CN107133975A - Heart CT TEE method for registering based on valve alignment and probability graph - Google Patents

Heart CT TEE method for registering based on valve alignment and probability graph Download PDF

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CN107133975A
CN107133975A CN201710242632.2A CN201710242632A CN107133975A CN 107133975 A CN107133975 A CN 107133975A CN 201710242632 A CN201710242632 A CN 201710242632A CN 107133975 A CN107133975 A CN 107133975A
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CN107133975B (en
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缑水平
陈琳琳
庄建
黄美萍
杨淑媛
焦李成
黄力宇
李军
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GUANGDONG PROV CARDIOVASCULAR DISEASE INST
Xidian University
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis
    • G06T7/30—Determination of transform parameters for the alignment of images, i.e. image registration
    • G06T7/33—Determination of transform parameters for the alignment of images, i.e. image registration using feature-based methods
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/10—Image acquisition modality
    • G06T2207/10072—Tomographic images
    • G06T2207/10081—Computed x-ray tomography [CT]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/30—Subject of image; Context of image processing
    • G06T2207/30004—Biomedical image processing
    • G06T2207/30048—Heart; Cardiac

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Abstract

The invention discloses a kind of heart CT TEE method for registering based on valve alignment and probability graph, the problem of prior art cardiac CT is difficult to registering with TEE images because mode difference is huge is mainly solved.Its implementation process is：Formula is interacted to CT and TEE images respectively to split and introduce cardiac valves endpoint location, is obtained segmentation figure picture and cardiac valves endpoint location, is regard the locus of valve as prior information；Basis registration is carried out to CT and TEE images based on prior information；Region enhancing is carried out to CT and TEE images, and grey level enhancement is carried out to its segmentation figure, the probability graph of CT and TEE images is generated；Normalization based on probability graph simultaneously uses the registering transformation matrix in basis as the initial parameter of optimizing algorithm in final registration, and finally registration is carried out to CT and TEE images.The present invention can more accurately realize it is registering with TEE cardiac images to CT, available for the recognition and tracking to cardiac anatomy.

Description

Heart CT-TEE method for registering based on valve alignment and probability graph
Technical field
It is more particularly to a kind of to heart CT and the method for registering of TEE images the invention belongs to technical field of image processing, can For the recognition and tracking to cardiac anatomy.
Background technology
With the fast development of medical imaging technology and computer processing technology, the mode of medical imaging is more and more richer Richness, such as CT, MR, PET, SPECT, ultrasonoscopy.There is very big otherness, multi-modal medical science between different image modes A variety of images are combined by merging the image-forming informations of different modalities, several are shown on same piece image by image registration The image-forming information of image, the purpose is to which diversified information is fused in same piece image exactly, so as to more smart Really focus and anatomical structure from all angles.
According to different weighing criterias, image registration has different mode classifications, for example, according to the classification of space dimensionality, The classification for the feature being based on according to the classification of mapping mode, the classification according to optimized algorithm, according to algorithm, according to what is used Classification of similarity measure etc.；According to Spatial Dimension, image registration can be divided into 2D-2D, 2D-3D, 3D-3D registration.According to sky Between mapping mode difference, can be divided into rigid body translation and non-rigid conversion.The selection of optimized algorithm is also in image registration Various, generally there are gradient descent method, Newton method, Powell methods, genetic algorithm etc..The feature that medical image can be extracted is very It is abundant, generally include characteristic point, surface texture, image pixel intensities and surface etc..The registration of distinguished point based refers to pass through The feature point set that can be positioned for geometrically having special meaning is chosen at, such as discontinuity point, the turning point of figure, line intersects Point, medically point with anatomically significant etc., and carry out coordinate matching；Registration based on surface refers to by way of segmentation The profile for extracting interesting image regions is used as the feature space of registration；Registration based on pixel value refers to utilize entire image Pixel value or voxel value constitutive characteristic space；For medical image, the registration based on surface refers to by person under inspection Internal fixation mark thing or to internal injection developing materials to obtain the mark point of the determination on image.According to the phase used The difference estimated like property, image registration can be divided into the registration based on cross-correlation, registration based on mutual information etc. again.
Mutual information method by propositions such as Collignon is one of focus for studying in recent years, particularly in multi-modal medical science In image registration field.Abroad, it is Viola etc. to carry out medical figure registration using mutual information method at first.Have again afterwards Person proposes many innovatory algorithms on the basis of mutual information, and Maes etc. proposes normalized mutual information, reduces traditional mutual Information is used as susceptibility of the measure function to the registering image overlapping region of two width.Josien proposes a kind of mutual information combination gradient Similarity measurement criterion GMI, be successfully applied to the heterologous image such as MR, CT, PET registration on.Fan et al. is by wavelet transformation Combined with mutual information, on the registration for being successfully applied to visible images and infrared light image.But in heart CT and TEE images On registration, due to two kinds of image modes, otherness is notable on pixel value, and the edge and texture representative model of heart TEE images Paste, these medical image registration methods are difficult to carry out it accurate effective registration.
The content of the invention
It is an object of the invention to the greatest differences for CT and TEE image image modes, propose a kind of based on valve Alignment and the heart CT-TEE method for registering of probability graph, it is real by merging structure and texture information under both image modes Now to the accuracy registration of heart CT-TEE images.
To achieve the above object, the present invention comprises the following steps：
(1) respectively to cardiac CT image IRAnd TEE images I (x)F(x) formula segmentation is interacted, CT images I is obtainedR(x) Segmentation figure, i.e. area-of-interest GR, and TEE images I (x)F(x) segmentation figure, i.e. area-of-interest GF(x)；
(2) CT images I is introduced while formula segmentation is interactedR(x) 3 cardiac valves end points or point midway are sat Mark x1r=(i1r,j1r),x2r=(i2r,j2r),x3r=(i3r,j3r), as 3 characteristic points of CT images, while introducing TEE figures As IF(x) with CT images I inR(x) the corresponding cardiac valves end points of 3 characteristic points or point midway coordinate x1f=(i1f,j1f), x2f=(i2f,j2f),x3f=(i3f,j3f), as 3 characteristic points of TEE images, by 3 characteristic points and TEE images of CT images 3 characteristic points constitute 3 pairs of characteristic points pair, by prior information registering based on this 3 pairs of characteristic points pair；
(3) by CT images IR(x) as reference picture, by TEE images IF(x) as floating image, based on valve priori letter Breath, basis registration is carried out to reference picture and floating image, obtains the transformation matrix T of basic registration1, and obtain basic registration knot Fruit S1(x)；
(4) setting CT images IR(x) enhancing matrix VR(x), respectively to CT images IR(x) with area-of-interest GR(x) enter Row region strengthens, and obtains enhanced CT images IRh(x) with enhanced area-of-interest GRh(x), setting TEE images IF(x) Enhancing matrix VF(x), respectively to TEE images IF(x) with area-of-interest GF(x) region enhancing is carried out, obtains enhanced TEE images IFh(x) with enhanced area-of-interest GFh(x)；
(5) it is based on the enhanced CT images I in regionRh(x) with enhanced area-of-interest GRh(x), generation CT images IR (x) probability graph PR(x), based on the enhanced TEE images I in regionFh(x) with enhanced area-of-interest GFh(x), generate TEE images IF(x) probability graph PF(x)；
(6) to two probability graph P of generation in (5)RAnd P (x)F(x) similarity measurement, and the base that will be obtained in (3) are carried out The transformation matrix T of plinth registration1As the initial parameter of optimizing algorithm in final registration, based on probability graph PRAnd P (x)F(x) phase Like property to CT images IR(x) with TEE images IF(x) final registration is carried out, transformation matrix T is tried to achieve2, and obtain final registration result S2(x)。
The present invention has advantages below compared with prior art：
1st, the present invention based in practical application to the demand of position of valve information, and valve imaging clearly in TEE images And the visible Realistic Analysis in position of valve in CT images, the spatial positional information of valve is introduced in basic registration, is made with this Feature Points Matching is carried out for prior information, CT and TEE image registrations validity is drastically increased；
2nd, initial ginseng of the transformation matrix that the present invention obtains basic registration as optimizing algorithm Powell in final registration Number, it is to avoid Powell algorithms are because initial parameter selection is improper and the problem of enter local optimum, improves local optimal searching The efficiency and accuracy of algorithm；
3rd, the present invention is based on carrying out region of interest in region enhancing generating probability figure, greatly simplify the life of probability graph It is combined into process, and by the probability graph generated in the present invention with normalized mutual information, is greatly improved similarity measurement Accuracy and reliability；
Brief description of the drawings
Fig. 1 be the present invention realize general flow chart；
Fig. 2 is cardiac CT image used in the present invention, i.e. registering reference picture；
Fig. 3 is heart TEE images used in the present invention, i.e. registering floating image；
Fig. 4 is the probabilistic image based on Fig. 2 generations in the present invention；
Fig. 5 is the probabilistic image based on Fig. 3 generations in the present invention；
Fig. 6 be the present invention Fig. 2 and Fig. 3 are carried out it is basic it is registering after registering image；
Fig. 7 is the fused images after the present invention is merged to Fig. 2 with Fig. 6；
Fig. 8 be the present invention Fig. 2 and Fig. 3 are carried out it is finally registering after registering image；
Fig. 9 is the fused images after the present invention is merged to Fig. 2 with Fig. 8.
Embodiment
Below in conjunction with accompanying drawing, specific embodiments of the present invention and effect are made further explanation and description：
Reference picture 1, heart CT-TEE method for registering images of the present invention based on valve alignment and probability graph mutual information
Implementation step is as follows：
Step 1：To the cardiac CT image I of inputR(x) with TEE images IF(x) formula segmentation is interacted.
1a) input cardiac CT image IR(x), as shown in Fig. 2 artificially choosing CT images IR(x) atrium dextrum and active in Region where arteries and veins, and a small amount of several target pixel points and several background dots in the region are chosen, iteration for several times is carried out, is obtained The area-of-interest G of CT imagesR(x)；
1b) input TEE images IF(x), as shown in figure 3, artificially choosing TEE images IF(x) atrium dextrum and sustainer in The region at place, and a small amount of several target pixel points and several background dots in the region are chosen, iteration for several times is carried out, is obtained The area-of-interest G of TEE imagesF(x)。
Step 2：Obtain cardiac valves prior information.
2a) while Interactive Segmentation, CT images I is introducedR(x) 3 cardiac valves end points or point midway coordinate x1r=(i1r,j1r),x2r=(i2r,j2r),x3r=(i3r,j3r), as 3 characteristic points of CT images, while introducing TEE images IF(x) with CT images I inR(x) the corresponding cardiac valves end points of 3 characteristic points or point midway coordinate x1f=(i1f,j1f), x2f=(i2f,j2f),x3f=(i3f,j3f), it is used as 3 characteristic points of TEE images；
It can 2b) be divided into the characteristic of bicuspid valve, tricuspid valve, aorta petal or pulmonary valve according to cardiac valves, be schemed with CT 3 characteristic points of picture constitute 3 pairs of characteristic points pair with 3 characteristic points of TEE images, and using this 3 pairs of characteristic points to first as valve Test information.
Step 3：To CT images IR(x) with TEE images IF(x) basis registration is carried out.
3a) by CT images IR(x) as reference picture, by TEE images IF(x) as floating image；
3b) it is based on the position coordinates x of valve prior information, i.e. 3 based on reference picture characteristic point1r=(i1r,j1r), x2r=(i2r,j2r),x3r=(i3r,j3r) and floating image 3 characteristic points position coordinates x1f=(i1f,j1f),x2f= (i2f,j2f),x3f=(i3f,j3f), the transformation matrix of coordinates T of 3 pairs of characteristic points pair is tried to achieve as follows1：
3c) it is based on transformation matrix T1, affine transformation is carried out to floating image, and basic registration is obtained by cubic interpolation tying Fruit S1(x)：S1(x)=T1×IF(x), as shown in fig. 6, Fig. 2 is merged with Fig. 6, fusion figure is obtained, as shown in fig. 7, can from Fig. 7 To find out, after basic registration, reference picture Fig. 2 and floating image Fig. 3 have geographically obtained matching substantially.
Step 4：To CT images IR(x) with its area-of-interest GR(x) region enhancing is carried out.
4a) according to CT images IR(x) pixel distribution setting enhancing matrix VR(x)：
Set VR(x) size and CT images IR(x) in the same size, and by VR(x) it is consistent with area-of-interest coordinate in Point be set to one be more than 0 fixed value, set is 80 in the present invention, and the point of remaining position is set to 0；
4b) to CT images IR(x) with area-of-interest GR(x) grey level enhancement is carried out, enhanced CT images I is obtainedRh(x) With enhanced area-of-interest GRh(x)：
IRh(x)=IR(x)+VR(x)
GRh(x)=GR(x)+VR(x)。
Step 5：To TEE images IF(x) with its area-of-interest GF(x) region enhancing is carried out.
5a) according to TEE images IF(x) pixel distribution setting enhancing matrix VF(x)：
Set VF(x) size and TEE images IF(x) in the same size, and by VF(x) with area-of-interest coordinate one in The point of cause is set to be set as 80 in a fixed value more than 0, the present invention, and the point of remaining position is set to 0；
5b) to TEE images IF(x) with its area-of-interest GF(x) grey level enhancement is carried out, enhanced TEE images are obtained IFh(x) with enhanced area-of-interest GFh(x)：
IFh(x)=IF(x)+VF(x)
GFh(x)=GF(x)+VF(x)。
Step 6：Generate CT images IR(x) probability graph PR(x)。
6a) the enhanced CT images I in region obtained based on step 4Rh(x) with enhanced area-of-interest GRh(x), Generation is by the enhanced CT images I in regionRh(x) on area-of-interest G after enhancingRh(x) probability density function：
Equivalent to one probability retrieval table of the probability density function, when inputting some pixel, output is the pixel Point is likely located at the probable value in area-of-interest；
6b) by the enhanced CT images I in regionRh(x) as probability density function fR(i) input, obtains CT images IR (x) probability graph PR(x)：PR(x)=fR(x),x∈IRh(x), as shown in Figure 4.
Step 7：Generate TEE images IF(x) probability graph PF(x)。
7a) the enhanced TEE images I in region obtained based on step 5Fh(x) with enhanced area-of-interest GFh(x), Generation is by the enhanced TEE images I in regionFh(x) on area-of-interest G after enhancingFh(x) probability density function：
7b) by the enhanced TEE images I in regionFh(x) as probability density function fF(i) input, obtains TEE images IF(x) probability graph PF(x)：PF(x)=fF(x),x∈IFh(x), as shown in Figure 5.
Step 8：To CT images IR(x) with TEE images IF(x) final registration is carried out.
8a) to probability graph PRAnd P (x)F(x) similarity measurement is carried out
Similarity measurement criterion can be mutual information, normalized mutual information, cross-correlation, gradient mutual information etc., and the present invention is adopted It is normalized mutual information, its solution procedure is as follows：
8a1) obtain image IR(x) probability graph PR(x) entropy HR(x) with image IF(x) probability graph PF(x) entropy
HF(x)：
Wherein, P (PR(x)) it is probability graph PR(x) probability density function, P (PF(x)) it is probability graph PF(x) probability is close Spend function；
8a2) obtain probability graph PRAnd P (x)F(x) combination entropy HR,F(x)：
Wherein, P (PR(x),PF(x)) it is probability graph PRAnd P (x)F(x) joint probability density function；
8a3) obtain probability graph PRAnd P (x)F(x) normalized mutual information NMPI：
8b) to probability graph PRAnd P (x)F(x) normalized mutual information NMPI carries out optimizing
The species of optimizing algorithm is a lot, such as particle cluster algorithm, simulated annealing, ant group algorithm, gradient descent method, Powell methods are used in Powell methods, the present invention, process are implemented as follows：
8b1) by the transformation matrix T of basic registration1It is used as the initial parameter of Powell methods；
8b2) obtain working as probability graph P by Powell method optimizingRAnd P (x)FWhen normalized mutual information NMPI (x) is maximum Transformation matrix of coordinates T2, by TEE images IF(x) carry out coordinate transform and obtain final registration result S2(x)：S2(x)=T2× IF(x), as shown in figure 8, Fig. 2 is merged with Fig. 8, fusion figure is obtained, as shown in Figure 9.
Come as can be seen from Figure 9, after final registration, reference picture Fig. 2 and floating image Fig. 3 has obtained accurately matching somebody with somebody Quasi- effect.
Above description is only example of the present invention, does not constitute any limitation of the invention, it is clear that for this , all may be without departing substantially from the principle of the invention, structure after present invention and principle has been understood for the professional in field In the case of, the various modifications and variations in form and details are carried out, but these modifications and variations based on inventive concept are still Within the claims of the present invention.

Claims (10)

1. it is a kind of based on valve alignment and the heart CT-TEE image registrations of probability graph, including：
(1) respectively to cardiac CT image IRAnd TEE images I (x)F(x) formula segmentation is interacted, CT images I is obtainedR(x) sense is emerging Interesting region GR(x) with TEE images IF(x) area-of-interest GF(x)；
(2) CT images I is introduced while formula segmentation is interactedR(x) 3 cardiac valves end points or point midway coordinate x1r =(i1r,j1r),x2r=(i2r,j2r),x3r=(i3r,j3r), as 3 characteristic points of CT images, while introducing TEE images IF (x) with CT images I inR(x) the corresponding cardiac valves end points of 3 characteristic points or point midway coordinate x1f=(i1f,j1f),x2f =(i2f,j2f),x3f=(i3f,j3f), as 3 characteristic points of TEE images, by 3 characteristic points of CT images and TEE images 3 characteristic points constitute 3 pairs of characteristic points pair, by prior information registering based on this 3 pairs of characteristic points pair；
(3) by CT images IR(x) as reference picture, by TEE images IF(x) as floating image, based on valve prior information, Basis registration is carried out to reference picture and floating image, the transformation matrix T of basic registration is obtained1, and obtain basic registration result S1 (x)；
(4) setting CT images IR(x) enhancing matrix VR(x), respectively to CT images IR(x) with area-of-interest GR(x) area is carried out Domain strengthens, and obtains enhanced CT images IRh(x) with enhanced area-of-interest GRh(x), setting TEE images IF(x) increasing Strong matrix VF(x), respectively to TEE images IF(x) with area-of-interest GF(x) region enhancing is carried out, enhanced TEE figures are obtained As IFh(x) with enhanced area-of-interest GFh(x)；
(5) it is based on the enhanced CT images I in regionRh(x) with enhanced area-of-interest GRh(x), generation CT images IR(x) Probability graph PR(x), based on the enhanced TEE images I in regionFh(x) with enhanced area-of-interest GFh(x) TEE images, are generated IF(x) probability graph PF(x)；
(6) to two probability graph P of generation in (5)RAnd P (x)F(x) similarity measurement is carried out, and the basis obtained in (3) is matched somebody with somebody Accurate transformation matrix T1As the initial parameter of optimizing algorithm in final registration, based on probability graph PRAnd P (x)F(x) similitude To CT images IR(x) with TEE images IF(x) final registration is carried out, transformation matrix T is tried to achieve2, and obtain final registration result S2 (x)。
2. according to the method described in claim 1, matching somebody with somebody to reference picture and floating image progress basis wherein described in step (3) Standard, is carried out as follows：
(3.1) based on the 3 CT images I introduced in step (2)R(x) feature point coordinates x1r=(i1r,j1r),x2r=(i2r, j2r),x3r=(i3r,j3r) and 3 TEE images IF(x) feature point coordinates x1f=(i1f,j1f),x2f=(i2f,j2f),x3f= (i3f,j3f) coordinate corresponding relation, the transformation matrix T of coordinate transform is tried to achieve as follows1：
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(3.2) it is based on transformation matrix T1Affine transformation is carried out to floating image, the result S of basic registration is tried to achieve1(x)：
S1(x)=T1×IF(x)。
3. according to the method described in claim 1, setting CT images I wherein in step (4)R(x) enhancing matrix VR(x), be by CT images IR(x) size setting VR(x) size is consistent with its, and by VR(x) point consistent with area-of-interest coordinate is equal in A fixed value more than 0 is set to, the point of remaining position is set to 0.
4. according to the method described in claim 1, respectively to CT images I wherein in step (4)R(x) with area-of-interest GR(x) Region enhancing is carried out, is carried out by equation below：
IRh(x)=IR(x)+VR(x)
GRh(x)=GR(x)+VR(x)
Wherein IRh(x) it is enhanced CT images, GRh(x) it is enhanced area-of-interest.
5. according to the method described in claim 1, setting TEE images I wherein in step (4)F(x) enhancing matrix VF(x), it is By TEE images IF(x) size setting VF(x) size is consistent with its, and by VF(x) it is consistent with area-of-interest coordinate in Point is set to a fixed value more than 0, and the point of remaining position is set to 0.
6. according to the method described in claim 1, respectively to TEE images I wherein in step (4)F(x) with area-of-interest GF(x) Region enhancing is carried out, is carried out by equation below：
IFh(x)=IF(x)+VF(x)
GFh(x)=GF(x)+VF(x)
Wherein IFh(x) it is enhanced TEE images, GFh(x) it is enhanced area-of-interest.
7. the enhanced CT images I in region according to the method described in claim 1, is based on wherein in step (5)Rh(x) and enhancing Area-of-interest G afterwardsRh(x), generation CT images IR(x) probability graph PR(x), carry out as follows：
(5.1) generation is by the enhanced CT images I in regionRh(x) on area-of-interest G after enhancingRh(x) probability density letter Number fR(i)：
(5.2) by the enhanced CT images I in regionRh(x) as probability density function fR(i) input, obtains CT images IR(x) Probability graph PR(x)：
PR(x)=fR(x),x∈IRh(x)。
8. the enhanced TEE images I in region according to the method described in claim 1, is based on wherein in step (5)Fh(x) and enhancing Area-of-interest G afterwardsFh(x), generation TEE images IF(x) probability graph PF(x), carry out as follows：
(5.3) generation is by the enhanced TEE images I in regionFh(x) on area-of-interest G after enhancingFh(x) probability density Function fF(i)：
(5.4) by the enhanced TEE images I in regionFh(x) as probability density function fF(i) input, obtains TEE images IF (x) probability graph PF(x)：
PF(x)=fF(x),x∈IFh(x)。
9. according to the method described in claim 1, two probability graph P wherein in step (6) to being generated in (5)RAnd P (x)F(x) Similarity measurement is carried out, is carried out as follows：
(6.1) probability graph P is used as using normalized mutual informationRAnd P (x)F(x) similarity measurement criterion；
(6.2) image I is obtainedR(x) probability graph PR(x) entropy HR(x) with image IF(x) probability graph PF(x) entropy HF(x)：
<mrow> <msub> <mi>H</mi> <mi>R</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>-</mo> <munder> <mi>&amp;Sigma;</mi> <mrow> <mi>x</mi> <mo>&amp;Element;</mo> <msub> <mi>I</mi> <mrow> <mi>R</mi> <mi>h</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </munder> <mi>P</mi> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mi>R</mi> </msub> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mo>)</mo> </mrow> <mi>log</mi> <mi> </mi> <mi>P</mi> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mi>R</mi> </msub> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mo>)</mo> </mrow> </mrow>
<mrow> <msub> <mi>H</mi> <mi>F</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>-</mo> <munder> <mi>&amp;Sigma;</mi> <mrow> <mi>x</mi> <mo>&amp;Element;</mo> <msub> <mi>I</mi> <mrow> <mi>F</mi> <mi>h</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </munder> <mi>P</mi> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mi>F</mi> </msub> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mo>)</mo> </mrow> <mi>log</mi> <mi> </mi> <mi>P</mi> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mi>F</mi> </msub> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mo>)</mo> </mrow> </mrow>
Wherein, P (PR(x)) it is probability graph PR(x) probability density function, P (PF(x)) it is probability graph PF(x) probability density letter Number；
(6.3) probability graph P is obtainedRAnd P (x)F(x) combination entropy HR,F(x)：
<mrow> <msub> <mi>H</mi> <mrow> <mi>R</mi> <mo>,</mo> <mi>F</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>-</mo> <munder> <mi>&amp;Sigma;</mi> <mrow> <mi>x</mi> <mo>&amp;Element;</mo> <msub> <mi>I</mi> <mrow> <mi>R</mi> <mi>h</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </munder> <munder> <mi>&amp;Sigma;</mi> <mrow> <mi>x</mi> <mo>&amp;Element;</mo> <msub> <mi>I</mi> <mrow> <mi>F</mi> <mi>h</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </munder> <mi>P</mi> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mi>R</mi> </msub> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mo>,</mo> <msub> <mi>P</mi> <mi>F</mi> </msub> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mo>)</mo> </mrow> <mi>log</mi> <mi> </mi> <mi>P</mi> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mi>R</mi> </msub> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mo>,</mo> <msub> <mi>P</mi> <mi>F</mi> </msub> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
Wherein, P (PR(x),PF(x)) it is probability graph PRAnd P (x)F(x) joint probability density function；
(6.4) according to probability graph PR(x) entropy HR(x), probability graph PF(x) entropy HF(x), probability graph PR(x) with probability graph PF(x) Combination entropy HR,F(x) two probability graph P, are obtainedRAnd P (x)F(x) normalized mutual information NMPI is：
<mrow> <mi>N</mi> <mi>M</mi> <mi>P</mi> <mi>I</mi> <mo>=</mo> <mfrac> <mrow> <msub> <mi>H</mi> <mi>R</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>H</mi> <mi>F</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>H</mi> <mrow> <mi>R</mi> <mo>,</mo> <mi>F</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>.</mo> </mrow>
10. according to the method described in claim 1, probability graph P will be based in (3) wherein in step (6)RAnd P (x)F(x) phase Like property to CT images IR(x) with TEE images IF(x) final registration is carried out, is carried out as follows：
(6.5) by the transformation matrix T of basic registration1It is used as the initial parameter of Powell methods；
(6.6) obtain working as probability graph P by Powell method optimizingRAnd P (x)F(x) seat when normalized mutual information NMPI is maximum Mark transformation matrix T2, by TEE images IF(x) carry out coordinate transform and obtain final registration result S2(x)：
S2(x)=T2×IF(x)。
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CN108492269A (en) * 2018-03-23 2018-09-04 西安电子科技大学 Low-dose CT image de-noising method based on gradient canonical convolutional neural networks
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