CN103077522B - Improved registration method for image with obvious local deformation - Google Patents

Abstract

The invention relates to an improved registration method for an image with obvious local deformation. The method comprises the following steps of: inputting a reference image I and a floating image J to be registered respectively; and registering by using a multi-resolution grid free deformation method of B spline, wherein in the multi-resolution grid free deformation method of the B spline, a registration process of the floating image T (J) and the reference image I after each layer of deformation comprises the steps of: correspondingly substituting components in a formula (1) with absolute values of being greater than gamma, keeping the rest unchanged, and finally iteratively solving by using a 1-BFGS (Broyden-Fletcher-Goldfarb-Shanno) method by taking the newly obtained function as a target function, and finishing registration of the floating image T (J) and the reference image I after the layer of deformation when two adjacent iterations meet the preset end conditions. According to the registration method, the accuracy and the robustness of the registration can be obviously improved.

Description

A kind of method for registering of the obvious image of local deformation of improvement

Technical field

The present invention relates to general purpose image data process, be specifically related to the graph image conversion method in the plane of delineation, the method is applicable to local deformation comparatively significantly image registration.

Background technology

Up to now, for local deformation comparatively significantly image registration problem, the most frequently used is traditional free deformation (FFD) method for registering, the objective function of the method is divided into similarity measure and bound term two, wherein, deformation adopts the FFD model based on B-spline, and bound term is then two Norm Model L ₂(i.e. European norm).This traditional FFD method is usually used in image registration, target tracking, motion analysis etc., and the local deformation of simulated target has good effect.Such as, D.Ruecker has just used this method when carrying out mammary gland registration, and the method is then used for the motion analysis of left ventricle and tracking by E.Bardinet, has good effect.

But above-mentioned traditional method is used for image registration, especially image exist local deformation comparatively significantly problem time, still Shortcomings part.As, D.Ruecker is when using the method to carry out mammary gland registration, and the objective function adopted is following formula C=C _similarity(I, T (J))+λ C _smooth(T), and in formula,

Similarity measure $C_{\mathrm{similarity}}=\frac{1}{N}\sqrt{\underset{x}{\mathrm{\Σ}}\underset{y}{\mathrm{\Σ}}\underset{z}{\mathrm{\Σ}}(I(x,y,z)-T\left(J(x,y,z)\right){)}^2},$

Bound term $C_{\mathrm{smooth}}=\frac{1}{V}{\∫}_0^X{\∫}_0^Y{\∫}_0^Z[{\left(\frac{{\∂}^{2}T}{{\∂x}^2}\right)}^2+{\left(\frac{{\∂}^{2}T}{{\∂y}^2}\right)}^2+{\left(\frac{{\∂}^{2}T}{{\∂z}^2}\right)}^2+{\left(\frac{{\∂}^{2}T}{\∂\mathrm{xy}}\right)}^2+{\left(\frac{{\∂}^{2}T}{\∂\mathrm{xz}}\right)}^2+{\left(\frac{{\∂}^{2}T}{\∂\mathrm{yz}}\right)}^2]\mathrm{dzdydx},$ In described similarity measure and bound term, V represents the volume of image, I represents reference picture, J represents floating image, T represents deformation model, and λ is weight parameter (D.Ruecker, L.I.Sonoda, C.Hayes, D.L.G.Hill, M.O.Leach, and D.J.Hawkes.Nonrigid Registration Using Free-Form Deformations:Application to Breast MRImages, IEEE Transactions on Medical Imaging, vol.18, no.8, pp.712-721, August, 1999).

At above-mentioned D.Ruecker adopt in method bound term ${\left(\frac{{\∂}^{2}T}{{\∂x}^2}\right)}^2,{\left(\frac{{\∂}^{2}T}{{\∂y}^2}\right)}^2{,\left(\frac{{\∂}^{2}T}{{\∂z}^2}\right)}^2,{\left(\frac{{\∂}^{2}T}{\∂\mathrm{xy}}\right)}^2,{\left(\frac{{\∂}^{2}T}{\∂\mathrm{xz}}\right)}^2,$ With be one parabola shaped, whole bound term is along with independent variable $\frac{{\∂}^{2}T}{{\∂x}^2},\frac{{\∂}^{2}T}{{\∂y}^2},\frac{{\∂}^{2}T}{{\∂z}^2},\frac{{\∂}^{2}T}{\∂\mathrm{xy}},\frac{{\∂}^{2}T}{\∂\mathrm{xz}}$ With increase be quadratic sum form increase severely.Like this, floating image is in the comparatively violent place of deformation, and the value of bound term is assembled and increased, and namely becomes large to the deformation constraint of floating image, occurs the problem of Planar Mechanisms.Therefore, adopt FFD model as deformation model, L ₂when norm constructs objective function as bound term, comparatively serious to local deformation ratio, there is the image of larger, violent displacement field, Planar Mechanisms and excessively level and smooth problem will be produced, and then cause the precise decreasing of registration.

Summary of the invention

Technical matters to be solved by this invention is to provide a kind of method for registering of the obvious image of local deformation of improvement, and the method significantly improves the precision of registration.

The technical solution that the present invention solves the problem is:

A method for registering for the obvious image of local deformation of improvement, the method comprises the following steps:

First input reference picture I subject to registration and floating image J respectively, then adopt the multi-resolution grid free deformation method of B-spline to carry out registration; In the multi-resolution grid free deformation method of described B-spline, the floating image T (J) after every one deck deformation with the registration process of reference picture I is:

By in following formula (I) $\frac{{\∂}^{2}T}{{\∂x}^2},\frac{{\∂}^{2}T}{{\∂y}^2},\frac{{\∂}^{2}T}{{\∂z}^2},\frac{{\∂}^{2}T}{\∂\mathrm{xy}},\frac{{\∂}^{2}T}{\∂\mathrm{xz}}$ With middle absolute value is greater than γ person and carries out corresponding replacement, that is, will replace with $2\mathrm{\γ}\left|\frac{{\∂}^{2}T}{{\∂x}^2}\right|-{\mathrm{\γ}}^2,$ Will replace with $2\mathrm{\γ}\left|\frac{{\∂}^{2}T}{{\∂y}^2}\right|-{\mathrm{\γ}}^2,$ Will replace with $2\mathrm{\γ}\left|\frac{{\∂}^{2}T}{{\∂z}^2}\right|-{\mathrm{\γ}}^2,$ Will replace with $2\mathrm{\γ}\left|\frac{{\∂}^{2}T}{\∂\mathrm{xy}}\right|-{\mathrm{\γ}}^2,$ Will replace with $2\mathrm{\γ}\left|\frac{{\∂}^{2}T}{\∂\mathrm{xz}}\right|-{\mathrm{\γ}}^2,$ Will replace with $2\mathrm{\γ}\left|\frac{{\∂}^{2}T}{\∂\mathrm{yz}}\right|-{\mathrm{\γ}}^2,$ All the other are constant, last then with the function newly obtained for objective function adopts l-BFGS method iterative, when adjacent twice iteration meets default end condition, namely the registration of the floating image T (J) after this layer of deformation and reference picture I is completed, above-mentioned γ, for being more than or equal to 0, is less than the constant of 0.005;

$C=\frac{1}{N}\sqrt{\underset{x}{\mathrm{\Σ}}\underset{y}{\mathrm{\Σ}}\underset{z}{\mathrm{\Σ}}(I(x,y,z)-T\left(J(x,y,z)\right){)}^2}+$ （I）

$\mathrm{\λ}\frac{1}{V}{\∫}_0^X{\∫}_0^Y{\∫}_0^Z({\left(\frac{{\∂}^{2}T}{{\∂x}^2}\right)}^2+{\left(\frac{{\∂}^{2}T}{{\∂y}^2}\right)}^2+{\left(\frac{{\∂}^{2}T}{{\∂z}^2}\right)}^2+{\left(\frac{{\∂}^{2}T}{\∂\mathrm{xy}}\right)}^2+{\left(\frac{{\∂}^{2}T}{\∂\mathrm{xz}}\right)}^2+{\left(\frac{{\∂}^{2}T}{\∂\mathrm{yz}}\right)}^2)\mathrm{dzdydx}$

In above formula (I), N represents the quantity of pixel in input picture, and V represents the volume of image, and I represents reference picture, and J represents floating image, and T represents deformation model, and λ is weight parameter.

In said method, described constant γ visual floating image deformation size is selected, and when floating image deformation is larger, γ gets smaller value, otherwise γ gets higher value.

The present inventor tests repeatedly, and the end condition described in said method is that the rate of change of the energy function of adjacent twice iteration is less than 10 ^-5.

In order to improve the accuracy of calculating, faster procedure convergence simultaneously, the reference picture described in step (1) in technique scheme and floating image before subsequent processing, preferably first carry out following pre-service: be converted into double-length floating with reference to image and floating image by unsigned integer type; Gray-scale value linear transformation with reference to each pixel of image and floating image is 0 ~ 1.

Above formula (I) and the objective function newly obtained are compared visible, when ${\left(\frac{{\∂}^{2}T}{{\∂x}^2}\right)}^2,{\left(\frac{{\∂}^{2}T}{{\∂y}^2}\right)}^2{,\left(\frac{{\∂}^{2}T}{{\∂z}^2}\right)}^2,{\left(\frac{{\∂}^{2}T}{\∂\mathrm{xy}}\right)}^2,$ with when being greater than γ, when $\left|\frac{{\∂}^{2}T}{{\∂x}^2}\right|>\mathrm{\γ}$ Time, then have ${\left(\frac{{\∂}^{2}T}{{\∂x}^2}\right)}^2>2\mathrm{\γ}\left|\frac{{\∂}^{2}T}{{\∂x}^2}\right|-{\mathrm{\γ}}^2;$ When $\left|\frac{{\∂}^{2}T}{{\∂y}^2}\right|>\mathrm{\γ}$ Time, then have ${\left(\frac{{\∂}^{2}T}{{\∂y}^2}\right)}^2>2\mathrm{\γ}\left|\frac{{\∂}^{2}T}{{\∂y}^2}\right|-{\mathrm{\γ}}^2;$ When $\left|\frac{{\∂}^{2}T}{{\∂z}^2}\right|>\mathrm{\γ}$ Time, then have ${\left(\frac{{\∂}^{2}T}{{\∂z}^2}\right)}^2>2\mathrm{\γ}\left|\frac{{\∂}^{2}T}{{\∂z}^2}\right|-{\mathrm{\γ}}^2;$ When $\left|\frac{{\∂}^{2}T}{{\∂\mathrm{zy}}^2}\right|>\mathrm{\γ}$ Time, then have ${\left(\frac{{\∂}^{2}T}{\∂\mathrm{xy}}\right)}^2>2\mathrm{\γ}\left|\frac{{\∂}^{2}T}{\∂\mathrm{xy}}\right|-{\mathrm{\γ}}^2;$ When $\left|\frac{{\∂}^{2}T}{{\∂\mathrm{xz}}^2}\right|>\mathrm{\γ}$ Time, then have ${\left(\frac{{\∂}^{2}T}{\∂\mathrm{xz}}\right)}^2>2\mathrm{\γ}\left|\frac{{\∂}^{2}T}{\∂\mathrm{xz}}\right|-{\mathrm{\γ}}^2;$ When $\left|\frac{{\∂}^{2}T}{{\∂\mathrm{yz}}^2}\right|>\mathrm{\γ}$ Time, then have ${\left(\frac{{\∂}^{2}T}{\∂\mathrm{yz}}\right)}^2>2\mathrm{\γ}\left|\frac{{\∂}^{2}T}{\∂\mathrm{yz}}\right|-{\mathrm{\γ}}^2.$ For the ease of understanding intuitively, with function with its corresponding function $2\mathrm{\γ}\left|\frac{{\∂}^{2}T}{{\∂x}^2}\right|-{\mathrm{\γ}}^2$ For example, make the curve map of two functions in the same coordinate system respectively, this figure as shown in Figure 2.As seen from Figure 2, the function in formula (I) be one section of para-curve between-γ and γ, and corresponding function $2\mathrm{\γ}\left|\frac{{\∂}^{2}T}{{\∂x}^2}\right|-{\mathrm{\γ}}^2$ Be then from the parabolical two of a section between-γ and γ outward extending oblique dotted line respectively.Therefore, the method for the invention suitably can select γ according to floating image deformation size, with the function newly obtained for objective function carries out registration, can avoid $\frac{{\∂}^{2}T}{{\∂x}^2},\frac{{\∂}^{2}T}{{\∂y}^2},\frac{{\∂}^{2}T}{{\∂z}^2},\frac{{\∂}^{2}T}{\∂\mathrm{xy}},\frac{{\∂}^{2}T}{\∂\mathrm{xz}}$ With in there is Planar Mechanisms when having the absolute value of more than to be greater than γ, and then improve registration accuracy.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of method for registering of the present invention.

Fig. 2 is function with curve map, wherein, solid line para-curve is function curve map, one section of solid line para-curve between-γ and γ and its two respectively outward extending oblique dotted line are function curve map.

Fig. 3 is two width simulated person body brain MR image in simulation brain database BrainWeb, and wherein, (a) figure is normal brain MR image; B () figure is the image manually add deformation on (a) figure basis after.

Fig. 4 is the result and residual plot that in Fig. 3, two width images obtain after carrying out registration with the method for registering of the obvious image of local deformation improved and traditional F FD method for registering respectively, wherein, a () is classified as the result of the method for registering using the obvious image of local deformation improved, upper figure is registration result, and figure below is residual plot; B () is classified as the result using FFD method for registering, upper figure is registration result, and figure below is residual plot.

Fig. 5 is that venous patient injects after contrast preparation, and carry out the liver image of CT scan acquisition respectively at arterial phase (contrast preparation arteria hepatica period) and venous phase (contrast preparation vena portae hepatica period), wherein, (a) figure is the image that arterial phase scans; B () figure is the image of venous phase scanning.

Fig. 6 is the result and residual plot that in Fig. 5, two width images obtain after carrying out registration with the method for registering of the obvious image of local deformation improved and traditional F FD method for registering respectively, wherein, a () is classified as the result of the method for registering using the obvious image of local deformation improved, upper figure is registration result, and figure below is residual plot; B () is classified as the result using FFD method for registering, upper figure is registration result, and figure below is residual plot.

Fig. 7 is for two width images in use Fig. 3 are as reference image and floating image, weight parameter λ is provided with 0.001 respectively, 0.005,0.01,0.05,0.1 these 5 different values, use the method for registering of the obvious image of local deformation improved and traditional F FD method for registering respectively to carry out the result of five groups of contrast experiments, wherein, (a) is classified as the result of the method for registering using the obvious image of local deformation improved; B () is classified as the result using FFD method for registering.

Fig. 8 (a) figure is human body normal brain MR image; B () figure is the image manually add deformation on (a) figure basis after.

Two width images are as reference image and floating image in order to use in Fig. 8 for Fig. 9, and parameter γ is provided with 0.0001,0.001 respectively, 0.005,0.01,0.1 these 5 different values, use the method for registering of the obvious image of local deformation improved to carry out the result of five groups of contrast experiments.

Embodiment

Example 1

The present embodiment describes method for registering of the present invention for two width simulated person body brain MR image in BrainWeb.

See Fig. 1, the concrete implementation step of the method for registering of the obvious image of local deformation of improvement of the present invention is as follows:

Step 1, reads in Fig. 3 (a) and Fig. 3 (b) respectively, and using Fig. 3 (a) as reference image I, Fig. 3 (b) is as floating image J.In order to improve the accuracy of calculating, and faster procedure convergence, first read in Fig. 3 (a) and Fig. 3 (b) is converted into double-length floating by unsigned integer type respectively, then is 0 ~ 1 by their gray-scale value linear transformation.

Step 2, with represent the position at reference mark, n _x× n _y× n _zrepresent sizing grid, adopt the multi-resolution grid free deformation model of the B-spline shown in following formula (II) to each position (x in floating image Fig. 3 (b), y, z) carry out free deformation, obtain the floating image T (J) after ground floor deformation:

$T_{\mathrm{local}}=(x,y,z)$

In formula (II) b _lrepresent l, x direction B-spline basis function, B _mrepresent m, y direction B-spline basis function, B _nrepresent z direction n-th B-spline basis function, wherein, when l is respectively 0,1,2,3,

B ₀(u)＝(1-u) ³/6,B ₁(u)＝(3u ³-6u ²+4)/6,B ₂(u)＝(-3u ³+3u ²+3u+1)/6,B ₃(u)＝u ³/6；

When m is respectively 0,1,2,3,

B ₀(v)＝(1-v) ³/6,B ₁(v)＝(3v ³-6v ²+4)/6,B ₂(v)＝(-3v ³+3v ²+3v+1)/6,B ₃(v)＝v ³/6；

When n is respectively 0,1,2,3,

B ₀(w)＝(1-w) ³/6,B ₁(w)＝(3w ³-6w ²+4)/6,B ₂(w)＝(-3w ³+3w ²+3w+1)/6,B ₃(w)＝w ³/6。

The sizing grid that in this example, ground floor adopts is n _x× n _y× n _z=32 × 32 × 32.

Step 3, carry out registration with reference to the floating image T (J) after image I and ground floor deformation, this registration is, first calculates each point in the floating image T (J) after ground floor deformation $\frac{{\∂}^{2}T}{{\∂x}^2},\frac{{\∂}^{2}T}{{\∂y}^2},\frac{{\∂}^{2}T}{{\∂z}^2},\frac{{\∂}^{2}T}{\∂\mathrm{xy}},\frac{{\∂}^{2}T}{\∂\mathrm{xz}}$ With value, then by formula (I) $\frac{{\∂}^{2}T}{{\∂x}^2},\frac{{\∂}^{2}T}{{\∂y}^2},\frac{{\∂}^{2}T}{{\∂z}^2},\frac{{\∂}^{2}T}{\∂\mathrm{xy}},\frac{{\∂}^{2}T}{\∂\mathrm{xz}}$ With middle absolute value is greater than γ person and carries out corresponding replacement, that is, will replace with $2\mathrm{\γ}\left|\frac{{\∂}^{2}T}{{\∂x}^2}\right|-{\mathrm{\γ}}^2,$ Will replace with $2\mathrm{\γ}\left|\frac{{\∂}^{2}T}{{\∂y}^2}\right|-{\mathrm{\γ}}^2,$ Will replace with $2\mathrm{\γ}\left|\frac{{\∂}^{2}T}{{\∂z}^2}\right|-{\mathrm{\γ}}^2,$ Will replace with $2\mathrm{\γ}\left|\frac{{\∂}^{2}T}{\∂\mathrm{xy}}\right|-{\mathrm{\γ}}^2,$ Will replace with $2\mathrm{\γ}\left|\frac{{\∂}^{2}T}{\∂\mathrm{xz}}\right|-{\mathrm{\γ}}^2,$ Will replace with $2\mathrm{\γ}\left|\frac{{\∂}^{2}T}{\∂\mathrm{yz}}\right|-{\mathrm{\γ}}^2,$ All the other are constant; Finally, adopt l-BFGS method iterative after above-mentioned replacement obtain new objective function, when the rate of change of the energy function of adjacent twice iteration is less than 10 ^-5time termination of iterations, obtain the image after ground floor deformation.In this example, the λ in formula (I) gets 0.01, γ and gets 0.001.

Step 4, arranging sizing grid is 16 × 16 × 16, and the floating image T (J) after deformation step 3 obtained, as the floating image of the second layer, carries out free deformation by formula (II).

Step 5, adopts step 2 and the same method of step 3 to obtain this layer of new objective function, adopts minimized this layer of new objective function of l-BFGS method iterative, when the rate of change of the energy function of adjacent twice iteration is less than 10 ^-5time termination of iterations, obtain the image after second layer deformation.

Step 6, arranging sizing grid is 8 × 8 × 8, repeats step 4 and step 5, obtains the image after third layer deformation, obtains as Fig. 4 (a) arranges the registration result shown in upper figure.

In order to verify the effect of the method for the invention, the present inventor carries out registration with reference to method described in the prior art to Fig. 3 (a) (reference picture I) and Fig. 3 (b) (floating image J), and gained registration result such as Fig. 4 (b) arranges shown in upper figure.Above-mentioned prior art is in August, 1999, Institute of Electrical and Electric Engineers medical image journal (IEEE Transactions on MedicalImaging), 18 volume the 8th phase, 712nd page to 721 pages " Nonrigid Registration Using Free-FormDeformations:Application to Breast MR Images " method for registering described in a literary composition published, wherein, sizing grid n _x× n _y× n _zand the value of weight parameter λ is identical with this routine above-mentioned method for registering.

For the ease of comparing, the present inventor deducts Fig. 4 (a) with Fig. 3 (a) and arranges the residual plot that upper figure obtains as shown in Fig. 4 (a) row figure below, then the residual plot using Fig. 3 (a) to deduct the upper figure of Fig. 4 (b) row to obtain as shown in Fig. 4 (b) row figure below.

The upper figure that Fig. 4 (a) row arrange with Fig. 4 (b) is compared visible, the upper figure that Fig. 4 (a) arranges and reference picture Fig. 3 (a) closer to, and the upper figure that Fig. 4 (b) arranges and reference picture Fig. 3 (a) have obvious difference in edge, and registration accuracy is lower; Figure below that Fig. 4 (a) row and Fig. 4 (b) arrange is compared visible, remains image edge information in figure below that Fig. 4 (b) arranges, in figure below that Fig. 4 (a) arranges, then can not see residual risk.The above results illustrates, the registration successful of the method for the invention is better than prior art.

Example 2

The present embodiment is to carry out the method for registering of liver image Fig. 5 (a) that CT scan obtains and Fig. 5 (b) respectively at arterial phase and venous phase after injection of contrast medium, concrete steps are as described below.

First read in Fig. 5 (a) and Fig. 5 (b) respectively, and using Fig. 5 (a) as reference image, Fig. 5 (b), as floating image, then carries out registration by step described in example 1.In this example, three layers of deformation sizing grid are followed successively by 32 × 32 × 32,16 × 16 × 16,8 × 8 × 8; λ in formula (I) gets 0.05, γ and gets 0.001.Registration result such as Fig. 6 (a) arranges shown in upper figure.

In order to verify the effect of the method for the invention, the prior art of this example still described in reference example 1 carries out registration to the floating image shown in the reference picture shown in Fig. 5 (a) and Fig. 5 (b), and registration result such as Fig. 6 (b) arranges shown in upper figure.Wherein, sizing grid n _x× n _y× n _zand the value of weight parameter λ is identical with this routine above-mentioned method for registering.Then adopt the method same with in effectiveness comparison described in example 1 to obtain Fig. 5 (a) and Fig. 6 (a) to arrange the residual plot that upper figure and Fig. 5 (a) and Fig. 6 (b) arrange upper figure then.

Respectively by 6(a) in row upper figure and Fig. 6 (b) arrange in upper figure and 6(a) arrange in figure below and Fig. 6 (b) arrange in figure below compare visible, at 6(a) in the two width figure up and down that arrange, because Fig. 5 (a) and Fig. 5 (b) different times after squeezing into contrast preparation obtained, two width images are in brightness, contrast exists certain difference, although the residual matrix of the image subtraction gained of reference picture and the complete rear output of registration also can not be zero, but the edge of liver has alignd well, do not occur in residual plot that too much marginal information remains, two width images registration is well described, and, at 6(b) in the upper figure that arranges, there is the unexpected increase of gray-scale value in liver edge place, at 6(b) in figure below of arranging, arrow pointed location in figure below that the wider highlighted phenomenon (see 6(b) in region, liver edge place arranges).The above results also illustrates, the registration successful of the method for the invention is better than prior art.

Example 3(λ value is to the research of registration influential effect)

The method proposed for checking the present inventor has higher registration accuracy than traditional free deformation method for registering, stronger to the robustness of weight parameter λ, in this example, λ is provided with 0.001 respectively, and 0.005,0.01,0.05,0.1 these 5 different values, carry out 5 groups of Experimental comparison.

In this example, use Fig. 3 (a) as with reference to image, Fig. 3 (b) is as floating image, and carry out registration by existing method described in the method for registering of the obvious image of local deformation of improvement and example 1 respectively, comparing result is shown in Fig. 7.Wherein Fig. 7 (a) is classified as the residual plot using the method for registering of the obvious image of local deformation improved to obtain, and Fig. 7 (b) is classified as existing method described in example 1 and carries out the residual plot that registration obtains.From top to bottom, λ is set to 0.001 respectively, and 0.005,0.01,0.05,0.1.

As shown in (b) row in Fig. 7, along with the increase of weight parameter λ, the residual error of traditional F FD method for registering gained is also larger, occurs the residual of too much image edge information, registration accuracy degradation.And from Fig. 7 (a) row, the method for registering of the obvious image of local deformation of improvement is more effective than existing method, less occur image edge information remain, description references image and floating image obtain good registration, precision is higher, and insensitive to weight parameter λ, and robustness is high.

Example 4(γ value is to the research of registration influential effect)

For research γ value is on the impact of registration effect, in this example, γ is provided with 0.0001 respectively, and 0.001,0.005,0.01,0.1 these 5 different values, carry out 5 groups of Experimental comparison.

In this example, use Fig. 8 (a) as reference image, Fig. 8 (b) is as floating image, and use the method for registering of the obvious image of local deformation improved to carry out registration, after registration, the residual plot of gained is shown in Fig. 9.From top to bottom, the value of parameter γ is set to 0.0001 respectively, and 0.001,0.005,0.01,0.1.Wherein sizing grid n _x× n _y× n _zsame as Example 1, weight parameter λ gets 0.1.

As shown in the figure, when parameter γ is more than or equal to 0.005, registration accuracy declines, and occurs the residual of too much image edge information.Therefore, in actual applications, the scope that parameter γ suggestion is selected, for being more than or equal to 0, is less than or equal to 0.005.

Claims (3)

1. a method for registering for the obvious image of local deformation improved, the method comprises the following steps:

First input reference picture I subject to registration and floating image J respectively, then adopt the multi-resolution grid free deformation method of B-spline to carry out registration; In the multi-resolution grid free deformation method of described B-spline, the floating image T (J) after every one deck deformation with the registration process of reference picture I is:

By in following formula (I) with middle absolute value is greater than γ person and carries out corresponding replacement, that is, will replace with will replace with will replace with will replace with will replace with will replace with all the other are constant, finally then with the function newly obtained for objective function adopts l-BFGS method iterative, when adjacent twice iteration meets default end condition, namely complete the registration of the floating image T (J) after this layer of deformation and reference picture I; Wherein, described γ is more than or equal to 0 constant being less than 0.005;

$\begin{array}{c}C=\frac{1}{N}\sqrt{\underset{x}{\mathrm{\Σ}}\underset{y}{\mathrm{\Σ}}\underset{z}{\mathrm{\Σ}}{(I(x,y,z)-T\left(J(x,y,z)\right))}^2}+\\ \mathrm{\λ}\frac{1}{V}{\∫}_0^X{\∫}_0^Y{\∫}_0^Z({\left(\frac{{\∂}^2}{{\∂x}^2}\right)}^2+{\left(\frac{{\∂}^{2}T}{{\∂y}^2}\right)}^2+\left(\frac{{\∂}^{2}T}{{\∂z}^2}\right)+{\left(\frac{{\∂}^{2}T}{\∂\mathrm{xy}}\right)}^2+{\left(\frac{{\∂}^{2}T}{\∂\mathrm{xz}}\right)}^2+{\left(\frac{{\∂}^{2}T}{\∂\mathrm{yz}}\right)}^2)\mathrm{dxdydz}\end{array}----\left(I\right)$

In above formula (I), N represents the quantity of pixel in input picture, and V represents the volume of image, and I represents reference picture, and J represents floating image, and T represents deformation model, and λ is weight parameter.

2. the method for registering of the obvious image of the local deformation of improvement according to claim 1, it is characterized in that, also comprise and inputted reference picture and floating image are carried out following pretreated step: be converted into double-length floating with reference to image I and floating image J by unsigned integer type; Gray-scale value linear transformation with reference to each pixel of image I and floating image J is 0 ~ 1.

3. the method for registering of the obvious image of the local deformation of improvement according to claim 1 and 2, is characterized in that, described end condition is that the rate of change of the energy function of adjacent twice iteration is less than 10 ^-5.