CN101048800A - Method and system for motion correction in a sequence of images - Google Patents

Abstract

A method for motion compensation between first and second images in a temporal sequence includes processing the first and second images in a reduction process for providing respective reduced resolution first and second images; deriving respective first and second feature maps from the respective reduced resolution first and second images, the feature maps including deriving the respective Laplacian of image data in the respective reduced resolution first and second images; deriving a displacement field by processing the first and second feature maps in accordance with a registration algorithm, the registration algorithm comprising solving, for each picture element or voxel, a local Gaussian weighted least mean square problem so as to derive respective vectors forming the displacement field; and warping the second image with the displacement field.

Description

In image sequence, carry out the method and system of motion correction

The cross reference of related application

Right of priority

Here be No.60/605 with particular reference to the application number of submitting on August 31st, 2004 with the name of present inventor CHRISTOPHE CHEFD ' HOTEL, 759 U.S. Provisional Patent Application, this U.S. Provisional Patent Application be entitled as " the Gaussian weighted least mean square registration Algorithm (A GAUSSIAN WEIGHTED LEAST MEAN SQUAREREGISTRATION ALGORITHM FOR BREAST MR MOTION CORRECTION) that is used for mammary gland MR motion correction " and attorney is 2004P14822US, and the application requires the right of priority of this U.S. Provisional Patent Application, and its disclosure is hereby incorporated by.

Technical field

The application is usually directed to the motion correction in the imaging, and relates more particularly to belong to the motion compensation of calibration object motion, and this object motion is as may be taking place in (such as what can obtain by medical imaging process) temporal sequence of images.

Background technology

Medical imaging technology is used to many medical procedures, comprise for example be used to the patient carry out cancer or pre-cancer situation detection.Important use is the detection to tumour in the breast cancer or potential tumor.Potential tumor is difficult to detect.In the available technology of helpful information potentially is provided, be well known that, for example, such tissue that relates to tumour is compared the suction faster (perfusion (wash-in)) that may present usually contrast preparation with contiguous, nonneoplastic tissue and is removed more quickly.Characteristic such as these and other may be helpful in some diagnosis, and these diagnosis relate to and detect suspect tissue and by carrying out a program (such as perfusion and/or remove contrast preparation) before and carry out image after this program and compare and discern tissue characteristics to the patient.Use can be compared between image by the formed this sequential chart picture of imaging technique (such as magnetic resonance imaging (MRI)), to detect the performance difference that zones of different was presented by the MR volume of being gathered.

The technology that is used for carrying out this detection advantageously requires to follow the tracks of the intensity of single voxel of the time series of such volume.Yet difficulty is that the patient moves usually between continuous collection, and introduces the difference that relates to motion between the image of being gathered thus, no longer can follow the tracks of a single point in the space thus, unless carry out motion correction.Such as used in this, the point in the space is not meant typical in the defined point that does not have size of geometry, and is meant the point with small size element that is produced by the digitizing program, and these small size elements are formed digitized image.

The art methods that addresses this problem has in the past calculated two light streams between the image, selects any one as the reference in this sequence image in these two images.For example, described two images can obtain from the image of being gathered by calculating laplacian pyramid.Light stream can for example be calculated by the minimization problem of finding the solution two point-to-point differences between the laplacian image.

Summary of the invention

Motion correction or compensation problem during the MR that the objective of the invention is to solve in an advantageous manner at for example mammary gland potential tumor detects, these potential tumors are detected as the tissue that has quick suction (perfusion) contrast preparation and remove contrast preparation fast.

According to an aspect of the present invention, first and second image of patient is obtained according to time sequencing by imaging process (such as MRI equipment), wherein second and later image can comprise because of for example patient moving causes after obtaining first image and first and the difference of the image of morning more.Handle these images with reducing process (reduction process), thereby cause as compare lower corresponding first and second image of resolution with original image.By the corresponding Laplace operator of the view data in first and second image of deriving low resolution, first and second Feature Mapping derives from first and second image of low resolution accordingly.Based on given initial displacement field, handle these Feature Mapping with registration procedure according to registration Algorithm.This algorithm comprises at each voxel finds the solution local Gaussian weighted least mean square problem, so that derive the respective vectors of the dense displacement field be formed for simulating distortion.Utilize this displacement field to come crooked (warp) second image, so that obtain second image that motion correction is crossed.

The default condition of given initial displacement field can for example be empty set or null displacement, and perhaps this given initial displacement field can be considered the priori of patient moving.

According to a further aspect in the invention, the method that is used for carrying out motion compensation between first and second image of time series comprises: derive corresponding first and second Feature Mapping by this first and second image; Derive displacement field by handle these first and second Feature Mapping according to registration Algorithm, described registration Algorithm comprises at each pixel or voxel finds the solution local Gaussian weighted least mean square problem, so that derive the respective vectors that forms described displacement field; And utilize crooked described second image of described displacement field.

According to a further aspect in the invention, derive the step of displacement field and utilize the displacement field of deriving previously to derive described displacement field, and, derive the step of displacement field and utilize given initial displacement field at the described displacement field of initial derivation.

The default condition of given initial displacement field is an empty set, and perhaps for example, given initial displacement field can be considered the priori of patient moving.

According to a further aspect in the invention, repeat to derive the step of displacement field, wherein on than first and second Feature Mapping that last time repeats to have more high-resolution first and second image, carrying out each the repetition.

According to a further aspect in the invention, the each recycling from the direct displacement field of deriving previously of step the preceding.

According to a further aspect in the invention, at initial derivation displacement field, derive the step of displacement field and utilize given displacement field.

According to a further aspect in the invention, the step of derivation displacement field comprises the level of resolution that the displacement field in preceding derivation is expanded to resolution increase version.

According to a further aspect in the invention, the method that is used to carry out motion compensation may further comprise the steps: utilize the displacement field that exists, derives at highest resolution for crooked this second image to produce the image that motion correction is crossed.

According to a further aspect in the invention, the step that derives corresponding first and second Feature Mapping comprises the corresponding Laplace operator that derives the view data in first and second image that corresponding resolution reduces.

According to a further aspect in the invention, the method that is used for carrying out motion compensation between first and second image of time series comprises: handle first and second image with the process of reducing, first and second image that provides corresponding resolution to reduce is provided; Derive corresponding first and second Feature Mapping by first and second image that corresponding resolution reduces, these Feature Mapping comprise the corresponding Laplace operator that derives the view data in first and second image that this corresponding resolution reduces; Derive displacement field by handle first and second Feature Mapping according to registration Algorithm, described registration Algorithm comprises at each pixel or voxel finds the solution local Gaussian weighted least mean square problem, so that derive the respective vectors that forms this displacement field; And utilize this displacement field to come crooked this second image.

According to a further aspect in the invention, the method that is used for carrying out motion compensation between first and second image of time series comprises: handle first and second image with the process of reducing, first and second image that provides corresponding resolution to reduce is provided; Derive corresponding first and second Feature Mapping by first and second image that this corresponding resolution reduces; Derive displacement field by handle first and second Feature Mapping according to registration Algorithm, described registration Algorithm comprises at each pixel or voxel finds the solution local Gaussian weighted least mean square problem, so that derive the respective vectors that forms this displacement field; And utilize crooked this second image of this displacement field.

According to a further aspect in the invention, the method that is used for carrying out motion compensation between the reference picture of time series and floating image comprises: derive first group of correction image that resolution reduces gradually by this reference picture; Derive second group of correction image that resolution reduces gradually by this floating image; Derive the mapping of first stack features by this first group of correction image; Derive the mapping of second stack features by this second group of correction image; According to registration Algorithm, derive first displacement field by lowest resolution ingredient and given initial displacement field in each Feature Mapping during first and second stack features shines upon respectively, described registration Algorithm comprises at each pixel or voxel finds the solution local Gaussian weighted least mean square problem, so that derive the respective vectors that forms this displacement field; According to described registration Algorithm, derive second displacement field by inferior lowest resolution ingredient in each Feature Mapping during first and second stack features shines upon respectively and first displacement field that in previous step, is obtained; The ingredient (if exist) higher continuously at the resolution in each Feature Mapping during first and second stack features shines upon respectively repeats abovementioned steps, and all use the displacement field that is obtained in the step before current step in each case, until the resolution that reaches floating image, and the if there is no higher ingredient of resolution then is directly to next step; And crooked this floating image of the displacement field that utilizes last acquisition.

According to a further aspect in the invention, the method that is used for carrying out motion compensation between the reference picture of time series and floating image comprises: (a) reduce process with the resolution of corresponding first and second a plurality of cascades and handle this reference picture and floating image, the reference picture and the floating image that provide corresponding a plurality of resolution to reduce continuously is provided, be called level 0 at this for the lowest resolution level, and be called level 1 for inferior higher levels of resolution, for the second time higher levels of resolution be called level 2, for any existing higher levels of resolution by that analogy; (b) be that reference picture and the floating image that corresponding a plurality of resolution of L0, L1, L2 etc. reduce continuously derived corresponding a plurality of fixed reference feature mapping and floated Feature Mapping by level of resolution; (c) derive first displacement field by handling according to registration Algorithm with the Feature Mapping of floating with the corresponding fixed reference feature mapping of horizontal L0, described registration Algorithm comprises based on given initial displacement field finds the solution local Gaussian weighted least mean square problem at each pixel or voxel, so that derive the respective vectors that forms this first displacement field; (d) this first displacement field is expanded to matched level of resolution, so that first displacement field that is expanded to be provided with resolution L1; (e) by handle based on first displacement field that is expanded according to this registration Algorithm and the mapping of the corresponding fixed reference feature of level of resolution L1 with float Feature Mapping, thereby derive second displacement field so that derive the respective vectors that forms described second displacement field; (f) this second displacement field is expanded to matched level of resolution, so that second displacement field that is expanded to be provided with resolution L1; (g) by handle based on second displacement field that is expanded according to this registration Algorithm and the mapping of the corresponding fixed reference feature of level of resolution L2 with float Feature Mapping, thereby derive the triple motion field so that derive the respective vectors that forms described second displacement field; And if (h) L2 is the level of resolution of reference picture and floating image, so by utilizing this floating image of triple motion field bend and finishing; And if L2 is not the level of resolution of reference picture and floating image, then (i) expands to this triple motion field and time matched level of resolution of higher levels of resolution, so that the triple motion field that is expanded to be provided; And (j) repeat series of steps from step (g) beginning, suitably revise level of resolution, to obtain displacement field based on the last displacement field that is expanded that obtains in front corresponding to more and more higher level of resolution, up to the level of resolution that reaches reference picture and floating image, and therefore utilize crooked this floating image of the last displacement field that is obtained and end.

According to a further aspect in the invention, provide the step of reference picture that corresponding a plurality of resolution reduces continuously and floating image to comprise to derive the reference picture that corresponding a plurality of resolution reduce continuously and the corresponding Laplace operator of the view data in the floating image.

According to a further aspect in the invention, the step that derives first displacement field comprises the initial displacement field that input is given.

According to a further aspect in the invention, the method that is used for carrying out motion compensation between first and second image of time series comprises: derive corresponding first and second Feature Mapping by first and second image that corresponding resolution reduces; Derive first displacement field by handle first and second Feature Mapping according to registration Algorithm, this registration Algorithm comprises at each pixel or voxel finds the solution local Gaussian weighted least mean square problem, so that derive the respective vectors that forms this displacement field; Expand this first displacement field, to be consistent with the resolution of this first and second image; Derive second displacement field by handling first and second image based on first displacement field according to registration Algorithm; And utilize crooked this second image of this second displacement field, so that obtain the image that motion correction is crossed.

According to a further aspect in the invention, the method that is used for carrying out motion compensation between first and second image of time series comprises: derived first image series with the resolution that reduces gradually by first image; Derive second series image with the resolution that reduces gradually by second image; Derive the first serial Feature Mapping by first image series; Derive the second series Feature Mapping by the second series image; Derive serial displacement field by the Feature Mapping (these Feature Mapping have equal resolution) of handling the first serial Feature Mapping of corresponding Feature Mapping according to registration Algorithm with second series Feature Mapping, so that corresponding displacement field to be provided, this registration Algorithm comprises at each pixel or voxel finds the solution local Gaussian weighted least mean square problem, so that derive the respective vectors that forms this displacement field, begin with given displacement field, this given displacement field is used to derive the first minimum displacement field of level of resolution, and the direct displacement field the preceding of utilization is after this derived the next displacement field corresponding to the inferior high-resolution in this series; And to utilize level of resolution be that the last displacement field of the level of resolution of first and second image comes crooked this second image.

According to a further aspect in the invention, the method that is used for carrying out motion compensation between the reference picture of time series and floating image comprises: (a) reduce process with the resolution of corresponding first and second a plurality of cascades and handle reference picture and floating image, the reference picture and the floating image that provide corresponding a plurality of resolution to reduce continuously is provided, be called level 0 at this for the lowest resolution level, and be called level 1 for inferior higher levels of resolution, for the second time higher levels of resolution be called level 2, for any existing higher levels of resolution by that analogy; (b) be that the reference picture that corresponding a plurality of resolution of L0, L1, L2 reduce is continuously derived the corresponding a plurality of fixed reference feature mapping and the Feature Mapping of floating with floating image by tactic, the level of resolution that increase according to resolution, wherein L2 is the level of resolution of this reference picture and floating image; (c) derive first displacement field by handling according to registration Algorithm with the Feature Mapping of floating with the corresponding fixed reference feature mapping of horizontal L0, this registration Algorithm comprises based on given initial displacement field finds the solution local Gaussian weighted least mean square problem at each pixel or voxel, so that derive the respective vectors that forms this first displacement field; (d) this first displacement field is expanded to matched level of resolution, so that first displacement field that is expanded to be provided with resolution L1; (e) derive second displacement field by handling with the corresponding fixed reference feature mapping of level of resolution L1 based on first displacement field that is expanded with the Feature Mapping of floating, so that derive the respective vectors that forms this second displacement field according to this registration Algorithm; (f) this second displacement field is expanded to matched level of resolution, so that second displacement field that is expanded to be provided with resolution L2; (g),, derive last displacement field by handling with the Feature Mapping of floating, so that derive the respective vectors that forms last displacement field with the corresponding fixed reference feature mapping of level of resolution L2 based on second displacement field that is expanded according to this registration Algorithm; And (h) by utilizing crooked this floating image of this last displacement field.

According to a further aspect in the invention, the system that is used for the carries out image motion compensation comprises: memory storage is used for stored programme and other data; And with the processor of this storage communication, this processor moves this program and carries out: be used for the method for carrying out motion compensation between first and second image of time series, this method comprises: handle this first and second image with the process of reducing, first and second image that provides corresponding resolution to reduce is provided; Derive corresponding first and second Feature Mapping by first and second image that this corresponding resolution reduces; Derive displacement field by handle this first and second Feature Mapping according to registration Algorithm, this registration Algorithm comprises at each pixel or voxel finds the solution local Gaussian weighted least mean square problem, so that derive the respective vectors that forms this displacement field; And utilize crooked this second image of this displacement field.

According to a further aspect in the invention, a kind of computer program product comprises computer usable medium, this computer usable medium has the computer program logic that is recorded at program code thereon, be used for coming the carries out image motion compensation by the method that is used between first and second image of time series, carrying out motion compensation, this method comprises: handle this first and second image with the process of reducing, first and second image that provides corresponding resolution to reduce is provided; Derive corresponding first and second Feature Mapping by first and second image that this corresponding resolution reduces; Derive displacement field by handle this first and second Feature Mapping according to registration Algorithm, this registration Algorithm comprises at each pixel or voxel finds the solution local Gaussian weighted least mean square problem, so that derive the respective vectors that forms this displacement field; And utilize crooked this second image of this displacement field.

Description of drawings

The present invention is more fully understood from describe in detail in conjunction with the accompanying drawings, and described detailed description comprises the exemplary embodiment of back, in described accompanying drawing:

Fig. 1 illustrates in accordance with the principles of the present invention motion correction to temporal sequence of images with flowchart format; And

The schematically illustrated application that is used to realize programmable digital machine of the present invention of Fig. 2.

Embodiment

According to embodiments of the invention, patient's reference picture obtains by medical imaging program (such as utilizing MRI equipment), and floating image is being obtained than the reference picture moment a little later usually.Floating image can comprise owing to for example obtain after first image patient movement that cause with difference reference picture.Handle these images with the process of reducing, thereby produce as compare with original respective image resolution lower corresponding reference picture and floating image.Corresponding reference picture and floating image Feature Mapping derive from lower reference picture of resolution and floating image by deriving the lower reference picture of resolution and the corresponding Laplace operator of the view data in the floating image.Based on given initial displacement field, Feature Mapping is handled according to registration Algorithm with registration procedure.This algorithm comprises at each voxel finds the solution local Gaussian weighted least mean square problem, so that derive the respective vectors of the dense displacement field be formed for simulating distortion.Utilize this displacement field to make the floating image bending, so that obtain second image that motion correction is crossed.As mentioned above, the possible default condition of given initial displacement field is an empty set, and perhaps for example, given initial displacement field can be considered the priori of patient moving.

The tissue that the Gaussian weighted least mean square registration Algorithm that is used for mammary gland MR motion correction is used to relate in detection tumour provides motion correction, provides motion correction and the non-rigid registration algorithm that is used for mammary gland MR motion correction is used to relate in detection the tissue of tumour.Described distortion is modeled as dense displacement field, and it is by forming by finding the solution the vector that a series of local Gaussian weighted least mean square problem obtain, as will be described.

Utilize the dense displacement field between the registration Algorithm estimation stereo-picture.Purpose is the motion artifacts in compensation magnetic resonance (MR) temporal sequence of images.Usually, motion artifacts mainly be owing to breathing, heart movement, and patient's motion cause.Main application fields of the present invention is the research of Strength Changes in the mammary gland MR research.The time variation that contrast preparation sucks in breast tissue can be used to provide the information that helps detect damage.Calculate the spacial alignment accurately that this variation requires the breast tissue between the image acquisition.

Recognize at this, introduce Gauss's weighting of using the quick filter technology to be realized at least two advantages are provided, that is:

Introduce Gauss's weighting and provide a kind of simple and calculate effective and efficient manner and guarantee the smoothness of displacement field, thereby prevent singular point and the implicit model (implicitmodel) of transformation rule is provided); And

Introduce Gauss's weighting and guarantee that least mean square problems is by suitably formulistic.

In addition, image similarity is measured the calculating that depends on image laplacian in accordance with the principles of the present invention, rather than uses image intensity.The inventor finds, and this method is effective handling because of contrast preparation sucks aspect the Strength Changes that causes.Use the multiresolution strategy to improve the robustness of capture range, speed and this method.

The present invention will make an explanation in further detail by illustrated example.Concerning illustrated example of the present invention, suppose that the right intensity of image that will be registered is two real-valued functions

With

Ω  R ³(on the regular grid) sampled version, wherein those symbols have its conventional sense; Therefore, in this example, I ₂Be the function that comprises the maplet of input Ω and output R, wherein Ω is R ³Proper subclass, or the like.What note is to handle the situation of stereo-picture here; But research and development subsequently extend to any dimension easily.

Below, with I ₁Be called reference picture, and with I ₂Be called floating image.Registration problems is defined as finds displacement field

(this will estimate with net point), this displacement field

With I ₁Curved version I with floating image ₂Similarity maximization between the ο (id+p) (wherein id is the sign mapping, and ο is a composite operator).

Image intensity is not always carried out the best feature of registration task.From this view point, with by I ₁And I ₂The auxiliary function that calculates

With

Working together is useful sometimes, and described auxiliary function is represented other characteristics of image (for example image laplacian, the perhaps norm of image gradient).Especially in the application to mammary gland MR, the computed image Laplace operator is very effective always in practice.

This algorithm is an iteration.This algorithm comprises that foundation is to " real " sports ground convergent displacement field sequence p ⁰, p ¹..., p ^kLast " motion correction is crossed " image is by I ₂ο (id+p ^k) provide.The iteration that displacement field is described below makes up, and the iteration of this displacement field makes up the core that forms this registration technology.

Iterative program is used to meticulous multiresolution strategy in conjunction with coarse.The advantage of this method is:

The risk that falls into local minimum by reduction improves capture range; And

Assess the cost by working to reduce with the lower data of resolution still less.

The multiresolution strategy can be described by following example:

By being averaged and sub sampling sets up two multiresolution pyramids at reference picture and floating image.Such pyramid construction is the standard technique of Flame Image Process; Detailed content is for example with reference to the textbook Digital ImageProcessing (second edition, Prentice-Hall, 2002) that is write by 2.R.Gonzales and R.Woods.

Make I ₁ ^lAnd I ₂ ^lBe that resolution is 1 resulting image.

Calculating is marked as J ₁ ^lAnd J ₂ ^lThe character pair image.

Make p ^{K, l}Be the displacement field that after the k time iteration in resolution 1 place, obtains.p ^0,0Initial displacement field (normally null field) when expression resolution is minimum.At resolution 1 place, as below will further explaining, the iteration of operation registration Algorithm fixed number.By trilinearly interpolated method and convergent-divergent displacement field is expanded to next resolution.This result is used as initial displacement field p ^{0, l+1}

Carry out the operation of front, until reaching original resolution.

Mode with summary diagrammatic in Fig. 1 illustrates these steps.With reference to Fig. 1, resolution is represented as " 1 ".By exemplary embodiment and for the purpose of graphic extension, three levels shown in this figure; More or less spread step is considered within the scope of the invention.In Fig. 1, be illustrated as I respectively ₁And I ₂, level of resolution is l=l _Max=2 reference picture and floating image reduce process through first, thereby obtain the respective image I that resolution is l=1 ₁ ¹And I ₂ ¹, another reduce process after, resulting image is respectively that level of resolution is the I of l=0 ₁ ⁰And I ₂ ⁰Feature Mapping J ₁ ⁰And J ₂ ⁰Derive from image I respectively ₁ ⁰And I ₂ ⁰Feature Mapping J ₁ ⁰And J ₂ ⁰Use given initial displacement field p ^0,0Experience registration process as the described herein.This initial displacement field can be arbitrarily and can be zero.Registration process obtains displacement field p ^{K, 0}, this displacement field p ^{K, 0}Compare with initial displacement field and to be considered to improved displacement field.Then, displacement field p ^{K, 0}Experience and corresponding expansion of image resolution ratio l=1 or expansion, thus cause producing the resolution field p that is expanded ^0,1

Feature Mapping J ₁ ¹And J ₂ ¹Derive from image I respectively ₁ ¹And I ₂ ¹Feature Mapping J ₁ ¹And J ₂ ¹Use the displacement field p that is expanded that derives previously ^0,1Experience registration process as the described herein, so that obtain displacement field p ^{K, 1}, this displacement field p ^{K, 1}Be extended to p ^0,2To image I ₁ ²And I ₂ ²Carry out and similar step, image I ₁ ²And I ₂ ²Cause producing last deformation field, this last deformation field is used to carry out the last bending to image I 2, with produce as here explained by I ₂The image that the motion correction of ο (id+p) representative is crossed.

What it should be noted that is only the intrinsic parameters of this algorithm to be set at as follows:

The number of pyramid level,

At the number of each horizontal iteration, and

The regularization parameter σ of the smoothness of control displacement field: this parameter of following discussion.

According to principle of the present invention, after describing Feature Mapping calculating, next set forth more detailed description according to Gaussian weighted least mean square algorithm of the present invention.

At first the key concept of registration technology will be described especially.Iterative program below given resolution place carries out.Level of resolution 1 in the following representation is omitted.

Make G _σ(x) be the isotropic three-dimensional gaussian kernel of standard deviation:

$G_{\mathrm{\σ}}\left(x\right)=\frac{1}{\sqrt{{\left(2\mathrm{\π}\right)}^3{\mathrm{\σ}}^6}}{e}^{\frac{{\left|\right|x\left|\right|}^2}{{\mathrm{\σ}}^2}}$

Each voxel comes mark by subscript j.Its coordinate is by vector x _j∈ R ³Provide.Will $p_j^k\∈R^3$ Be called the k time iteration of this algorithm afterwards in a displacement vector that the xj place regains.Suppose one group of displacement vector p _j ^k, the correction versions of the unsteady Feature Mapping when the k time iteration is represented as J _{2, k}:

$\&ForAll;j,{\mathrm{<figure-callout\; id="2"\; label="J"\; filenames="A20058003734800241.png"\; state="\{\{state\}\}">J</figure-callout>}}_{2,k}\left(x_j\right)=J_2(x_j+p_j^k)$

At each voxel j place, the s that separates with non-linear least mean square problems is proposed _j ^kDefine update rule $p_j^{k+1}=p_j^k+s_j^k:$

$\underset{s_j^k}{\min }\underset{i}{\mathrm{\&Sigma;}}{G}_{\mathrm{\&sigma;}}(x_j-x_i)\&CenterDot;{\left(z_i^k\left(s_j^k\right)\right)}^2$

Wherein, $z_i^k\left(s\right)=J_1\left(x_i\right)-{\mathrm{<figure-callout\; id="2"\; label="J"\; filenames="A20058003734800241.png"\; state="\{\{state\}\}">J</figure-callout>}}_{2,k}(x_i+s).$ Gauss's weighting allows control to be used to estimate the neighborhood size (implicity) of displacement.As spinoff, the whole smoothness of deformation field is also guaranteed in Gauss's weighting.

In practice, the linearization version of front problem is found the solution by minimizing following benchmark:

$E\left(s_j^k\right)=\underset{i}{\mathrm{\&Sigma;}}{G}_{\mathrm{\&sigma;}}(x_j-x_i)\&CenterDot;{(z_i^k\left(0\right)+{\&dtri;z}_i^k{\left(0\right)}^T\&CenterDot;s_j^k)}^2$

Wherein,  z _i ^k(s) be defined as ${\&dtri;z}_i^k\left(s\right)=-{\&dtri;\mathrm{<figure-callout\; id="2"\; label="J"\; filenames="A20058003734800241.png"\; state="\{\{state\}\}">J</figure-callout>}}_{2,k}(x_i+s).$

By calculating E (s _j ^k) first modification, the necessary condition of optimality

$\&ForAll;h,\mathrm{dE}\left(s_j^k\right)\&CenterDot;h=0$

Produce s _j ^kRecurrence, closed form separate (closed-form solution):

$s_j^k=-{\left(\underset{i}{\mathrm{\&Sigma;}}{G}_{\mathrm{\&sigma;}}(x_j-x_i){\&dtri;z}_i^k\left(0{\&dtri;z}_i^k{\left(0\right)}^T\right)\right)}^{-1}\left(\underset{i}{\mathrm{\&Sigma;}}{G}_{\mathrm{\&sigma;}}(x_j-x_i){\&dtri;z}_i^k\left(0\right)z_i^k\left(0\right)\right).$

That notices is matrix  z _i ^k(0)  z _i ^k(0) ^TBe the symmetry and can characterize by 6 coefficients.Vector  z _i ^k(0) z _i ^k(0) by 3 coefficient definition.

In case calculated these coefficients, as can be seen, estimated that the displacement renewal reduces to execution and by gaussian kernel matrix and vector coefficients carried out convolution, and reduce to 3 * 3 symmetrical linear problems of finding the solution each net point place.

Convolution is used as document " Fast algorithms for low-level vision " (the IEEE Transactions on Pattern Analysis andMachine Intelligence at R.Deriche, 1 (12), nineteen ninety, 78-88 page or leaf) the second order regressive filter that is proposed is similar to.These wave filters have reduced the level and smooth and desired amount of calculation of derivative of approximate Gaussian.Utilize this method, irrespectively multiplication and addition that each output point carries out fixed number are carried out these operations with the wave filter size.

Recurrence, closed form are separated and are used to 3 * 3 linear problems.If $\underset{i}{\mathrm{\&Sigma;}}{G}_{\mathrm{\&sigma;}}(x_j-x_i)\&dtri;z_i^k\left(0\right)\&dtri;z_i^k{\left(0\right)}^T$ Provide by following symmetric matrix:

$A=\left(\begin{array}{ccc}{a}_1& a_2& a_3\\ a_2& a_4& a_5\\ a_3& a_5& a_6\end{array}\right)$

Its inverse matrix is so

$A^{-1}=\frac{1}{a_6{a}_1{a}_4-a_1{a_5}^2-a_6{a_2}^2+2a_2{a}_3{a}_5-a_4{a_3}^2}\left(\begin{array}{ccc}{c}_1& c_2& c_3\\ c_2& c_4& c_5\\ c_3& c_5& c_6\end{array}\right)$

Wherein

$\left\{\begin{array}{c}{c}_1=a_6{a}_4-{a_5}^2\\ c_2=a_3{a}_5-a_6{a}_2\\ c_3=a_2{a}_5-a_3{a}_4\\ c_4=a_1{a}_6-{a_3}^2\\ c_5=a_3{a}_2-a_1{a}_5\\ c_6=a_1{a}_4-{a_2}^2\end{array}\right.$

In all in front calculating, when outside net point, needing numerical value, use the trilinearly interpolated method.

What Feature Mapping was calculated is described below.In mammary gland MR, contrast preparation sucks may be significantly or changed the intensity level of observed tissue partly.Do not rely on intensity, get function J at registration ₁And J ₂Value as the Laplace operator of raw data.This idea mainly concentrates on the marginal information in the image (characterizing the zero passage of the Laplace operator at edge), the influence that this is sucked by contrast preparation seldom.It is very effective in practice that this method is proved to be.Use now cartesian coordinate system with ternary integer (i ₁, i ₂, i ₃) identify voxel, and following method of finite difference is used to Laplace operator:

$J_2({\mathrm{<figure-callout\; id="1"\; label="i"\; filenames="A20058003734800241.png"\; state="\{\{state\}\}">i</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="A20058003734800241.png"\; state="\{\{state\}\}">i</figure-callout>}}_2,i_3)=\frac{I_2({\mathrm{<figure-callout\; id="1"\; label="i"\; filenames="A20058003734800241.png"\; state="\{\{state\}\}">i</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="A20058003734800241.png"\; state="\{\{state\}\}">i</figure-callout>}}_2,i_3+1)}{{\mathrm{\&lambda;}}^2}+\frac{I_2({\mathrm{<figure-callout\; id="1"\; label="i"\; filenames="A20058003734800241.png"\; state="\{\{state\}\}">i</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="A20058003734800241.png"\; state="\{\{state\}\}">i</figure-callout>}}_2,i_3-1)}{{\mathrm{\&lambda;}}^2}+I_2({\mathrm{<figure-callout\; id="1"\; label="i"\; filenames="A20058003734800241.png"\; state="\{\{state\}\}">i</figure-callout>}}_1,i_2+1,i_3)+I_2({\mathrm{<figure-callout\; id="1"\; label="i"\; filenames="A20058003734800241.png"\; state="\{\{state\}\}">i</figure-callout>}}_1,i_2-1,i_3)$

$+I_2({\mathrm{<figure-callout\; id="1"\; label="i"\; filenames="A20058003734800241.png"\; state="\{\{state\}\}">i</figure-callout>}}_1+1,{\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="A20058003734800241.png"\; state="\{\{state\}\}">i</figure-callout>}}_2,i_3)+I_2(i_1-1,{\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="A20058003734800241.png"\; state="\{\{state\}\}">i</figure-callout>}}_2,i_3)-(4+\frac{2}{{\mathrm{\&lambda;}}^2})I_2({\mathrm{<figure-callout\; id="1"\; label="i"\; filenames="A20058003734800241.png"\; state="\{\{state\}\}">i</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="A20058003734800241.png"\; state="\{\{state\}\}">i</figure-callout>}}_2,i_3)$

What note is, the central difference method that is used to estimate Laplace operator is considered the anisotropy of voxel.Coefficient lambda corresponding to along the 3rd voxel spacing (distance between the section) with along the ratio between the pel spacing (it is identical being assumed to be here) of preceding two axles.

Same equation is used for by I ₁Calculate J ₁

As will be apparent, the invention is intended to use and application programming digital machine realizes.Fig. 2 shows to be coupled with the form of basic signal and is used for input media, output unit and is used for stored programme and the memory storage of other data carries out the digital processing unit of bidirectional data communication.Input media is designated as the device of the one or more images that are used to provide suitable with term widely, and these images are used for handling according to the present invention.For example, input can come from imaging device, such as from the device that is merged in CATSCAN, x ray machine, MRI or other device, maybe this input is the image of being stored, maybe should input (for example pass through direct infrared beam, radio, landline, fax or the satellite that connects, modulated, by WWW or the Internet) communicate with another computing machine or device, maybe this input is any other suitable this data source.Output unit can comprise the computer type display device of using any suitable equipment (such as cathode-ray kinescope, plasma display, LCD or the like), or this output unit can or can not comprise the device that is used for reproduced image and the memory storage that can comprise Fig. 2 for convenience or this memory storage of part, this memory storage is used for memory image further handling or to check or assess, or this output unit can utilize and comprises connection relevant with input media as mentioned above or coupling.The program that is used to realize step of the present invention that the processor operation is set up according to the present invention.This computing machine that is programmed is easy to connect through communication media (such as landline, radio, the Internet etc.), is used for gathering and transmit image data.

The present invention easily (to small part) realizes or is encapsulated in the software memory storage that forms software product with the software memory storage.This can be the form of computer program, this computer program comprises computer usable medium, this computer usable medium has the computer program logic that is recorded at program code thereon, is used to utilize method carries out image of the present invention motion compensation.

Though the present invention explains by the example that makes the exemplary embodiment that illustrates, this embodiment relates to the motion compensation of the temporal sequence of images in the potential tumor of MRI human body breast, but the present invention also can be used to usually solve the spacial alignment that requires in other (such as, but be not limited to the example of PET-CT registration) problem.

Should be understood that the explanation by exemplary embodiment is not intended to limit, and do not breaking away under the situation of its scope by subsequently the spirit of the present invention that claim limited, also can carry out various variations and the displacement clearly do not described at this.

Claims (44)

1. one kind is used for the method for carrying out motion compensation between first and second image of time series, and described method comprises:

Derive corresponding first and second Feature Mapping by described first and second image;

Derive displacement field by handling described first and second Feature Mapping according to registration Algorithm, described registration Algorithm comprises at each pixel or voxel finds the solution local Gaussian weighted least mean square problem, so that derive the respective vectors that forms described displacement field; And

Utilize crooked described second image of described displacement field.

2. the method that is used to carry out motion compensation according to claim 1, wherein, the step of described derivation displacement field utilizes the displacement field of deriving previously to derive described displacement field.

3. the method that is used to carry out motion compensation according to claim 2, wherein, the step of described derivation displacement field is utilized given initial displacement field at the described displacement field of initial derivation.

4. the method that is used to carry out motion compensation according to claim 3, wherein: the default condition of described given initial displacement field is an empty set.

5. the method that is used to carry out motion compensation according to claim 3, wherein: described given initial displacement field is considered the priori of patient moving.

6. the method that is used to carry out motion compensation according to claim 2, comprise the step that repeats to derive displacement field, wherein on than first and second Feature Mapping that last time repeats to have more high-resolution described first and second image, carrying out each the repetition.

7. the method that is used to carry out motion compensation according to claim 2, wherein, each recycling is by the displacement field from direct derivation before preceding step.

8. the method that is used to carry out motion compensation according to claim 7, wherein, the step of described derivation displacement field is utilized given displacement field at the described displacement field of initial derivation.

9. the method that is used to carry out motion compensation according to claim 7, wherein:

The step of described derivation displacement field comprises the level of resolution that described displacement field of deriving is previously expanded to the version of described resolution increase.

10. the method that is used to carry out motion compensation according to claim 7 comprises that utilization produces the image that motion correction is crossed for the displacement field that described second image of bending exists, derives at highest resolution.

11. the method that is used to carry out motion compensation according to claim 7, wherein:

The step of corresponding first and second Feature Mapping of described derivation comprises the corresponding Laplace operator that derives the view data in first and second image that corresponding resolution reduces.

12. one kind is used for the method for carrying out motion compensation between first and second image of time series, described method comprises:

Handle described first and second image with the process that reduces, first and second image that provides corresponding resolution to reduce is provided;

Derive corresponding first and second Feature Mapping by first and second image that corresponding resolution reduces, described Feature Mapping comprises the corresponding Laplace operator that derives the view data in first and second image that corresponding resolution reduces;

Derive displacement field by handling described first and second Feature Mapping according to registration Algorithm, described registration Algorithm comprises finds the solution the local Gaussian least mean square problems to each pixel or voxel, so that derive the respective vectors that forms this displacement field; And

Utilize crooked this second image of described displacement field.

13. one kind is used for the method for carrying out motion compensation between first and second image of time series, described method comprises:

Handle described first and second image with the process that reduces, first and second image that provides corresponding resolution to reduce is provided;

Derive corresponding first and second Feature Mapping by first and second image that corresponding resolution reduces;

Derive displacement field by handling described first and second Feature Mapping according to registration Algorithm, described registration Algorithm comprises finds the solution local Gaussian weighted least mean square problem to each pixel or voxel, so that derive the respective vectors that forms described displacement field; And

Utilize crooked described second image of described displacement field.

14. the method that is used to carry out motion compensation according to claim 13, wherein:

The step of corresponding first and second Feature Mapping of described derivation comprises the corresponding Laplace operator that derives the view data in first and second image that corresponding resolution reduces.

15. the method that is used to carry out motion compensation according to claim 13, wherein:

The step of described derivation displacement field is utilized initial displacement field.

16. the method that is used to carry out motion compensation according to claim 15, wherein:

The default condition of described initial displacement field is an empty set.

17. the method that is used to carry out motion compensation according to claim 15, wherein: described initial displacement field is considered the priori of patient moving.

18. the method that is used to carry out motion compensation according to claim 13, wherein:

The described step of handling described first and second Feature Mapping according to registration Algorithm comprises described displacement field is expanded to step with the matched level of resolution of level of resolution of described second image.

19. one kind is used for the method for carrying out motion compensation between the reference picture of time series and floating image, described method comprises:

Derive first group of correction image that resolution reduces gradually by described reference picture;

Derive second group of correction image that resolution reduces gradually by described floating image;

Derive the mapping of first stack features by described first group of correction image;

Derive the mapping of second stack features by described second group of correction image;

According to registration Algorithm, lowest resolution ingredient and given initial displacement field in each Feature Mapping from first and second stack features shines upon respectively derive first displacement field, described registration Algorithm comprises at each pixel or voxel finds the solution the local Gaussian least mean square problems, so that derive the respective vectors that forms described displacement field;

According to described registration Algorithm, inferior lowest resolution ingredient in each Feature Mapping from first and second stack features shines upon respectively and described first displacement field that is obtained in previous step are derived second displacement field;

If there is resolution higher ingredient continuously in each Feature Mapping in first and second stack features mapping, then repeat abovementioned steps at these ingredients, and all use the displacement field that is obtained in the step before current step in each case, until the resolution that reaches described floating image, if there is no the higher ingredient of resolution then is directly to next step; And

Utilize the crooked described floating image of the last displacement field that obtains.

20. the method that is used to carry out motion compensation according to claim 19, wherein:

The step of described derivation Feature Mapping comprises the Laplace operator that derives the view data in the respective image.

21. the method that is used to carry out motion compensation according to claim 19, wherein:

The step of described derivation displacement field may further comprise the steps: expansion if desired then expands to described displacement field and described the matched level of resolution of higher levels of resolution.

22. the method that is used to carry out motion compensation according to claim 19, wherein:

The default condition of described given initial displacement field is an empty set.

23. the method that is used to carry out motion compensation according to claim 19, wherein:

Described given initial displacement field is considered the priori of patient moving.

24. one kind is used for the method for carrying out motion compensation between the reference picture of time series and floating image, described method comprises:

(a) reduce process with the resolution of corresponding first and second a plurality of cascades and handle described reference picture and floating image, the reference picture and the floating image that provide corresponding a plurality of resolution to reduce continuously is provided, be called level 0 at this for the lowest resolution level, and be called level 1 for inferior higher levels of resolution, to the second time higher levels of resolution be called level 2, to any existing higher levels of resolution by that analogy;

(b) be that reference picture and the floating image that described corresponding a plurality of resolution of L0, L1, L2 etc. reduce continuously derived corresponding a plurality of fixed reference feature mapping and floated Feature Mapping by level of resolution;

(c) derive first displacement field by handling according to registration Algorithm with the Feature Mapping of floating with the corresponding fixed reference feature mapping of horizontal L0, described registration Algorithm comprises based on given initial displacement field finds the solution local Gaussian weighted least mean square problem at each pixel or voxel, so that derive the respective vectors that forms described first displacement field;

(d) described first displacement field is expanded to matched level of resolution, so that first displacement field that is expanded to be provided with resolution L1;

(e) derive second displacement field by handling with the corresponding fixed reference feature mapping of level of resolution L1 based on described first displacement field that is expanded with the Feature Mapping of floating, so that derive the respective vectors that forms described second displacement field according to described registration Algorithm;

(f) described second displacement field is expanded to and the matched level of resolution of the displacement field of resolution L1, so that second displacement field that is expanded to be provided;

(g) derive the triple motion field by handling with the corresponding fixed reference feature mapping of level of resolution L2 based on described second displacement field that is expanded with the Feature Mapping of floating, so that derive the respective vectors that forms described second displacement field according to described registration Algorithm; And

(h) if L2 is the level of resolution of described reference picture and floating image, so by utilizing described triple motion field to come crooked described floating image and end; And if L2 is not the level of resolution of described reference picture and floating image, then

(i) described triple motion field is expanded to and time matched level of resolution of higher levels of resolution, so that the triple motion field that is expanded to be provided; And

(j) repeat from the series of steps of step (g) beginning, suitably revise level of resolution, to obtain and the more and more higher corresponding displacement field of level of resolution based on the last displacement field that is expanded that obtains in front, up to the level of resolution that reaches described reference picture and floating image, and therefore utilize crooked described floating image of the last displacement field that is obtained and end.

25. the method that is used to carry out motion compensation according to claim 24, wherein: the described step that reference picture that corresponding a plurality of resolution reduces continuously and floating image be provided comprises derives the reference picture that described corresponding a plurality of resolution reduce continuously and the corresponding Laplace operator of the view data in the floating image.

26. the method that is used to carry out motion compensation according to claim 24, wherein: the step of described derivation first displacement field comprises the initial displacement field that input is given.

27. one kind is used for the method for carrying out motion compensation between first and second image of time series, described method comprises:

Derive corresponding first and second Feature Mapping by first and second image that corresponding resolution reduces;

Derive first displacement field by handling described first and second Feature Mapping according to registration Algorithm, described registration Algorithm comprises at each pixel or voxel finds the solution local Gaussian weighted least mean square problem, so that derive the respective vectors that forms described displacement field;

Expand described first displacement field, to be consistent with the resolution of described first and second image;

Derive second displacement field by handling described first and second image based on described first displacement field according to described registration Algorithm; And

Utilize crooked described second image of described second displacement field, so that obtain the image that motion correction is crossed.

28. the method that is used to carry out motion compensation according to claim 27, wherein: the step of described derivation first displacement field comprises the step of the initial displacement field that input is given.

29. the method that is used to carry out motion compensation according to claim 28, wherein: the default condition of described given initial displacement field is an empty set.

30. the method that is used to carry out motion compensation according to claim 28, wherein: described given initial displacement field is considered the priori of patient moving.

31. the method that is used to carry out motion compensation according to claim 27, wherein: the step of corresponding first and second Feature Mapping of described derivation comprises the corresponding Laplace operator that derives the view data in first and second image that corresponding resolution reduces.

32. one kind is used for the method for carrying out motion compensation between first and second image of time series, described method comprises:

Derive first image series with the resolution that reduces gradually from described first image;

Derive second series image with the resolution that reduces gradually from described second image;

Derive the first serial Feature Mapping from described first image series;

Derive the second series Feature Mapping from described second series image;

Derive serial displacement field by the Feature Mapping of handling the described first serial Feature Mapping of corresponding Feature Mapping according to the registration Algorithm that is used to provide corresponding displacement field with described second series Feature Mapping, the described second series Feature Mapping and the described first serial Feature Mapping belong to equal resolution, described registration Algorithm comprises at each pixel or voxel finds the solution local Gaussian weighted least mean square problem, so that derive the respective vectors that forms described displacement field, begin with given displacement field, this given displacement field is used to derive the first minimum displacement field of level of resolution, and after this utilize directly displacement field the preceding derive with described series in corresponding next displacement field of inferior high-resolution; And

Utilization comes crooked described second image at the last displacement field of the level of resolution derivation of described first and second image.

33. the method that is used to carry out motion compensation according to claim 32 comprises:

Except described given and described back court, expand described each resolution field, to be consistent with inferior high-resolution.

34. one kind is used for the method for carrying out motion compensation between the reference picture of time series and floating image, described method comprises:

(a) reduce process with the resolution of corresponding first and second a plurality of cascades and handle described reference picture and floating image, the reference picture and the floating image that provide corresponding a plurality of resolution to reduce continuously is provided, be called level 0 at this for the lowest resolution level, and be called level 1 for inferior higher levels of resolution, for the second time higher levels of resolution be called level 2, to any existing higher levels of resolution by that analogy;

(b) be that the reference picture that described corresponding a plurality of resolution of L0, L1, L2 reduce is continuously derived the corresponding a plurality of fixed reference feature mapping and the Feature Mapping of floating with floating image by tactic, the level of resolution that increase according to resolution, wherein L2 is the level of resolution of described reference picture and floating image;

(c) derive first displacement field by handling according to registration Algorithm with the Feature Mapping of floating with the corresponding fixed reference feature mapping of horizontal L0, described registration Algorithm comprises based on given initial displacement field finds the solution local Gaussian weighted least mean square problem to each pixel or voxel, so that derive the respective vectors that forms described first displacement field;

(d) described first displacement field is expanded to matched level of resolution, so that first displacement field that is expanded to be provided with resolution L1;

(e) derive second displacement field by handling with the corresponding fixed reference feature mapping of level of resolution L1 based on described first displacement field that is expanded with the Feature Mapping of floating, so that derive the respective vectors that forms described second displacement field according to described registration Algorithm;

(f) described second displacement field is expanded to matched level of resolution, so that second displacement field that is expanded to be provided with resolution L2;

(g) derive last displacement field by handling with the corresponding fixed reference feature mapping of level of resolution L2 based on described second displacement field that is expanded with the Feature Mapping of floating, so that derive the respective vectors that forms described last displacement field according to described registration Algorithm; And

(h) by utilizing the crooked described floating image of described last displacement field.

35. the method that is used to carry out motion compensation according to claim 34, wherein: the default condition of described given initial displacement field is an empty set.

36. the method that is used to carry out motion compensation according to claim 34, wherein: described given initial displacement field is considered the priori of patient moving.

37. the method that is used to carry out motion compensation according to claim 34, wherein:

The step of described derivation Feature Mapping comprises the corresponding Laplace operator that derives the view data in first and second image that corresponding resolution reduces.

38. the method that is used to carry out motion compensation according to claim 34, wherein:

The step (c) that derives first displacement field may further comprise the steps:

With each voxel of subscript j mark, the coordinate of this voxel is by vector x _j∈ R ³Provide;

Will $p_j^k\&Element;R^3$ Be defined as described algorithm and carry out the k time iteration afterwards at x _jThe displacement vector that the some place regains;

Given one group of displacement vector p _j ^k, by J _{2, k}The corrected version of described unsteady Feature Mapping when being illustrated in iteration k:

$\&ForAll;j,J_{2,k}\left(x_j\right)=J_2(x_j+p_j^k);$

At each voxel j s _j ^kWith update rule $p_j^{k+1}=p_j^k+s_j^k$ Be defined as separating of non-linear least mean square problems:

$\underset{s_j^k}{\min }\underset{i}{\mathrm{\&Sigma;}}{G}_{\mathrm{\&sigma;}}(x_j-x_i)\&CenterDot;{\left(z_i^k\left(s_j^k\right)\right)}^2$

Wherein $z_i^k\left(s\right)=J_1\left(x_i\right)-J_{2,k}(x_i+s)$ And G _σ(x) be the three-dimensional gaussian kernel of isotropy of standard deviation:

$G_{\mathrm{\&sigma;}}\left(x\right)=\frac{1}{\sqrt{{\left(2\mathrm{\&pi;}\right)}^3{\mathrm{\&sigma;}}^6}}{e}^{-\frac{{\left|\right|x\left|\right|}^2}{{\mathrm{\&sigma;}}^2}};$

Find the solution the linearization version of described non-linear least mean square problems by minimizing following standard:

$E\left(s_j^k\right)=\underset{i}{\mathrm{\&Sigma;}}{G}_{\mathrm{\&sigma;}}(x_j-x_i)\&CenterDot;{(z_i^k\left(0\right)+\&dtri;z_i^k{\left(0\right)}^T\&CenterDot;s_j^k)}^2$

Wherein,  z _i ^k(s) be defined as $\&dtri;z_i^k\left(s\right)=-\&dtri;J_{2,k}(x_i+s);$

Calculate E (s _j ^k) first modification, the necessary condition of optimality

$\&ForAll;h,\mathrm{dE}\left(s_j^k\right)\&CenterDot;h=0$

To produce s _j ^kRecurrence, closed form separate:

$s_j^k=-{(\underset{i}{\mathrm{\&Sigma;}}{G}_{\mathrm{\&sigma;}}(x_j-x_i){\&dtri;z}_i^k\left(0\right)\&dtri;z_i^k{\left(0\right)}^T)}^{-1}(\underset{i}{\mathrm{\&Sigma;}}{G}_{\mathrm{\&sigma;}}(x_j-x_i)\&dtri;z_i^k\left(0\right)z_i^k\left(0\right)).$

39. a system that is used for the carries out image motion compensation, it comprises:

Memory storage is used for stored programme and other data; And

With the processor that described memory storage communicates, described processor moves described program and carries out:

Be used for the method for carrying out motion compensation between first and second image of time series, described method comprises:

Handle described first and second image with the process that reduces, first and second image that provides corresponding resolution to reduce is provided;

Derive corresponding first and second Feature Mapping by first and second image that corresponding resolution reduces;

Derive displacement field by handling described first and second Feature Mapping according to registration Algorithm, described registration Algorithm comprises finds the solution local Gaussian weighted least mean square problem to each pixel or voxel, so that derive the respective vectors that forms described displacement field; And

Utilize crooked described second image of described displacement field.

40. a computer program product that comprises computer usable medium, this computer usable medium have the computer program logic that is recorded at program code thereon, are used for carries out image motion compensation by the following method:

Be used for the method for carrying out motion compensation between first and second image of time series, described method comprises:

Handle described first and second image with the process that reduces, first and second image that provides corresponding resolution to reduce is provided;

Derive corresponding first and second Feature Mapping by first and second image that corresponding resolution reduces;

Derive displacement field by handling described first and second Feature Mapping according to registration Algorithm, described registration Algorithm comprises at each pixel or voxel finds the solution local Gaussian weighted least mean square problem, so that derive the respective vectors that forms described displacement field; And

Utilize crooked described second image of described displacement field.

41. one kind is used for the method for carrying out motion compensation between first and second image of time series, described method comprises:

Derive displacement field by handling described first and second image according to a process, described process comprises registration Algorithm, described registration Algorithm comprises at each pixel or voxel finds the solution local Gaussian weighted least mean square problem, so that derive the respective vectors that forms described displacement field; And

Utilize crooked described second image of described displacement field.

42. according to the described method that is used to carry out motion compensation of claim 41, wherein, described step according to described first and second image of process processing comprises the step that is derived corresponding first and second Feature Mapping and described registration Algorithm is used for described Feature Mapping by described first and second image respectively.

43. according to the described method that is used to carry out motion compensation of claim 41, wherein, the step of described derivation displacement field utilizes the displacement field of deriving previously to derive described displacement field.

44. according to the described method that is used to carry out motion compensation of claim 41, wherein, the step of described derivation displacement field is utilized given initial displacement field at the described displacement field of initial derivation.

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