of next iteration structure ₁(x) satisfy f ₁(r _i)=p _i, new displacement field u _K+1(x)=u _k(x)+α (f ₁(x)-x).Consider the situation of step-length α=1,

u _k+1(q _i)=u _k(q _i)+α(f ₁(q _i)-q _i)

=r _i-q _i+f ₁(q _i)-q _i

≠p _i-q _i

This explanation, when α=1, q _iBe mapped to p _iNear, but be difficult to be mapped to exactly p _iThe position of point.This will cause in the iteration of back, r _iThe position can be at p _iNear swing, and can't be mapped to exactly p _iThe position on, there is error in the position at reference mark.Similarly, oppositely also there are the problems referred to above in displacement field.

(2) r _i, s _iCorrection position and displacement field inconsistent.

In the iterative process of algorithm, there is twice displacement field correction, be according to deformation function f for the first time ₁(x) and f ₂(x) carry out (step 3) for the second time is (step 6), the r according to the inverse function correction of forward and reverse conversion _i, s _iCorrection position be at forward, oppositely revise the first time of displacement function after.But owing to forward, oppositely for the second time adjustment of displacement function existence, will cause r like this _i, s _iThe position inaccurate, and then next time iterative computation f of impact ₁(x) and f ₂(x).

In addition, r _i, s _iCorrection position be r _i=q _i+ u (r _i), s _i=p _i+ w (s _i), this method of adjustment causes u (q _i) ≠ r _i-q _i, w (p _i)=s _i-p _i, i.e. r _iBe not q _iNext interim mapping point, s _iNeither p _iNext interim mapping point.In next iteration, utilize

With

Corresponding relation tectonic transition function f ₁(x) and f ₂(x) time, just be difficult to guarantee that this transforming function transformation function can make q _iBe mapped to exactly p _iThe position of point, p _iBe mapped to exactly q _iThe position of point, the corresponding relation between can't retentive control point.

Summary of the invention

But the purpose of the embodiment of the invention is to provide a kind of consistance image conversion method and system of retentive control point correspondence, is intended to solve the irretentive problem of the corresponding relation in the reference mark that exists in the existing consistance transform method based on the corresponding relation in reference mark.

But the embodiment of the invention is achieved in that a kind of consistance image conversion method of retentive control point correspondence, and described method comprises the steps:

Steps A, according to reference mark, source and target control point correspondence, structure from the source mapping of control points to target control point the positive-going transition function and be mapped to the reciprocal transformation function at reference mark, source from the target control point, and the displacement function of the forward of computed image and reciprocal transformation function;

Step B carries out reorientation, the displacement function of the forward after being adjusted and reciprocal transformation function to the forward that obtains in the steps A and the displacement function of reciprocal transformation function;

Step C adjusts the displacement function of the current forward of image and reciprocal transformation function for the first time according to the displacement function of the forward after the adjustment that obtains among the step B and reciprocal transformation function;

Step D is according to the inverse function of the current positive-going transition function of displacement function computed image of the current forward of the image that obtains among the step C and reciprocal transformation function and the inverse function of current reciprocal transformation function;

Step e is adjusted the displacement function of the current positive-going transition function of image and the displacement function of reciprocal transformation function for the second time according to the inverse function of the current positive-going transition function of the image that obtains among the step D and the inverse function of current reciprocal transformation function; Then determine the interim mapping position at reference mark, source and the interim mapping position of target control point according to the displacement function of the current positive-going transition function of image after adjusting and the displacement function of reciprocal transformation function;

Step F, displacement function and the interim mapping position at reference mark, source and the interim mapping position of target control point according to displacement function and the reciprocal transformation function of the current positive-going transition function of the image that obtains in the step e, reference mark error and the conformity error of computed image conversion, if reference mark error and the conformity error of image conversion do not reach preset value, according to the interim mapping position at reference mark, source and the corresponding relation of target control point, and the corresponding relation at interim mapping position and reference mark, source is put in target control, repeating step A is to step e, until reference mark error and the conformity error of image conversion reach preset value.

The present invention also provides a kind of consistance image transformation system of retentive control point correspondence, comprises following unit:

Forward, reciprocal transformation construction of function unit, be used for according to reference mark, source and target control point correspondence, structure from the source mapping of control points to target control point the positive-going transition function and be mapped to the reciprocal transformation function at reference mark, source from the target control point, and the displacement function of the forward of computed image and reciprocal transformation function;

The reorientation unit is used for the displacement function of forward and reciprocal transformation function is carried out reorientation, the displacement function of the forward after being adjusted and reciprocal transformation function;

Adjustment unit, the forward after the adjustment that obtains according to the reorientation unit and the displacement function of reciprocal transformation function are adjusted the displacement function of the current forward of image and reciprocal transformation function for the first time;

Inverse function is found the solution the unit, is used for the inverse function of the current positive-going transition function of displacement function computed image of the current forward of the image that obtains according to the first adjustment unit and reciprocal transformation function and the inverse function of current reciprocal transformation function;

The mapping determining unit is used for finding the solution the inverse function of the current positive-going transition function of image that the unit obtains and the inverse function of current reciprocal transformation function is adjusted the displacement function of the current positive-going transition function of image and the displacement function of reciprocal transformation function for the second time according to inverse function; Then determine the interim mapping position at reference mark, source and the interim mapping position of target control point according to the displacement function of the current positive-going transition function of image after adjusting and the displacement function of reciprocal transformation function;

The estimation of error unit, for the displacement function of the current positive-going transition function of image that obtains according to the mapping determining unit and displacement function and the interim mapping position at reference mark, source and the interim mapping position of target control point of reciprocal transformation function, reference mark error and the conformity error of computed image conversion, if reference mark error and the conformity error of image conversion do not reach preset value, according to the interim mapping position at reference mark, source and the corresponding relation of target control point, and the corresponding relation at interim mapping position and reference mark, source is put in target control, with described forward, reciprocal transformation construction of function unit, the reorientation unit, adjustment unit, inverse function is found the solution the unit, the mapping determining unit repeats to cooperate and processes, until reference mark error and the conformity error of image conversion reach preset value.

Compared with prior art, the invention has the beneficial effects as follows: but the present invention has realized the consistance image conversion of retentive control point correspondence, can be used for solving the consistance transformation problem of image elastic registrating, under the prerequisite of finding the solution the consistance image conversion, kept as far as possible the corresponding relation at original reference mark.

Description of drawings

But the FB(flow block) of the consistance image conversion method of the retentive control point correspondence that Fig. 1 provides for the embodiment of the invention;

Fig. 2 be the embodiment of the invention provide find the solution the contrafunctional FB(flow block) of transforming function transformation function;

Fig. 3 is the consistance image transformation system configuration diagram of the retentive control point correspondence that provides of the embodiment of the invention.

Embodiment

In order to make purpose of the present invention, technical scheme and advantage clearer, below in conjunction with drawings and Examples, the present invention is further elaborated.Should be appreciated that specific embodiment described herein only in order to explain the present invention, is not intended to limit the present invention.

In embodiments of the present invention, but consistance transform method and image transformation system by the retentive control point correspondence, but realized the consistance image conversion of retentive control point correspondence, can be used for solving the consistance transformation problem of image elastic registrating, under the prerequisite of finding the solution the consistance image conversion, kept as far as possible the corresponding relation at original reference mark.。

But the FB(flow block) of the consistance image conversion method of the retentive control point correspondence that Fig. 1 is the present embodiment of the present invention to be provided, details are as follows:

In step S101, according to reference mark, source and target control point correspondence, structure from the source mapping of control points to target control point the positive-going transition function and be mapped to the reciprocal transformation function at reference mark, source from the target control point, and the displacement function of the forward of computed image and reciprocal transformation function.

Reference mark, the source q that at first makes the user input _iBe r _i, target control point p _iBe s _i, utilize radial basis function tectonic transition function, obtain from reference mark, source r _iBe mapped to target control point s _iThe positive-going transition function f ₁(x), and from target control point s _iBe mapped to reference mark, source r _iThe reciprocal transformation function f ₂(x).Calculate the displacement function u of positive-going transition function _t(x)=f ₁(x)-and x, the displacement function w of reciprocal transformation function _t(x)=f ₂(x)-x.

$f_1\left(x\right)=a_{11}+a_{1x}{x}_x+a_{1y}{x}_y+\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\ω}}_{1i}U\left(\right||r_i-x|\left|\right)---\left(1\right)$

$f_2\left(x\right)=a_{21}+a_{2x}{x}_x+a_{2y}{x}_y+\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\ω}}_{2i}U\left(\right||s_i-x|\left|\right)---\left(2\right)$

Wherein, r _iReference mark, source q _iInterim mapping position, s _iTarget control point p _iInterim mapping position,

The thin plate spline basis function, coefficient (a ₁₁, a _1x, a _1y, ω _1i) be equation P=L ₁* W ₁Solution,

$L_1={\left[\begin{array}{cc}{K}_1& R\\ R^T& 0\end{array}\right]}_{(n+3)\×(n+3)},$ $K_1={\left[\begin{array}{cccc}0& U\left(d_{12}\right)& ...& U\left(d_{1n}\right)\\ U\left(d_{21}\right)& 0& ...& U\left(d_{2n}\right)\\ ...& ...& ...& ...\\ U\left(d_{n1}\right)& U\left(d_{n2}\right)& ...& 0\end{array}\right]}_{n\×n},$ d _ij=||r _i-r _j||， $W_1={\left(\begin{array}{c}{\mathrm{\ω}}_{11}\\ ...\\ {\mathrm{\ω}}_{1n}\\ a_{11}\\ a_{1x}\\ a_{1y}\end{array}\right),}_{(n+3)\×3}$

$P={\left[\begin{array}{cc}1& p_1\\ 1& p_2\\ ...& ...\\ 1& p_n\end{array}\right]}_{n\×3},$ $R={\left[\begin{array}{cc}1& r_1\\ 1& r_2\\ ...& ...\\ 1& r_n\end{array}\right]}_{n\×3}$

L ₁Be (n+3) * (n+3) matrix, 0 is 3 * 3 null matrix; W ₁Be (n+3) * 3 matrixes, represent deformation function f ₁Coefficient vector on X and Y-direction, K ₁N * n matrix, according to r _iBetween distance calculate, P is target control point set, target control point p _i∈ P, R are reference mark, source q _iThe set of interim mapping position, d _IjR _iAnd r _jBetween Euclidean distance.

Coefficient (a ₂₁, a _2x, a _2y, ω _2i) be equation Q=L ₂* W ₂Solution,

$L_2={\left[\begin{array}{cc}{K}_2& S\\ S^T& 0\end{array}\right]}_{(n+3)\×(n+3)},$ $K_2={\left[\begin{array}{cccc}0& U\left(d_{12}\right)& ...& U\left(d_{1n}\right)\\ U\left(d_{21}\right)& 0& ...& U\left(d_{2n}\right)\\ ...& ...& ...& ...\\ U\left(d_{n1}\right)& U\left(d_{n2}\right)& ...& 0\end{array}\right]}_{n\×n},$ d _ij=||s _i-s _j||， $W_2={\left(\begin{array}{c}{\mathrm{\ω}}_{21}\\ ...\\ {\mathrm{\ω}}_{2n}\\ a_{21}\\ a_{2x}\\ a_{2y}\end{array}\right),}_{(n+3)\×3}$

$Q={\left[\begin{array}{cc}1& q_1\\ 1& q_2\\ ...& ...\\ 1& q_n\end{array}\right]}_{n\×3},$ $S={\left[\begin{array}{cc}1& s_1\\ 1& s_2\\ ...& ...\\ 1& s_n\end{array}\right]}_{n\×3}$

L ₂Be (n+3) * (n+3) matrix, 0 is 3 * 3 null matrix; W ₂Be (n+3) * 3 matrixes, represent deformation function f ₂Coefficient vector on X and Y-direction, K ₂N * n matrix, according to s _iBetween distance calculate, Q is reference mark, source set, reference mark, source q _i∈ Q, S are target control point p _iThe set of interim mapping position, d _IjS _iAnd s _jBetween Euclidean distance.

In step S102, the displacement function of forward and reciprocal transformation function is carried out reorientation, the displacement function of the forward after being adjusted and reciprocal transformation function.

The displacement function of supposing the image positive-going transition function that last iteration is determined is u _k(x), the displacement function of the reciprocal transformation function determined of last iteration is w _k(x), the displacement function u of positive-going transition function _t(x) reorientation is The displacement function w of reciprocal transformation function _k(x) reorientation is

u ^*(x)=u _t(u _k(x)+x)，u _t(x)=f ₁(x)-x （3）

w ^*(x)=w _t(w _k(x)+x)，w _t(x)=f ₂(x)-x （4）

Displacement field through after redefining along with the increase of iterations, can guarantee q _iMapping position r _iConstantly to p _iApproach, and in the iteration of back, r _iThe position more and more to p _iApproach, rather than at p _iNear swing, this will help algorithm after convergence, the mapping error at reference mark in the scope that can control, thereby improve the precision of image registration.

In step S103, adjust for the first time the displacement function of the current forward of image and reciprocal transformation function according to the displacement function of the forward after adjusting and reciprocal transformation function.

The displacement function of the image positive-going transition function that this iteration is determined is u _K+1(x), the displacement function of reciprocal transformation function is w _K+1(x), adjust the forward of image the first time, the displacement function of reciprocal transformation function is

u _k+1(x)＝u _k(x)+αu ^*(x) （5）

w _k+1(x)＝w _k(x)+αw ^*(x) （6）

In step S104, according to the inverse function of the current positive-going transition function of displacement function computed image of the current forward of image and reciprocal transformation function and the inverse function of current reciprocal transformation function.

The positive-going transition function of image is h (x)=x+u (x), and the reciprocal transformation function is g (x)=x+w (x).Inverse function with the positive-going transition function is solved to example,

Ω is the image space territory, finds the solution h (x by following iterative process ^*)=n, i.e. h ^-1(n)=x ^*, process flow diagram as shown in Figure 2.

Step S201 chooses initial point x ₀, given permissible error ε, but maximum iterations iternumber, k=0;

Step S202 checks whether satisfy || h (x _k)-n||＜ε.If satisfy, then iteration finishes, optimum solution x ^*=x _kOtherwise, turn to Step 203;

Step S203, structure direction of search d _k, d _k=[n-h (x _k)];

Step S204, x _K+1=x _k+ λ _kd _k, λ _k=0.5, k=k+1, λ _k

To adjust step-length;

If step S205 is k〉iternumber, iteration finishes, otherwise turns step 202.

In step S105, adjust for the second time the displacement function of the current positive-going transition function of image and the displacement function of reciprocal transformation function according to the inverse function of the current positive-going transition function of the image that obtains and the inverse function of current reciprocal transformation function; Then determine the interim mapping position at reference mark, source and the interim mapping position of target control point according to the displacement function of the current positive-going transition function of image after adjusting and the displacement function of reciprocal transformation function.

The second time adjusts the displacement function of the current positive-going transition function of image and the displacement function of reciprocal transformation function is:

u _k+1(x)=u _k(x)-β[u _k(x)-g ^-1(x)+x] （7）

w _k+1(x)=w _k(x)-β[w _k(x)-h ^-1(x)+x] （8）

Wherein, g ^-1(x) be the inverse function of image reversal transforming function transformation function, h ^-1(x) be the inverse function of image positive-going transition function, β is for adjusting coefficient.

According to the image forward after adjusting for the second time, the displacement function of reciprocal transformation function, determine reference mark, source q _iInterim mapping position r _iWith target control point p _iInterim mapping position s _i

r _i=q _i+u(q _i) （9）

s _i=p _i+w(p _i) （10）

In step S106, according to displacement function and the interim mapping position at reference mark, source and the interim mapping position of target control point of displacement function and the reciprocal transformation function of the current positive-going transition function of the image that obtains, reference mark error and the conformity error of computed image conversion.

The present invention calculates maximum reference mark error and maximum uniform error, and each error is defined as follows:

Maximum reference mark error (Maximum Landmark Error, MaxLE):

MaxLE=max{||h(q ₁)-g ^-1(q ₁)|| ²,…,||h(q _N)-g ^-1(q _N)|| ²,||g(p ₁)-h ^-1(p ₁)|| ²,…,||g(p _N)-h ^-1(p _N)|| ²}

（11）

Wherein, q _iBe reference mark, source, p _iBe the target control point.

Most homogeneous error (Maximum Consistency Error, MaxCE):

MaxCE=max{||h(x)-g ^-1(x)|| ²,x∈Ω} （12）

Wherein x is the point in the image space territory, and MN is the image pixel number.

If reference mark error and the conformity error of image conversion do not reach preset value, according to the interim mapping position at reference mark, source and the corresponding relation of target control point, and target control puts the corresponding relation at interim mapping position and reference mark, source, goes to step S101.

Fig. 3 is the consistance image transformation system configuration diagram of the retentive control point correspondence that provides of the embodiment of the invention, for convenience of explanation, only shows the relevant part of the embodiment of the invention.Wherein, but the consistance transform method device of this retentive control point correspondence can be the software unit that is built in image transformation system, the unit of hardware cell or soft or hard combination.

With reference to Fig. 3, in the present embodiment, but the consistance converting means that is somebody's turn to do the retentive control point correspondence comprises: forward, reciprocal transformation construction of function unit 31, reorientation unit 32, adjustment unit 33, inverse function are found the solution unit 34, mapping determining unit 35, estimation of error unit 36.

Forward, reciprocal transformation construction of function unit 31 are according to reference mark, source and target control point correspondence, structure from the source mapping of control points to target control point the positive-going transition function and be mapped to the reciprocal transformation function at reference mark, source from the target control point, and the displacement function of the forward of computed image and reciprocal transformation function.Concrete principle does not repeat them here as mentioned above.

Reorientation unit 32, according to the displacement function of the definite image positive-going transition function of last iteration and the displacement function of reciprocal transformation function, and forward, reciprocal transformation construction of function unit 31 positive-going transition function and the direction transformation function, the displacement function of reorientation positive-going transition function and the displacement function of reciprocal transformation function that obtain.Through the displacement field after redefining, along with the increase of iterations, can guarantee that the mapping position at reference mark, source is constantly approached to the target control point, and in the iteration of back, mapping position is more and more approached to the target control point, rather than near swing target control point.Concrete condition does not repeat them here as mentioned above.

Adjustment unit 33, the forward after the adjustment that obtains according to the reorientation unit and the displacement function of reciprocal transformation function are adjusted the displacement function of the current forward of image and reciprocal transformation function for the first time.

Inverse function is found the solution unit 34, the forward that the image that obtains according to adjustment unit is current and the inverse function of the current positive-going transition function of displacement function computed image of reciprocal transformation function and the inverse function of current reciprocal transformation function.

Mapping determining unit 35 is found the solution the inverse function of the current positive-going transition function of image that the unit obtains and the inverse function of current reciprocal transformation function is adjusted the displacement function of the current positive-going transition function of image and the displacement function of reciprocal transformation function for the second time according to inverse function; Then determine the interim mapping position at reference mark, source and the interim mapping position of target control point according to the displacement function of the current positive-going transition function of image after adjusting and the displacement function of reciprocal transformation function.

Estimation of error unit 36, according to the displacement function of the current positive-going transition function of image that obtains of mapping determining unit and displacement function and the interim mapping position at reference mark, source and the interim mapping position of target control point of reciprocal transformation function, reference mark error and the conformity error of computed image conversion, if reference mark error and the conformity error of image conversion do not reach preset value, according to the interim mapping position at reference mark, source and the corresponding relation of target control point, and the corresponding relation at interim mapping position and reference mark, source is put in target control, with described forward, reciprocal transformation construction of function unit 31, reorientation unit 32, adjustment unit 33, inverse function is found the solution unit 34, the mapping determining unit repeats to cooperate processes 35, until reference mark error and the conformity error of image conversion reach preset value.

Wherein, it is as indicated above that above-mentioned forward, reciprocal transformation construction of function unit 31, reorientation unit 32, adjustment unit 33, inverse function are found the solution the algorithmic formula of concrete operation time institute foundation of unit 34, mapping determining unit 35, estimation of error unit 36, gives unnecessary details no longer one by one.

In the embodiment of the invention, but consistance transform method and image transformation system by the retentive control point correspondence, but realized the consistance image conversion of retentive control point correspondence, can be used for solving the consistance transformation problem of image elastic registrating, under the prerequisite of finding the solution the consistance image conversion, kept as far as possible the corresponding relation at original reference mark.

The above only is preferred embodiment of the present invention, not in order to limiting the present invention, all any modifications of doing within the spirit and principles in the present invention, is equal to and replaces and improvement etc., all should be included within protection scope of the present invention.

Claims (10)

1. but the consistance image conversion method of a retentive control point correspondence is characterized in that, described method comprises the steps:

Steps A, according to reference mark, source and target control point correspondence, structure from the source mapping of control points to target control point the positive-going transition function and be mapped to the reciprocal transformation function at reference mark, source from the target control point, and the displacement function of the forward of computed image and reciprocal transformation function;

Step B carries out reorientation, the displacement function of the forward after being adjusted and reciprocal transformation function to the forward that obtains in the steps A and the displacement function of reciprocal transformation function;

Step C adjusts the displacement function of the current forward of image and reciprocal transformation function for the first time according to the displacement function of the forward after the adjustment that obtains among the step B and reciprocal transformation function;

Step D is according to the inverse function of the current positive-going transition function of displacement function computed image of the current forward of the image that obtains among the step C and reciprocal transformation function and the inverse function of current reciprocal transformation function;

Step e is adjusted the displacement function of the current positive-going transition function of image and the displacement function of reciprocal transformation function for the second time according to the inverse function of the current positive-going transition function of the image that obtains among the step D and the inverse function of current reciprocal transformation function; Then determine the interim mapping position at reference mark, source and the interim mapping position of target control point according to the displacement function of the current positive-going transition function of image after adjusting and the displacement function of reciprocal transformation function;

Step F, displacement function and the interim mapping position at reference mark, source and the interim mapping position of target control point according to displacement function and the reciprocal transformation function of the current positive-going transition function of the image that obtains in the step e, reference mark error and the conformity error of computed image conversion, if reference mark error and the conformity error of image conversion do not reach preset value, according to the interim mapping position at reference mark, source and the corresponding relation of target control point, and the corresponding relation at interim mapping position and reference mark, source is put in target control, repeating step A is to step e, until reference mark error and the conformity error of image conversion reach preset value.

2. the method for claim 1 is characterized in that, described steps A is according to the forward of following formula computed image and the displacement function of reciprocal transformation function:

The displacement function of positive-going transition function: u _t(x)=f ₁(x)-x;

The displacement function of reciprocal transformation function: w _t(x)=f ₂(x)-x;

Wherein, $f_1\left(x\right)=a_{11}+a_{1x}{x}_x+a_{1y}{x}_y+\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\ω}}_{1i}U\left(\right||r_i-x|\left|\right)$

$f_2\left(x\right)=a_{21}+a_{2x}{x}_x+a_{2y}{x}_y+\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\ω}}_{2i}U\left(\right||s_i-x|\left|\right)$

X is the point coordinate of two-dimensional space, r _iReference mark, source q _iInterim mapping position, s _iTarget control point p _iInterim mapping position, The thin plate spline basis function, coefficient (a ₁₁, a _1x, a _1y, ω _1i) be equation P=L ₁* W ₁Solution,

$L_1={\left[\begin{array}{cc}{K}_1& R\\ R^T& 0\end{array}\right]}_{(n+3)\×(n+3)},$ $K_1={\left[\begin{array}{cccc}0& U\left(d_{12}\right)& ...& U\left(d_{1n}\right)\\ U\left(d_{21}\right)& 0& ...& U\left(d_{2n}\right)\\ ...& ...& ...& ...\\ U\left(d_{n1}\right)& U\left(d_{n2}\right)& ...& 0\end{array}\right]}_{n\×n},$ dij=||ri-rj||， $W_1={\left(\begin{array}{c}{\mathrm{\ω}}_{11}\\ ...\\ {\mathrm{\ω}}_{1n}\\ a_{11}\\ a_{1x}\\ a_{1y}\end{array}\right)}_{(n+3)\×3},$

$P={\left[\begin{array}{cc}1& p_1\\ 1& p_2\\ ...& ...\\ 1& p_n\end{array}\right]}_{n\×3},$ $R={\left[\begin{array}{cc}1& r_1\\ 1& r_2\\ ...& ...\\ 1& r_n\end{array}\right]}_{n\×3}$

L ₁(n+3) * (n+3) matrix, wherein 0 be 3 * 3 null matrix; W ₁Be (n+3) * 3 matrixes, represent deformation function f ₁Coefficient vector on X and Y-direction, K ₁N * n matrix, according to r _iBetween distance calculate, P is target control point set, target control point p _i∈ P, R are reference mark, source q _iThe set of interim mapping position, d _IjR _iAnd r _jBetween Euclidean distance;

Coefficient (a ₂₁, a _2x, a _2y, ω _2i) be equation Q=L ₂* W ₂Solution,

$L_2={\left[\begin{array}{cc}{K}_2& S\\ S^T& 0\end{array}\right]}_{(n+3)\×(n+3)},$ $K_2={\left[\begin{array}{cccc}0& U\left(d_{12}\right)& ...& U\left(d_{1n}\right)\\ U\left(d_{21}\right)& 0& ...& U\left(d_{2n}\right)\\ ...& ...& ...& ...\\ U\left(d_{n1}\right)& U\left(d_{n2}\right)& ...& 0\end{array}\right]}_{n\×n},$ d _ij=||s _i-s _j||， $W_2={\left(\begin{array}{c}{\mathrm{\ω}}_{21}\\ ...\\ {\mathrm{\ω}}_{2n}\\ a_{21}\\ a_{2x}\\ a_{2y}\end{array}\right)}_{(n+3)\×3},$

$Q={\left[\begin{array}{cc}1& q_1\\ 1& q_2\\ ...& ...\\ 1& q_n\end{array}\right]}_{n\×3},$ $S={\left[\begin{array}{cc}1& s_1\\ 1& s_2\\ ...& ...\\ 1& s_n\end{array}\right]}_{n\×3}$

L ₂Be (n+3) * (n+3) matrix, 0 is 3 * 3 null matrix; W ₂Be (n+3) * 3 matrixes, represent deformation function f ₂Coefficient vector on X and Y-direction, K ₂N * n matrix, according to s _iBetween distance calculate, Q is reference mark, source set, reference mark, source q _i∈ Q, S are target control point p _iThe set of interim mapping position, d _IjS _iAnd s _jBetween Euclidean distance.

3. method as claimed in claim 2 is characterized in that, described step B carries out reorientation, the displacement function of the forward after being adjusted and reciprocal transformation function according to following formula to the forward that obtains in the steps A and the displacement function of reciprocal transformation function:

u ^*(x)=u _t(u _k(x)+x)，u _t(x)=f ₁(x)-x

w ^*(x)=w _t(w _k(x)+x)，w _t(x)=f ₂(x)-x

Wherein, u _k(x) be the displacement function of the definite image positive-going transition function of last iteration, w _k(x) be the displacement function of the definite reciprocal transformation function of last iteration, u ^*(x) be the displacement function u of interim positive-going transition function _t(x) reorientation result, w ^*(x) be the displacement function w of interim reciprocal transformation function _t(x) reorientation result.

4. but the consistance image conversion method of retentive control point correspondence as claimed in claim 3 is characterized in that, described step C is according to following the formula for the first time current forward of image and the displacement function of reciprocal transformation function:

The displacement function of the positive-going transition function that image is current: u _K+1(x)=u _k(x)+α u ^*(x)

The displacement function of the reciprocal transformation function that image is current: w _K+1(x)=w _k(x)+α w ^*(x);

Wherein α adjusts coefficient.

5. the method for claim 1 is characterized in that, described step e is adjusted the displacement function of the current positive-going transition function of image and the displacement function of reciprocal transformation function for the second time according to following formula:

The displacement function of the current positive-going transition function of image: u _K+1(x)=u _k(x)-β [u _k(x)-g ^-1(x)+x]

The displacement function of the current reciprocal transformation function of image: w _K+1(x)=w _k(x)-β [w _k(x)-h ^-1(x)+x]

Wherein, g ^-1(x) be the inverse function of image reversal transforming function transformation function, h ^-1(x) be the inverse function of image positive-going transition function, β is for adjusting coefficient; u _k(x) be the displacement function of the positive-going transition function that obtains of last iteration, w _k(x) be the displacement function of the reciprocal transformation function that obtains of last iteration, u _K+1(x) be the displacement function of the positive-going transition function that obtains of this iteration, w _K+1(x) be the displacement function of the reciprocal transformation function that obtains of this iteration;

Described step F is determined the interim mapping position at reference mark, source and the interim mapping position of target control point according to the displacement function of the current positive-going transition function of image and the displacement function of reciprocal transformation function:

Reference mark, source q _iInterim mapping position: r _i=q _i+ u _K+1(q _i)

Target control point p _iInterim mapping position: s _i=p _i+ w _K+1(p _i)

Wherein, q _iThe reference mark, source, p _iThe target control point, r _iReference mark, source q _iInterim mapping position, s _iTarget control point p _iInterim mapping position, u _K+1(x) be the displacement function of the positive-going transition function that obtains of this iteration, w _K+1(x) be the displacement function of the reciprocal transformation function that obtains of this iteration.

6. the consistance image transformation system of a retentive control point correspondence is characterized in that, described system comprises following unit:

Forward, reciprocal transformation construction of function unit, be used for according to reference mark, source and target control point correspondence, structure from the source mapping of control points to target control point the positive-going transition function and be mapped to the reciprocal transformation function at reference mark, source from the target control point, and the displacement function of the forward of computed image and reciprocal transformation function;

The reorientation unit is used for the displacement function of forward and reciprocal transformation function is carried out reorientation, the displacement function of the forward after being adjusted and reciprocal transformation function;

Adjustment unit, the forward after the adjustment that obtains according to the reorientation unit and the displacement function of reciprocal transformation function are adjusted the displacement function of the current forward of image and reciprocal transformation function for the first time;

Inverse function is found the solution the unit, is used for the inverse function of the current positive-going transition function of displacement function computed image of the current forward of the image that obtains according to adjustment unit and reciprocal transformation function and the inverse function of current reciprocal transformation function;

The mapping determining unit is used for finding the solution the inverse function of the current positive-going transition function of image that the unit obtains and the inverse function of current reciprocal transformation function is adjusted the displacement function of the current positive-going transition function of image and the displacement function of reciprocal transformation function for the second time according to inverse function; Then determine the interim mapping position at reference mark, source and the interim mapping position of target control point according to the displacement function of the current positive-going transition function of image after adjusting and the displacement function of reciprocal transformation function;

The estimation of error unit, for the displacement function of the current positive-going transition function of image that obtains according to the mapping determining unit and displacement function and the interim mapping position at reference mark, source and the interim mapping position of target control point of reciprocal transformation function, reference mark error and the conformity error of computed image conversion, if reference mark error and the conformity error of image conversion do not reach preset value, according to the interim mapping position at reference mark, source and the corresponding relation of target control point, and the corresponding relation at interim mapping position and reference mark, source is put in target control, with described forward, reciprocal transformation construction of function unit, the reorientation unit, adjustment unit, inverse function is found the solution the unit, the mapping determining unit repeats to cooperate and processes, until reference mark error and the conformity error of image conversion reach preset value.

7. system as claimed in claim 6 is characterized in that, described forward, reciprocal transformation construction of function unit calculate the displacement function of forward and reciprocal transformation function according to following formula:

The displacement function of positive-going transition function: u _t(x)=f ₁(x)-x;

The displacement function of reciprocal transformation function: w _t(x)=f ₂(x)-x;

Wherein, $f_1\left(x\right)=a_{11}+a_{1x}{x}_x+a_{1y}{x}_y+\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\ω}}_{1i}U\left(\right||r_i-x|\left|\right)$

$f_2\left(x\right)=a_{21}+a_{2x}{x}_x+a_{2y}{x}_y+\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\ω}}_{2i}U\left(\right||s_i-x|\left|\right)$

X is the point coordinate of two-dimensional space, r _iReference mark, source q _iInterim mapping position, s _iTarget control point p _iInterim mapping position,

The thin plate spline basis function, coefficient (a ₁₁, a _1x, a _1y, ω _1i) be equation P=L ₁* W ₁Solution,

$L_1={\left[\begin{array}{cc}{K}_1& R\\ R^T& 0\end{array}\right]}_{(n+3)\×(n+3)},$ $K_1={\left[\begin{array}{cccc}0& U\left(d_{12}\right)& ...& U\left(d_{1n}\right)\\ U\left(d_{21}\right)& 0& ...& U\left(d_{2n}\right)\\ ...& ...& ...& ...\\ U\left(d_{n1}\right)& U\left(d_{n2}\right)& ...& 0\end{array}\right]}_{n\×n},$ d _ij=||r _i-r _j||， $W={\left(\begin{array}{c}{\mathrm{\ω}}_{11}\\ ...\\ {\mathrm{\ω}}_{1n}\\ a_{11}\\ a_{1x}\\ a_{1y}\end{array}\right)}_{(n+3)\×3},$

$P={\left[\begin{array}{cc}1& p_1\\ 1& p_2\\ ...& ...\\ 1& p_n\end{array}\right]}_{n\×3},$ $R={\left[\begin{array}{cc}1& r_1\\ 1& r_2\\ ...& ...\\ 1& r_n\end{array}\right]}_{n\×3}$

L ₁Be (n+3) * (n+3) matrix, 0 is 3 * 3 null matrix; W ₁Be (n+3) * 3 matrixes, represent deformation function f ₁Coefficient vector on X and Y-direction, K ₁N * n matrix, according to r _iBetween distance calculate, P is target control point set, target control point p _i∈ P, R are reference mark, source q _iThe set of interim mapping position, d _IjR _iAnd r _jBetween Euclidean distance;

Coefficient (a ₂₁, a _2x, a _2y, ω _2i) be equation Q=L ₂* W ₂Solution,

$L_2={\left[\begin{array}{cc}{K}_2& S\\ S^T& 0\end{array}\right]}_{(n+3)\×(n+3)},$ $K_2={\left[\begin{array}{cccc}0& U\left(d_{12}\right)& ...& U\left(d_{1n}\right)\\ U\left(d_{21}\right)& 0& ...& U\left(d_{2n}\right)\\ ...& ...& ...& ...\\ U\left(d_{n1}\right)& U\left(d_{n2}\right)& ...& 0\end{array}\right]}_{n\×n},$ d _ij=||s _i-s _j||， $W_2={\left(\begin{array}{c}{\mathrm{\ω}}_{21}\\ ...\\ {\mathrm{\ω}}_{2n}\\ a_{21}\\ a_{2x}\\ a_{2y}\end{array}\right)}_{(n+3)\×3},$

$Q={\left[\begin{array}{cc}1& q_1\\ 1& q_2\\ ...& ...\\ 1& q_n\end{array}\right]}_{n\×3},$ $S={\left[\begin{array}{cc}1& s_1\\ 1& s_2\\ ...& ...\\ 1& s_n\end{array}\right]}_{n\×3}$

L ₂Be (n+3) * (n+3) matrix, 0 is 3 * 3 null matrix; W ₂Be (n+3) * 3 matrixes, represent deformation function f ₂Coefficient vector on X and Y-direction, K ₂N * n matrix, according to s _iBetween distance calculate, Q is reference mark, source set, reference mark, source q _i∈ Q, S are target control point p _iThe set of interim mapping position, d _IjS _iAnd s _jBetween Euclidean distance.

8. system as claimed in claim 7 is characterized in that, described reorientation unit carries out reorientation, the displacement function of the forward after being adjusted and reciprocal transformation function according to following formula to the displacement function of forward and reciprocal transformation function:

u ^*(x)=u _t(u _k(x)+x)，u _t(x)=f ₁(x)-x

w ^*(x)=w _t(w _k(x)+x)，w _t(x)=f ₂(x)-x

Wherein, u _k(x) be the displacement function of the definite image positive-going transition function of last iteration, w _k(x) be the displacement function of the definite reciprocal transformation function of last iteration, u ^*(x) be the displacement function u of interim positive-going transition function _t(x) reorientation result, w ^*(x) be the displacement function w of interim reciprocal transformation function _t(x) reorientation result.

9. system as claimed in claim 8 is characterized in that, described adjustment unit is determined forward that image is current and the displacement function of reciprocal transformation function according to following formula:

The displacement function of the positive-going transition function that image is current: u _K+1(x)=u _k(x)+α u ^*(x)

The displacement function of the reciprocal transformation function that image is current: w _K+1(x)=w _k(x)+α w ^*(x).

Wherein α adjusts coefficient.

10. system as claimed in claim 6 is characterized in that, described mapping determining unit is determined the displacement function of the current positive-going transition function of image and the displacement function of reciprocal transformation function according to following formula:

The displacement function of the current positive-going transition function of image: u _K+1(x)=u _k(x)-β [u _k(x)-g ^-1(x)+x]

The displacement function of the current reciprocal transformation function of image: w _K+1(x)=w _k(x)-β [w _k(x)-h ^-1(x)+x]

Wherein, g ^-1(x) be the inverse function of image reversal transforming function transformation function, h ^-1(x) be the inverse function of image positive-going transition function, β is for adjusting coefficient; u _k(x) be the displacement function of the positive-going transition function that obtains of last iteration, w _k(x) be the displacement function of the reciprocal transformation function that obtains of last iteration, u _K+1(x) be the displacement function of the positive-going transition function that obtains of this iteration, w _K+1(x) be the displacement function of the reciprocal transformation function that obtains of this iteration;

Described mapping determining unit is also determined the interim mapping position at reference mark, source and the interim mapping position of target control point according to the displacement function of the current positive-going transition function of image and the displacement function of reciprocal transformation function:

Reference mark, source q _iInterim mapping position: r _i=q _i+ u _K+1(q _i)

Target control point p _iInterim mapping position: s _i=p _i+ w _K+1(p _i)

Wherein, q _iThe reference mark, source, p _iThe target control point, r _iReference mark, source q _iInterim mapping position, s _iTarget control point p _iInterim mapping position, u _K+1(x) be the displacement function of the positive-going transition function that obtains of this iteration, w _K+1(x) be the displacement function of the reciprocal transformation function that obtains of this iteration.

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