CN101493936A - Multi- resolution non-rigid head medicine image registration method based on image edge - Google Patents

Abstract

The invention relates to a multi-resolution non-rigid head medical image registration method on the basis of image edges, which pertains to the field of information fusion. The method utilizes searches gradually becoming accurate to transform parameters during the registration process. At first, wavelet transformation is used for detecting the edge of an image; a edge pyramid image is formed on the basis of an edge image; then relatively wide search is carried out in the lowest scale level (the roughest level) of the edge pyramid image; the best transformation for registering the two images is found; each subsequent level takes the search result of the former level as a center; and search scope is reduced to continually search until the search in the highest scale level is carried out. Compared with the registration directly using the original image, the method can reduce calculated amount, improve accuracy and can register images of different spatial resolution.

Description

A kind of multi-resolution non-rigid head medicine method for registering images based on the image border

Technical field

The present invention relates to a kind of head medicine method for registering images based on wavelet transformation, is resolution image method for registering more than in the information fusion field, all can be widely used in systems such as Telemedicine System, Medical Image Processing.

Background technology

Image registration is a very important technology in the graphical analysis, main by seeking certain conversion, make the corresponding point of two width of cloth images reach the unanimity of locus, in medical diagnostic procedures, owing to there is different mode image appearance physical mechanism of different nature, the patient puts the difference of position, the variation of imaging parameters, the not equal realistic problem of spatial resolution between different imaging devices, be subjected to a lot of limitations so only rely on the doctor manually the image of two or two groups different modes spatially to be done to aim at, and often have bigger subjectivity, its reliability is often not high, can produce error inevitably.Particularly, very high to the accuracy requirement of image registration in applications such as directional emittance surgery and operations on cranium and brain are visual, make medical figure registration become the necessity and the suitable task of difficulty.

The basic process of image registration techniques mainly is divided into three steps:

1. seek the character pair amount in the image and extract;

2. seek the optimum matching conversion according to characteristic quantity;

3. utilize the optimal mapping obtain to treat that registering images carries out conversion and reference picture mates.Wherein first two steps are keys of registration process, also are the core contents of registration Algorithm research.

Summary of the invention

The object of the present invention is to provide a kind of registration Algorithm that is suitable for the gray level image characteristics, strengthen the specific aim of registration Algorithm, the picture quality with behind the raising registration reaches desirable practical function.

In registration process, utilize by thick to smart search transformation parameter.At first by wavelet transformation detected image edge, structure edge pyramid diagram picture on the edge image basis, smallest dimension layer (promptly rough layer) at edge pyramid diagram picture carries out search in a big way then, seek the optimal mapping of registration two width of cloth images, the Search Results of one deck is the center before each layer later on, dwindle the hunting zone and continue search, up to the out to out layer.This method with directly carry out registration and compare with original image, can reduce calculated amount, improve accuracy and image that can the registration different spatial resolutions.During the both full-pixel layering and matching, the corresponding more than problem of same place often occurs, be difficult to realize the coupling of global point.This method adopts the edge image pyramid based on wavelet decomposition, has utilized mutual information as the similarity measurement criterion, and layering realizes the registration of entire image.

Pre-service and the registration rule of the innovative point of technical solution of the present invention before image co-registration, for realizing such purpose, technical scheme of the present invention is: the outline map registration Algorithm based on wavelet decomposition is characterized in that:

(1) use wavelet decomposition to carry out the edge image pyramid construction, wavelet decomposition is a kind of non-loss transformation, and its DC component is smooth, and each layer all is made up of a DC component and three characteristic components, can utilize characteristic component to carry out characteristic matching.

(2) data on every layer of the image are the same with original image size after the pre-service, and can rebuild, so can discharge original image in internal memory, like this, needed memory size does not increase after the pyramid layering.Compare with method for registering based on mutual information, it is more accurate to mate, the division of each of entire image layer low resolution, because pixel is still more relatively, the situation that occurs the more than position of matching result possibility easily, and the edge image pyramid can well address this problem, and reduces matching error and improves registration accuracy.

A kind of multi-resolution non-rigid head medicine method for registering images based on the image border provided by the invention is characterized in that, may further comprise the steps:

1) Edge extraction

If two dimensional image signal f (x, the y) pixel value of presentation video,

If η (x y) is two-dimentional smooth function and satisfied:

$\∫\∫\mathrm{\η}(x,y)\mathrm{dxdy}=1---\left(1\right)$

$\underset{x,y\→\∞}{\lim }\mathrm{\η}(x,y)=0---\left(2\right)$

To smooth function η (x y) asks the partial derivative of x direction and y direction respectively, then has:

${\mathrm{\μ}}^1(x,y)=\frac{\∂\mathrm{\η}(x,y)}{\∂x};$ ${\mathrm{\μ}}^2(x,y)=\frac{\∂\mathrm{\η}(x,y)}{\∂y}$ μ wherein ¹(x, y) and μ ²(x y) regards the 2-d wavelet function as.

Then (x, y) Dui Ying wavelet transformation is f: W ^xF (x, y)=f (x, y) * μ ¹

W ^yf(x，y)＝f(x，y)*μ ²

Image is carried out smoothly, the image g after level and smooth (x y) is:

g(x，y)＝η(x，y)*f(x，y) (3)

Image after level and smooth is asked the single order differential:

$\frac{\∂g(x,y)}{\∂x}=\frac{\∂}{\∂x}[\mathrm{\η}(x,y)*f(x,y)]$

$=\frac{\∂g(x,y)}{\∂x}*f(x,y)---\left(4\right)$

$\frac{\∂g(x,y)}{\∂y}=\frac{\∂}{\∂y}[\mathrm{\η}(x,y)*f(x,y)]$

$=\frac{\∂g(x,y)}{\∂y}*f(x,y)---\left(5\right)$

The right-hand member of formula (4) and (5) be actually function f (x, two wavelet transformations y), promptly

$\frac{\∂g(x,y)}{\∂x}=W^{x}f(x,y)=f(x,y)*{\mathrm{\μ}}^1(x,y)---\left(6\right)$

$\frac{\∂g(x,y)}{\∂y}=W^{y}f(x,y)=f(x,y)*{\mathrm{\μ}}^2(x,y)---\left(7\right)$

The marginal point of the modulus maximum correspondence image of first order derivative, these two first order derivatives equal f (x, two wavelet transformations y), the maximum value of the mould of these two wavelet transformations is just corresponding edge of image point, thereby

By said method, obtain edge image I (x, y) and I ' (x y), carries out image registration, and wherein (x y) is the edge image of reference picture correspondence to I, and (x y) is the edge image of image correspondence subject to registration to I ';

2). image registration

2.1) with above-mentioned to edge image I (x, y) and I ' (x y) is transformed to the edge pyramid image I of each layers of resolution _k(x, y) and I ' _k(x, y),

Process is as follows: by with the original edge image I (x, y) and I ' (x, y) adjacent 2 * 2 pixel arithmetic means are a pixel structure first order edge pyramid image I ₁(x, y) and I ' ₁(x, y), then in first order edge pyramid image I ₁(x, y) and I ' ₁(x constructs second level image I as stated above on basis y) ₂(x, y) and I ' ₂(x, y), the rest may be inferred constitutes required layer edge pyramid image I _k(x, y) and I ' _k(x, y);

2.2) resolving into from low to high each of resolution layer edge pyramid subgraph image set I _k(x, y) and I ' _k(x, y) after, by the layers of resolution I of low one-level _k(x, y) and I ' _k(x, Search Results y) is as higher leveled layers of resolution I _K-1(x, y) and I ' _K-1(x, initial value y), and the like realize the registration of original image;

Search at k layer direction of passage accelerated process, step-size in search be set, the low-frequency edge image of reference picture and image subject to registration is carried out the registration computing, must with I _k(x y) goes up some P _K(x is y) at I ' _k(x, y) the best corresponding point P ' on _k(x y), determines the transformation parameter between image, and the rough position of one deck search under the conduct;

Wherein k is the k layer of edge pyramid picture breakdown, P _K(x y) is image I _k(x, the y) pixel on, x, y are its horizontal ordinate, P ' _k(x, y) be image I ' _k(x, y) pixel on;

2.3) in k-1 layer registration with k layer P ' as a result _k(x is y) as initial position, at P ' _k(x carries out the registration search in neighborhood y), seek P ' in image subject to registration _K-1(x y) makes it and reference picture mid point P _K-1(x, y) correspondence, thus obtain the best corresponding point P ' of this layer _K-1(x, y);

2.4) make k=k-1, repeat step 2.3) registration search;

2.5) dwindle step-size in search, repeating step 2.3) and step 2.4, realize successively searching for up to k=0, realize on the promptly top layer of k=0 P on the original image that obtains ₀(x is y) with its best corresponding point P ' ₀(x, y), the final Search Results that is is finished registration process.

Image interfusion method of the present invention has following beneficial effect:

(1) algorithm of the present invention and general comparing based on the rim detection method for registering, reduced searching position, thereby improved registration speed greatly, image for width of cloth n * n pixel, when adopting both full-pixel edge registration Algorithm, searching for the time that needs in theory is that O (n) is inferior, and algorithm is O (log n) inferior (0 (x) is with the value monotone variation of x) among the present invention, the deduction pre-service makes up the time that edge pyramid diagram picture is spent, and still reduces a lot of times.

(2) algorithm of the present invention with based on both full-pixel pyramid method for registering relatively, registration is more accurate, when both full-pixel pyramid registration makes up each tomographic image, because pixel is still more relatively in the entire image, the situation that the more than position of pixel of the same name often occurs cause endless loop easily, and algorithm can well address this problem among the present invention, reduce registration error, improved registration accuracy.

(3) the present invention uses wavelet decomposition to carry out the pyramidal structure in image border, wavelet transformation is a kind of non-loss transformation, and its DC component is smooth, pyramidal each layer in image border all is made up of a DC component and three characteristic components, can utilize characteristic component to carry out characteristic matching.Data on every layer of the image pyramid are the same with original image size, and can rebuild, so can discharge original image in internal memory, the needed memory size in the image layered back of edge pyramid does not increase like this, wavelet transformation has fast algorithm simultaneously, and the little speed of registration calculated amount is fast.

Description of drawings

Fig. 1 embodiment of the invention sub-process figure.

Fig. 2 picture structure pyramid.What show among the figure is the secondary pyramid decomposition synoptic diagram that original image is carried out.

Fig. 3 image registration algorithm process flow diagram.

Fig. 4 image registration design sketch.Fig. 4 .1 is the CT1109 reference picture, and Fig. 4 .2 is PD1110 figure subject to registration, and Fig. 4 .1 and Fig. 4 .2 all are the standard pictures in the Visual Human image library.Fig. 4 .3 utilizes image behind the registration of the present invention with Fig. 4 .1 and Fig. 4 .2.

Fig. 5 is vector " conjugated degree " synoptic diagram.

Embodiment

The research of the edge feature of various structures is most important for pattern-recognition in the image.The edge is the most basic feature of image, and the main information major part of image all is present in the edge of image, and this distinguishes that with the profile that people draw from a width of cloth object is similar.Rim detection plays an important role in application such as computer vision, graphical analysis, is the important step of graphical analysis and identification.This is because edge of image has comprised the useful information that is used to discern, and it provides important characteristic parameter for people's description or recognition objective and interpretation of images.Therefore, our rim detection is the principal character extraction means of graphical analysis and pattern-recognition.

1. Edge extraction

Wavelet transformation is the strong instrument that detects jump signal, can portray the signal of various different frequency components, rim detection based on wavelet transformation is carried out wavelet transformation with original image exactly, it is decomposed at different frequency range, after finding out the maximum value of HFS mould, obtain the image border thereby screen.

Use a smooth function η (x exactly based on the rim detection of wavelet transformation, y), the level and smooth signal that detects under different yardsticks, according to once or second differential find out its catastrophe point (zero cross point of the maximum point of a subdifferential and corresponding second differential and the flex point of level and smooth back signal), wherein selected wavelet function $\mathrm{\μ}\left(t\right)=\frac{\mathrm{d\η}\left(t\right)}{\mathrm{dt}},$ Carry out rim detection according to the wavelet conversion coefficient extreme value.

If two dimensional image signal f (x, y), g (x, y), wherein f (x, y), g (x, the y) pixel value of presentation video respectively,

If η (x y) is two-dimentional smooth function and satisfied:

$\∫\∫\mathrm{\η}(x,y)\mathrm{dxdy}=1---\left(1\right)$

$\underset{x,y\→\∞}{\lim }\mathrm{\η}(x,y)=0---\left(2\right)$

To smooth function η (x y) asks the partial derivative of x direction and y direction respectively, then has:

${\mathrm{\μ}}^1(x,y)=\frac{\∂\mathrm{\η}(x,y)}{\∂x};$ ${\mathrm{\μ}}^2(x,y)=\frac{\∂\mathrm{\η}(x,y)}{\∂v}$ μ wherein ¹(x, y) and μ ²(x y) can regard the 2-d wavelet function as.

Corresponding wavelet transformation is: W ^xF (x, y)=f (x, y) * μ ¹

W ^yf(x，y)＝f(x，y)*μ ²

Image is carried out smoothly, and smoothly the image after is:

g(x，y)＝η(x，y)*f(x，y) (3)

Image after level and smooth is asked the single order differential:

$\frac{\∂g(x,y)}{\∂x}=\frac{\∂}{\∂x}[\mathrm{\η}(x,y)*f(x,y)]$

$=\frac{\∂g(x,y)}{\∂x}*f(x,y)---\left(4\right)$

$\frac{\∂g(x,y)}{\∂y}=\frac{\∂}{\∂y}[\mathrm{\η}(x,y)*f(x,y)]$

$=\frac{\∂g(x,y)}{\∂y}*f(x,y)---\left(5\right)$

The right-hand member of formula (4) and (5) be actually function f (x, two wavelet transformations y), promptly

$\frac{\∂g(x,y)}{\∂x}=W^{x}f(x,y)=f(x,y)*{\mathrm{\μ}}^1(x,y)---\left(6\right)$

$\frac{\∂g(x,y)}{\∂y}=W^{y}f(x,y)=f(x,y)*{\mathrm{\μ}}^2(x,y)---\left(7\right)$

The marginal point of the modulus maximum correspondence image of first order derivative, these two first order derivatives equal f (x, two wavelet transformations y), so the maximum value of the mould of these two wavelet transformations just corresponding the edge of image point.

By said method, obtain edge image I (x, y) and I ' (x y), carries out image registration.((x y) is the edge image of reference picture correspondence to I, I ' (x y) is the edge image of image correspondence subject to registration)

2. image registration

Multiresolution resolution based on orthogonal wavelet transformation all is decomposed into new low frequency smoothed image and high frequency detail pictures with each tomographic image in the pyramid diagram picture, its medium and low frequency smoothed image has been concentrated most of energy of original image, the most information that reflected image are so we can use low-frequency image in the different layers pyramid diagram picture to carry out the layering registration of image.

Algorithm need have certain precision in image registration, so it is strict corresponding that reference picture and image characteristic point subject to registration are wanted, promptly to find characteristic of correspondence point (same place) on reference picture and the image subject to registration, existing algorithm is many to be handled by each point to the region of search, seek same place, and in overall work and except to the effective same place of registration, can be regarded as " inaction " work to the work of other all pixels, not only wasted the time but also influenced precision.So the algorithm in invention adopts accelerating algorithm, utilizes hierarchical search strategy head it off.

The used algorithm of the present invention roughly is divided into following two steps:

(1) reference picture and image subject to registration are carried out wavelet transformation, obtain edge image I (x, y) and I ' (x y), is transformed to edge image the edge pyramid image I of each layers of resolution _k(x, y) and I ' _k(x, y), process is summarized as follows: by with the original edge image I (x, y) and I ' (x, y) a pixel structure of adjacent " 2 * 2 " individual pixel average out to first order edge pyramid image I ₁(x, y) and I ' ₁(x, y), then in first order edge pyramid image I ₁(x, y) and I ' ₁(x constructs second level image I as stated above on basis y) ₂(x, y) and I ' ₂(x, y), the rest may be inferred constitutes required layer edge pyramid image I _k(x, y) and I ' _k(x, y).(wherein pixel average out to arithmetic mean)

(2) resolving into from low to high each of resolution layer edge pyramid subgraph image set I _k(x, y) and I ' _k(x, y) after, utilize by thick and realize the registration of image subject to registration and reference picture, also promptly by the layers of resolution I that hangs down one-level to smart picture search scheme _k(x, y) and I ' _k(x, Search Results y) is as higher leveled layers of resolution I _K-1(x, y) and I ' _K-1(x, initial value y), and the like realize the registration of original image.The approximate location P ' of certain unique point in itself and the reference picture of search in the k layer edge image of image subject to registration at first _k(x, y), at definite P ' _k(x, y) after, again with P ' _k(x y) is the interior search of the neighborhood last layer corresponding point P ' at center _K-1(x, y), and the like realize the correspondence of unique point between original image.

With the explanation of the parts of images among Visible Human using method of the present invention.

Fig. 4 .1 is the CT1109 reference picture, and Fig. 4 .2 is PD1110 figure subject to registration, and Fig. 4 .3 is with the image behind the registration of the present invention.

Process of image registration can contrast Fig. 3, and concrete steps are:

(1) at first reference picture Fig. 4 .1 and image graph subject to registration 4.2 are carried out wavelet decomposition, decomposing the level degree of depth is the k layer, obtains the edge image on each layer, and sets up edge image pyramid (see figure 2).

The structure of image pyramid can utilize following step:

To an image of being made up of n * n pixel, we define uppermost the 0th layer (k=0 is an original image) and are top layer, and bottom one deck is a bottom, and the value of one deck pixel is obtained by the last layer calculated for pixel values under the pyramid diagram picture, and computing formula is as follows:

$I_{k+1}[\left(\frac{x+1}{2}\right),\left(\frac{y+1}{2}\right)]=\left[\frac{I_k(x,y)+I_k(x,y+1)+I_i(x+1,y)+I_k(x+1,y+1)}{4}\right]$

X wherein, y=1,2,3 ..., 2 ^I-1, [t] expression rounds t=0.5.I _k(x, y) coordinate is (x, gray values of pixel points y) in the expression K layer edge pyramid diagram picture.

(2) search for by improved direction accelerated process (Powell) at the k layer, step-size in search be set,, the low-frequency edge image of reference picture and image subject to registration is carried out the registration computing according to the similarity criterion of mutual information maximum, must with I _k(x y) goes up some P _K(x is y) at I ' _k(x, y) the best corresponding point P ' on _k(x y), determines the transformation parameter between image, and the rough position of one deck search under the conduct.(k is the K layer of edge pyramid picture breakdown, P _K(x y) is image I _k(x, the y) pixel on, x, y are its horizontal ordinate, P ' _k(x, y) be image I ' _k(x, y) pixel on).

The search procedure of basic Powell method is as follows:

1. suppose initial point P _K(x, y), inceptive direction set of vectors d ₁, d ₂..., d _n, error ε＞0.(the individual little positive number of ε) for being provided with

2. from P _K(x y) sets out, along d _n, search z _k

3. from z _kSet out, successively along d ₁, d ₂..., d _nSearch for X ₁ ^(k)X ₂ ^(k)..., X _n ^(k), wherein

${X_j}^{\left(k\right)}={X_{j-1}}^{\left(k\right)}-{\mathrm{\λ}}_j{d}_j(j=1,...,n,{X_0}^{\left(k\right)}=z_k)$

4. judge $\left|\right|X_n^{\left(k\right)}-P_k(x,y)\left|\right|\≤\mathrm{\ϵ}?$ If, $P_k^{\′}(x,y)\⇐X_n^{\left(k\right)},$ Stop search; Otherwise produce new direction $d=X_n^{\left(k\right)}-Z_k.$

5. construct new direction vector group $d_{}$ ${}_1\⇐d_2,d_2\⇐d_3,...,d_{n-1}\⇐d_n,d_n\⇐d,$ And new initial point is set $X_0\⇐X_n^{\left(k\right)},$ $k\⇐k+1.$ Return 2.

There is a defective in basic Powell method, and new direction group might be a linear dependence, and they can not open into n-dimensional space R ⁿ, later search is all carried out an affine subclass, if minimal point does not drop in this affine subclass, will not reach minimal point X forever ⁺

That is to say that basic Powell is by the direction Substitution Rules ${\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="A20091000053600152.png"\; state="\{\{state\}\}">d</figure-callout>}}_1\&DoubleLeftArrow;d_2,d_2\&DoubleLeftArrow;d_3,...,d_{n-1}\&DoubleLeftArrow;d_n,d_n\&DoubleLeftArrow;d$

The new direction group that produces might cause new direction group linear dependence.In fact first direction vector has no reason only to replace at every turn.The main points of improved Powell method are: replace some direction vectors of original direction group with new direction vector d after, make new direction group " grip degree altogether " and improve as much as possible, do not reduce at least.If any one direction of replacement original direction group all can not improve it and " grip degree altogether ", that is not just replaced, and original direction group is still used in the next round circulation.

Grip between the vector or altogether, or do not grip altogether, the available Fig. 5 of " gripping degree altogether " of direction group vector or " quadrature degree " explains, a1 and a2 obviously than b1 and b2 more near quadrature, it also is like this gripping altogether.

Theorem: establishing A is n rank positive definite symmetric matricess, direction vector group D=(d ₁, d ₂..., d _n) satisfy:

$d_j^{T}A{d}_j=1,(j=\mathrm{1,2},...,n)$

Then have:

$\left(1\right),\left|\det \left(D\right)\right|\&le;\sqrt{\frac{1}{\det \left(A\right)}}$

$\left(2\right),\left|\det \left(D\right)\right|=\sqrt{\frac{1}{\det \left(A\right)}}$ Necessary and sufficient condition be d ₁, d ₂..., d _nAbout A conjugation in twos.

This theorem explanation is if direction vector group D=is (d ₁, d ₂..., d _n) satisfy $d_j^{T}A{d}_j=1,$ When | det (D) | when reaching maximal value, d ₁, d ₂..., d _nGrip altogether in twos about A, therefore, in improved Powell algorithm, just determine new direction d to change and replace original direction group d as standard ₁, d ₂..., d _nIn which vector, perhaps do not replace, again the search.

(3) in k-1 layer registration with k layer P ' as a result _k(x, y) as initial position,, at P ' _k(x carries out the registration search in 8 fields y), seek P ' in image subject to registration _K-1(x y) makes it and reference picture mid point P _K-1(x, y) correspondence, thus obtain the best corresponding point P ' of this layer _K-1(x, y).

(4) make k=k-1, repeat the registration search of step (3), dwindle step-size in search, repeating step (3) and step (4) realize successively searching for up to k=0, realize top layer I (x, y) and I ' (x, y) the unique point registration of (being original reference image and image subject to registration);

(5) on the k=0 layer, P on the original image that obtains ₀(x is y) with its best corresponding point P ' ₀(x, y), the final Search Results that is carries out corresponding conversion with image subject to registration, finishes registration process.

Table 1 image registration effect relatively

Claims (1)

1. the multi-resolution non-rigid head medicine method for registering images based on the image border is characterized in that, may further comprise the steps:

1) Edge extraction

If two dimensional image signal f (x, the y) pixel value of presentation video,

If η (x y) is two-dimentional smooth function and satisfied:

∫∫η(x，y)dxdy＝1 (1)

$\underset{x,y\&RightArrow;\&infin;}{\lim }\mathrm{\&eta;}(x,y)=0---\left(2\right)$

To smooth function η (x y) asks the partial derivative of x direction and y direction respectively, then has:

${\mathrm{\&mu;}}^1(x,y)=\frac{\&PartialD;\mathrm{\&eta;}(x,y)}{\&PartialD;x};$ ${\mathrm{\&mu;}}^2(x,y)=\frac{\&PartialD;\mathrm{\&eta;}(x,y)}{\&PartialD;y}$ μ wherein ¹(x, y) and μ ²(x y) regards the 2-d wavelet function as;

Then (x, y) Dui Ying wavelet transformation is f: W ^xF (x, y)=f (x, y) * μ ¹

W ^yf(x，y)＝f(x，y)*μ ²

Image is carried out smoothly, the image g after level and smooth (x y) is:

g(x，y)＝η(x，y)*f(x，y) (3)

Image after level and smooth is asked the single order differential:

$\frac{\&PartialD;g(x,y)}{\&PartialD;x}=\frac{\&PartialD;}{\&PartialD;x}[\mathrm{\&eta;}(x,y)*f(x,y)]$

$=\frac{\&PartialD;g(x,y)}{\&PartialD;x}*f(x,y)---\left(4\right)$

$\frac{\&PartialD;g(x,y)}{\&PartialD;y}=\frac{\&PartialD;}{\&PartialD;y}[\mathrm{\&eta;}(x,y)*f(x,y)]$

$=\frac{\&PartialD;g(x,y)}{\&PartialD;y}*f(x,y)---\left(5\right)$

The right-hand member of formula (4) and (5) be actually function f (x, two wavelet transformations y), promptly

$\frac{\&PartialD;g(x,y)}{\&PartialD;x}=W^{x}f(x,y)=f(x,y)*{\mathrm{\&mu;}}^1(x,y)---\left(6\right)$

$\frac{\&PartialD;g(x,y)}{\&PartialD;y}=W^{y}f(x,y)=f(x,y)*{\mathrm{\&mu;}}^2(x,y)---\left(7\right)$

The marginal point of the modulus maximum correspondence image of first order derivative, these two first order derivatives equal f (x, two wavelet transformations y), the maximum value of the mould of these two wavelet transformations is just corresponding edge of image point, thereby

By said method, obtain edge image I (x, y) and I ' (x y), carries out image registration; Wherein (x y) is the edge image of reference picture correspondence to I, and (x y) is the edge image of image correspondence subject to registration to I ';

2). image registration

2.1) with above-mentioned to edge image I (x, y) and I ' (x y) is transformed to the edge pyramid image I of each layers of resolution _k(x, y) and I ' _k(x, y),

Process is as follows: by with the original edge image I (x, y) and I ' (x, y) adjacent 2 * 2 pixel arithmetic means are a pixel structure first order edge pyramid image I ₁(x, y) and I ' ₁(x, y), then in first order edge pyramid image I ₁(x, y) and I ' ₁(x constructs second level image I as stated above on basis y) ₂(x, y) and I ' ₂(x, y), the rest may be inferred constitutes required layer edge pyramid image I _k(x, y) and I ' _k(x, y);

2.2) resolving into from low to high each of resolution layer edge pyramid subgraph image set I _k(x, y) and I ' _k(x, y) after, by the layers of resolution I of low one-level _k(x, y) and I ' _k(x, Search Results y) is as higher leveled layers of resolution I _K-1(x, y) and I ' _K-1(x, initial value y), and the like realize the registration of original image;

Search at k layer direction of passage accelerated process, step-size in search be set, the low-frequency edge image of reference picture and image subject to registration is carried out the registration computing, must with I _k(x y) goes up some P _K(x is y) at I ' _k(x, y) the best corresponding point P ' on _k(x y), determines the transformation parameter between image, and the rough position of one deck search under the conduct;

Wherein k is the k layer of edge pyramid picture breakdown, P _K(x y) is image I _k(x, the y) pixel on, x, y are its horizontal ordinate, P ' _k(x, y) be image I ' _k(x, y) pixel on;

2.3) in k-1 layer registration with k layer P ' as a result _k(x is y) as initial position, at P ' _k(x carries out the registration search in neighborhood y), seek P ' in image subject to registration _K-1(x y) makes it and reference picture mid point P _K-1(x, y) correspondence, thus obtain the best corresponding point P ' of this layer _K-1(x, y);

2.4) make k=k-1, repeat step 2.3) registration search,

2.5) dwindle step-size in search, repeating step 2.3) and step 2.4, realize successively searching for up to k=0, realize on the promptly top layer of k=0 P on the original image that obtains ₀(x is y) with its best corresponding point P ' ₀(x, y), the final Search Results that is is finished registration process.

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