CN103886586A - Medical image registration method based on combination of mutual information and gradient information - Google Patents

Abstract

The invention provides a medical image registration method based on combination of mutual information and gradient information, comprising steps of performing weighting on mutual information similarity and adding difference values of a gradient model into gradient similarity, performing space changing on a floating image to be registered and calculating similarity measure of a reference image and the changed floating image. The invention provides a similarity measure function of weighting mutual information and gradient information. The similarity measure can attain a maximization value through constantly optimizing search and changing space, and the registration is successful. The similarity measure function is employed in the process of the registration, which can effectively solve the problems that the medical image registration algorism is low in accuracy and the robustness is not strong.

Description

A kind of medical image registration method based on mutual information and gradient information combination

Technical field

The present invention relates to a kind of medical image registration method based on mutual information and gradient information combination, relate in particular to a kind of medical image registration method based on weighting normalized mutual information and gradient information combination, belong to field of medical image processing.

Background technology

Along with the development of medical science, computer technology and biotechnology, Medical Imaging provides the medical image (CT, MRI, PET) of multiple modalities for clinical diagnosis, in practical clinical, conventionally need to be by the image co-registration of different modalities together, obtain abundanter information to understand the integrated information of pathological tissues or organ, diagnose accurately or work up suitable therapeutic scheme thereby make.And image registration is the important prerequisite of image co-registration, image registration starts from the nineties in 20th century, refer to piece image (floating image) is wherein carried out to spatial variations, make itself and the corresponding point position consistency of another piece image (reference picture), thereby can express exactly respective organization structure after both are merged.Therefore, efficient, high-quality registration process is an important component part of modern medical service image processing system.

In recent years, the method for registering based on mutual information (mutual information, MI) due to do not need image subject to registration other about priori, without manual intervention, and applicable multimodal medical image registration, therefore obtained extensive attention.But, the calculating of mutual information is subject to the impact of overlapping region size, thereby the registration leading to errors, Studholme etc. have proposed regularization mutual information (normalized mutual information NMI) as the tolerance of mutual information between two width images, have reduced the sensitivity to overlay region size in traditional mutual information calculating.Then thisly only utilized based on maximum normalized mutual information the information that corresponding point are right, still do not excavate and application image in inner link between pixel, thereby registration accuracy is not high.Pluim etc. are on the basis of statistical picture gray scale, introduce the space characteristics information of image, normalized mutual information and a kind of new mutual information measure function (GNMI) of gradient information combination structure are carried out to registering images, experiment shows that the method not only utilized the half-tone information of image, but also introduce the spatial information of image, suppress to a great extent the impact of local extremum, registration results than employing standard mutual information, normalized mutual information is more accurate, robustness is better, has shown the importance that mutual information between image is combined with image inner space information.The present invention further makes respectively improvement from mutual information and gradient two aspects on this basis, proposes a kind of new method for registering that mutual information and gradient similarity are combined.

Summary of the invention

Technical matters: the not high problem of precision that the present invention is directed to the medical science figure method for registering based on mutual information, a kind of similarity measure that weighting mutual information and gradient information are combined is proposed, the method effectively combines the spatial information of image on the basis based on mutual information, strengthen the robustness of registration, and improved the precision of registration.

Technical scheme: a kind of medical image registration method based on mutual information and gradient information combination of the present invention, comprises the steps:

1) image acquisition: directly obtain digital picture from the DICOM interface of CT, MRI or ultrasonic imaging device etc., this acquisition mode real-time is good, and efficiency is high is main a kind of medical image source;

2) carry out pre-service to collecting image subject to registration: as denoising, enhancing etc., must enter pretreated floating image A and reference picture B;

3) floating image is carried out to spatial alternation, transformation parameter: [Δ x, Δ y, Δ θ], translation pixel, Δ θ that pixel, the Δ y that wherein Δ x is illustrated in translation on x axle is illustrated on y axle represent the angle of rotation, thereby obtain floating image;

4) to step 3) floating image after the conversion that obtains carries out PV interpolation;

5) the similarity measure function of the floating image after computing reference image and conversion: the gradient information after the present invention adopts weighting mutual information and improves is combined as similarity measure;

6) judge whether similarity measure reaches optimum: adopt Optimizing Search algorithm to judge whether to reach optimum, if reached optimum, represent registration success, enter step 7), otherwise continue search, find best transformation parameter, make similarity measure reach as early as possible optimum;

7) output after the success of floating image registration.

The step 5 of the inventive method) in, calculate according to the following step the similarity measure GWNMI (gradient and weighted normalized mutual information) that the present invention proposes:

(1) calculate weighting mutual information similarity measure:

$I_u(A,B)=\underset{a_k=0}{\overset{K}{\mathrm{\Σ}}}\underset{b_j=0}{\overset{J}{\mathrm{\Σ}}}u(a_k,b_j)p(a_k,b_j)\log \frac{p(a_k,b_j)}{p\left(a_k\right)p\left(b_j\right)}$

Wherein a _k, b _jfor the gray-scale value of difference presentation video A, B.(ak, bj) presentation video A, the locational gray scale of B the same space, be called gray scale pair.P (a _k, b _j) _{k=0～K, j=0～J}for the associating gray probability of image A, B distributes, represent that the gray scale of two width image same positions is to (a _k, b _j) probability, u (a _k, b _j)=e ^-D,

U ∈ (0,1], D is distance, D >=1.

(2) calculate weighting normalized mutual information similarity measure:

${\hat{I}}_u(A,B)=\frac{I_u(A,B)}{\min (H\left(A\right),H\left(B\right))}$

The wherein entropy of H (A) presentation video A, the entropy of H (B) presentation video B.Scope is:

(3) the gradient similarity measure T of computed improved _Δ(A, B):

$\begin{array}{c}{T}_{\mathrm{\Λ}}(A,B)\underset{(x,y)\∈(A\∩B)}{\mathrm{\Σ}}w(x,y)g_{\mathrm{\Δ}}(x,y)\\ =\underset{(x,y)\∈(A\∩B)}{\mathrm{\Σ}}\frac{\cos (2\∂(x,y))+1}{2}{g}_{\mathrm{\Λ}}(x,y)\end{array}$

$=\begin{array}{cc}\underset{(x,y)\∈(A\∩B)}{\mathrm{\Σ}}\frac{\cos (2\∂(x,y))+1}{2}\frac{g(x,y)}{\max \left(\right|\▿A|,|\▿B\left|\right)-\min \left(\right|\▿A|,|\▿B\left|\right)}& \max \left(\right|\▿A|,|\▿B\left|\right)\≠\min \left(\right|\▿A|,|\▿B\left|\right)\\ \underset{(x,y)\∈(A\∩B)}{\mathrm{\Σ}}\frac{\cos (2\∂(x,y))+1}{2}& \max \left(\right|\▿A|,|\▿B\left|\right)=\min \left(\right|\▿A|,|\▿B\left|\right)\end{array}$

Wherein w (x, y) represents the similarity measure of gradient direction, and its size is

(x, y) presentation video A, B locate the angle of gradient, g at point (x, y) _Δ(x, y) represents the gradient-norm similarity measure that the present invention proposes, and it is that the difference of gradient-norm is fused to g (x, y) in traditional gradient-norm similarity measure, g _Δthe formula of (x, y) is:

$g_{\mathrm{\Δ}}(x,y)=\begin{array}{cc}\frac{g(x,y)}{\max \left(\right|\▿A|,|\▿B\left|\right)-\min \left(\right|\▿A|,|\▿B\left|\right)}& \max \left(\right|\▿A|,|\▿B\left|\right)\≠\min \left(\right|\▿A|,|\▿B\left|\right)\\ 1& \max \left(\right|\▿A|,|\▿B\left|\right)=\min \left(\right|\▿A|,|\▿B\left|\right)\end{array}$

Wherein, g (x, y) size is:

$g(x,y)=\begin{array}{cc}\frac{\min \left(|\▿A(x,y)\right|,|\▿B(x,y)|)}{\max \left(\right|\▿A(x,y)|,|\▿B(x,y)\left|\right)}& \max \left(\right|\▿A(x,y)|,|\▿B(x,y)\left|\right)\\ 1& \max \left(\right|\▿A(x,y)|,|\▿B(x,y)\left|\right)\end{array}$

(4) calculate the similarity measure GWNMI that weighting normalized mutual information and improved gradient information combine:

$\mathrm{GWNMI}(A,B)={\hat{I}}_u(A,B)T_{\mathrm{\Δ}}(A,B)$

Its scope is: GWNMI (A, B) ∈ (0,1].

Beneficial effect: the present invention compared with prior art, has the following advantages:

A) because the imaging parameters of human normal tissue is (as CT value, T1, T2 value etc.) relatively fixing, so isostructural gradation of image value has corresponding relation, can think that when the gray scale that is made up of the gray scale of two image the same space positions is to coupling, registration accuracy is the highest.Therefore, the present invention proposes weighting factor, for this gray scale pair being made up of the gray scale of corresponding relation, by their mutual information being increased the weight of to power, increase the mutual information I (A, B) of image A, B, make it larger to the contribution of registration degree, thereby improve registration accuracy.Can, by the right mutual information of the gray scale being made up of not corresponding gray scale is added to light power, reduce registration error simultaneously;

B) difference of considering the gradient-norm of two image the same space positions has reflected the fierce degree of grey scale change, therefore herein this information added in gradient similarity measure, and then in conjunction with mutual information similarity measure, thus the similarity of more effective description two width figure.

Brief description of the drawings

Fig. 1 is the frame diagram of medical figure registration.

Fig. 2 is the particular flow sheet of the registration based on GWNMI of the present invention.

Embodiment

Below in conjunction with accompanying drawing and embodiment, the present invention is described in further detail.

Fig. 1 is the frame diagram of medical figure registration.First carry out image acquisition, design two equipment: imaging device and collecting device, medical imaging devices has CT, MRI, B ultrasonic etc.; Next carries out image pre-service, has image denoising, figure image intensifying two parts; Then pretreated image is carried out to registration, adopt the method for registering based on weighting normalized mutual information and improved gradient information combination, registration is successfully exportable.The present invention makes corresponding improvement for the similarity measure of registration.

Fig. 2 is the particular flow sheet of the medical figure registration based on GWNMI.After pre-service, floating image is carried out to spatial alternation, afterwards to its PV interpolation, calculating its GWNMI with reference picture, judge whether to reach optimum, if reach optimum, think registration success, just can output image, otherwise employing Powell optimized algorithm, continue search, find optimal spatial conversion.What the present invention considered is the design of similarity measure, wherein, compared with traditional Medical Image Registration, improves and comprises 2 points: the one, and weighting normalized mutual information similarity measure; The 2nd, improved gradient similarity measure.

One: weighting normalized mutual information similarity measure:

The mutual information I (A, B) of image A, B is exactly the mathematical expectation of the even single mutual information of gray scale order.And from formula, the mutual information I (a of each gray scale order idol _k, b _j) to image A, the contribution of the mutual information I (A, B) of B only depends on that associating gray probability distributes, irrelevant with spatial positional information.But for two good width images of two width registration, their gray scale has corresponding relation.

Because the imaging parameters (as CT value, T1, T2 value etc.) of human normal tissue is relatively fixing, so isostructural gray-scale value has corresponding relation, can think the corresponding even registration of gray scale order of two gray scales time, be that registration accuracy is the highest.Therefore, even for this gray scale order being formed by the gray scale of corresponding relation, by increasing the weight of their mutual information, increase the mutual information I (A, B) of image A, B, make it larger to the contribution of registration degree, thereby improve registration accuracy.Can, by alleviating the mutual information of the gray scale order idol being formed by not corresponding gray scale, reduce registration error simultaneously.

The present invention is standard registration set R by the set expression of the gray scale order idol by being made up of the gray scale of corresponding relation, the set of gray scale order idol when this set is standard registration.Describe the registration degree of correlation of gray scale order couple image registration with registration factor u, can use the weighting coefficient of u as the even mutual information of single gray scale order.Gray scale order in set R is even, and gray scale is corresponding, and therefore registration degree is high, desirable its registration factor u=1.The gray scale order in set R is not even, determines according to its minimum distance from standard registration set R, and the size of u is 0 < u≤1.

Definition 1: establish the even p (a of gray scale order _k, b _j) not in set R, be D from the distance of gathering nearest gray scale order idol in R, the registration factor: u (a _k, b _j)=e ^-D

Wherein D is distance, and D >=1 has ensured 0 < u≤1, and distance is far away, and the registration factor is less, and distance is 0, is illustrated in set R, and the registration factor is 1.

For isostructural multiple images of patient, because the imaging parameters of human normal tissue is relatively fixing, two gray-scale values that can be similar to each element of thinking in the set of standard registration equate.Be R={ (a _k, b _j), a _k=b _j.As piece image and self registration, its joint histogram is a principal diagonal, illustrates that its identical gray scale is one-to-one relationship, and the gray scale order in set R is even all on this straight line, their u=1, the gray scale order on this straight line is even, they from this straight line more away from, illustrate that registration degree is lower, therefore the mutual information of their combinations is less, therefore, can adopt the function of distance to describe u, the even p (a of gray scale order _k, b _j) be D=|a from the distance of this straight line _k-b _j|/√ 2, therefore registration factor u=e ^-D.Work as a _k=b _jtime, this gray scale order is even in set R, u=1.

In traditional mutual information, the registration degree of each gray scale order idol is the same, this does not meet the fact, because isostructural two width figure, their gray-scale value has corresponding relation, therefore, if there are two gray scale combination gray scale orders of corresponding relation even, this gray scale order couple registration degree contribution is large, therefore can be by being weighted, increase its mutual information, make it large to the contribution of registration degree.In theory, the registration factor has been described the matching degree of gray scale order idol, and different registration Factors Weighting for the mutual information of different gray scale order idols more can be described registration accuracy.The correlativity that more can describe two width images by the registration factor as the mutual information of weighting coefficient, therefore registration process is estimated weighting mutual information exactly as registration, constantly finds optimal mapping, its registration is estimated and reached maximum.

The mutual information I of weighting _u(A, B):

$I_u(A,B)=\underset{a_k=0}{\overset{K}{\mathrm{\&Sigma;}}}\underset{b_j=0}{\overset{J}{\mathrm{\&Sigma;}}}u(a_k,b_j)p(a_k,b_j)\log \frac{p(a_k,b_j)}{p\left(a_k\right)p\left(b_j\right)}$

Mutual information is normalized, avoids being subject to the impact of overlapping region size variation and number of greyscale levels.

${\hat{I}}_u(A,B)=\frac{I_u(A,B)}{\min (H\left(A\right),H\left(B\right))}$

Span:

size is irrelevant with overlapping region size variation and number of greyscale levels.

Two: improved gradient similarity measure:

What gradient was described is the variation of gray scale, and gradient direction has been described change direction, and gradient-norm has been described and changed size.Therefore gradient direction and gradient-norm can be described the similarity of two width images, are respectively gradient direction similarity measure and gradient-norm similarity measure.Traditional gradient-norm similarity measure g (x, y) and gradient direction similarity measure w (x, y) formula are as follows respectively:

$g(x,y)=\begin{array}{cc}\frac{\min \left(|\&dtri;A(x,y)\right|,|\&dtri;B(x,y)|)}{\max \left(\right|\&dtri;A(x,y)|,|\&dtri;B(x,y)\left|\right)}& \max \left(\right|\&dtri;A(x,y)|,|\&dtri;B(x,y)\left|\right)\&NotEqual;0\\ 1& \max \left(\right|\&dtri;A(x,y)|,|\&dtri;B(x,y)\left|\right)=0\end{array}$

$w(x,y)=\frac{\cos (2\&PartialD;(x,y))+1}{2}$

Wherein (x, y) represents the gradient angle of two width images on point (x, y).| ▽ A (x, y) |, | ▽ B (x, y) | the gradient-norm of presentation graphs A, B respectively.

But represent that with the ratio of gradient-norm gradient-norm estimates the similarity that can not well describe two width figure.For example, image A and image B are at point (x ₁, y ₁) gradient be respectively 1 and 10; At point (x ₂, y ₂) gradient be respectively 10 and 100; According to gradient-norm similarity function defined above, known they be all 0.1, represent that their similarity equates, but at (x ₁, y ₁) on point, gradient 1 and 10 differs 9 gray levels, at (x ₂, y ₂) gradient 10 and 100 differs 90 gray levels on point, and each gray level expressing gray scale difference is the same, thus key diagram A with figure B at (x ₂, y ₂) on some grey scale change than at (x ₁, y ₁) grey scale change is fiercer on point, also with regard to key diagram A with figure B at (x ₁, y ₁) put ratio at (x ₂, y ₂) point more similar.Therefore herein gradient-norm similarity function is improved, consider the poor of gradient-norm, embody the fierce degree of grey scale change, thereby more can describe the similarity of two width figure, the formula of the gradient-norm similarity measure that the present invention proposes is as follows:

$g_{\mathrm{\&Delta;}}(x,y)=\begin{array}{cc}\frac{g(x,y)}{\max \left(\right|\&dtri;A|,|\&dtri;B\left|\right)-\min \left(\right|\&dtri;A|,|\&dtri;B\left|\right)}& \max \left(\right|\&dtri;A|,|\&dtri;B\left|\right)\&NotEqual;\min \left(\right|\&dtri;A|,|\&dtri;B\left|\right)\\ 1& \max \left(\right|\&dtri;A|,|\&dtri;B\left|\right)=\min \left(\right|\&dtri;A|,|\&dtri;B\left|\right)\end{array}$

The gradient-norm similarity measure that the present invention is proposed and gradient direction similarity measure combine and obtain gradient similarity measure T Δ (A, B), and its formula is as follows:

$T_{\mathrm{\&Delta;}}(A,B)=\underset{(x,y)\&Element;(A\&cap;B)}{\mathrm{\&Sigma;}}w(x,y)g_{\mathrm{\&Delta;}}(x,y)$

Finally the gradient information by weighting normalized mutual information and after improving is in conjunction with forming similarity measure GWNMI of the present invention (A, B), and its formula is as follows:

$\mathrm{GWNMI}(A,B)={\hat{I}}_u(A,B)T_{\mathrm{\&Delta;}}(A,B)$

Its scope is: GWNMI (A, B) ∈ (0,1].

Registration process of the present invention is the similarity measure using GWNMI as registration Algorithm, by continuous search, the send as an envoy to registration parameter of GWNMI maximum of calculating, thereby hit pay dirk registration, the present invention combines the advantage of gradient information and mutual information, and gradient information is the edge feature between different tissues in identification image effectively.And mutual information is a kind of statistic correlation, reflect the same right overlapping situation of pixel forming in two width images that is organized in.Therefore, mutual information is combined and estimated as registration with gradient information, will make registration Algorithm robust more.

Main improvement step is: in the medical image registration method based on mutual information, to being weighted, adopt weighting normalized mutual information as similarity measure to gray scale; The difference of gradient-norm is fused in gradient similarity measure simultaneously, finally weighting normalized mutual information and improved gradient information is combined as the similarity measure of the present invention's proposition.The method not only can improve precision, can also add strong robustness, has effectively solved the low precision problem of the medical image registration method based on mutual information.

Claims (2)

1. the medical image registration method based on mutual information and gradient information combination, is characterized in that comprising following steps:

1) image acquisition: directly obtain digital picture from the DICOM interface of CT, MRI or ultrasonic imaging device etc.;

2) carry out pre-service to collecting image subject to registration: as denoising, enhancing etc., must enter pretreated reference picture A and floating image;

3) floating image is carried out to spatial alternation, transformation parameter: [Δ x, Δ y, Δ θ], translation pixel, Δ θ that pixel, the Δ y that wherein Δ x is illustrated in translation on x axle is illustrated on y axle represent the angle of rotation, thereby obtain floating image B;

4) to step 3) floating image after the conversion that obtains carries out PV interpolation;

5) the similarity measure function of the floating image after computing reference image and conversion: the gradient information after adopting weighting mutual information and improving is combined as similarity measure;

6) judge whether similarity measure reaches optimum: adopt Optimizing Search algorithm to judge whether to reach optimum, if reached optimum, represent registration success, enter step 7), otherwise continue search, find best transformation parameter, make similarity measure reach as early as possible optimum;

7) output after the success of floating image registration.

2. a kind of medical image registration method based on mutual information and gradient information combination according to claim 1, it is characterized in that step 5) in, gradient information after described weighting mutual information and improvement is combined as similarity measure, be the similarity measure GWNMI that weighting normalized mutual information and improved gradient information combine:

$\begin{array}{c}\mathrm{GWNMI}(A,B)=\widehat{I_u(A,B)T_{\mathrm{\&Delta;}}(A,B)}\\ =\frac{I_u(A,B)}{\min (H\left(A\right),H\left(B\right))}\&times;\underset{(x,y)\&Element;(A\&cap;B)}{\mathrm{\&Sigma;}}w(x,y)g_{\mathrm{\&Delta;}}(x,y)\end{array}$

Its scope is: GWNMI (A, B) ∈ (0,1];

the normalized mutual information of the weighting of the floating image B for reference picture A and after converting:

${\hat{I}}_u(A,B)=\frac{I_u(A,B)}{\min (H\left(A\right),H\left(B\right))}=\frac{\underset{a_k=0}{\overset{K}{\mathrm{\&Sigma;}}}\underset{b_j=0}{\overset{J}{\mathrm{\&Sigma;}}}u(a_k,b_j)p(a_k,b_j)\log \frac{p(a_k,b_j)}{p\left(a_k\right)p\left(b_j\right)}}{\min (H\left(A\right),H\left(B\right))}$

Wherein p (a _k, b _j) _{k=0～K, j=0～J}for the associating gray probability of image A, B distributes, represent that the gray scale of two width image same positions is to (a _k, b _j) probability, the entropy of H (A) presentation video A, the entropy of H (B) presentation video B; U (a _k, b _j) be weighting factor, its size is: u (a _k, b _j)=e ^-D, wherein a _k, b _jfor the gray-scale value of difference presentation video A, B; (a _k, b _j) presentation video A, the locational gray scale of B the same space, be called gray scale pair; D is distance, D >=1;

T _Δ(A, B) is the gradient similarity measure of the floating image B after computing reference image A and conversion:

$T_{\mathrm{\&Delta;}}(A,B)=\underset{(x,y)\&Element;(A\&cap;B)}{\mathrm{\&Sigma;}}w(x,y)g_{\mathrm{\&Delta;}}(x,y)$

Wherein w (x, y) represents the similarity measure of gradient direction, and its size is

(x, y) presentation video A, B locate the angle of gradient, g at point (x, y) _Δ(x, y) represents the gradient-norm similarity measure that the present invention proposes, and it is that the difference of gradient-norm is fused to g (x, y) in traditional gradient-norm similarity measure, g _Δthe formula of (x, y) is:

$g_{\mathrm{\&Delta;}}(x,y)=\begin{array}{cc}\frac{g(x,y)}{\max \left(\right|\&dtri;A|,|\&dtri;B\left|\right)-\min \left(\right|\&dtri;A|,|\&dtri;B\left|\right)}& \max \left(\right|\&dtri;A|,|\&dtri;B\left|\right)\&NotEqual;\min \left(\right|\&dtri;A|,|\&dtri;B\left|\right)\\ 1& \max \left(\right|\&dtri;A|,|\&dtri;B\left|\right)=\min \left(\right|\&dtri;A|,|\&dtri;B\left|\right)\end{array}$

Wherein, g (x, y) size is:

$g(x,y)=\begin{array}{cc}\frac{\min \left(|\&dtri;A(x,y)\right|,|\&dtri;B(x,y)|)}{\max \left(\right|\&dtri;A(x,y)|,|\&dtri;B(x,y)\left|\right)}& \max \left(\right|\&dtri;A(x,y)|,|\&dtri;B(x,y)\left|\right)\\ 1& \max \left(\right|\&dtri;A(x,y)|,|\&dtri;B(x,y)\left|\right)\end{array},.$

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