CN104933672B - Method based on quick convex optimized algorithm registration three dimensional CT with ultrasonic liver image - Google Patents
Method based on quick convex optimized algorithm registration three dimensional CT with ultrasonic liver image Download PDFInfo
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- 210000004185 liver Anatomy 0.000 title claims abstract description 22
- 238000004422 calculation algorithm Methods 0.000 title claims abstract description 16
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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
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- G—PHYSICS
- 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
- G06T7/344—Determination of transform parameters for the alignment of images, i.e. image registration using feature-based methods involving models
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
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- G06T2207/00—Indexing scheme for image analysis or image enhancement
- G06T2207/10—Image acquisition modality
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- G06T2207/10081—Computed x-ray tomography [CT]
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- G06T2207/30004—Biomedical image processing
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Abstract
The present invention relates to medical images to post-process field, it is desirable to provide the method based on quick convex optimized algorithm registration three dimensional CT with ultrasonic liver image.This includes following processes based on quick convex optimized algorithm registration three dimensional CT and the method for ultrasonic liver image：Ultrasound and CT image resolution ratios are adjusted to identical；To the rough registration based on rigid body translation of ultrasound and CT images；Extract the uniform characteristics information of multi-modality image registration；It calculates under current non-rigid shape deformations field u (x), the gradient fields of the D (u) in data item and D (u)Model solution is carried out to each step of progressively convex optimization method, the optimal correction value h (x) of Deformation Field is obtained, Deformation Field is updated, until h (x) very littles；According to the non-rigid shape deformations field of solution, ultrasonoscopy is converted, with CT image registrations.The present invention designs fast, accurately three-D ultrasonic CT liver images registration Algorithm, improves the accuracy, security and validity of ablative surgery by establishing rational model.
Description
Technical Field
The invention relates to the field of medical image post-processing, in particular to a method for registering three-dimensional CT and ultrasonic liver images based on a fast convex optimization algorithm.
Background
At present, liver diseases are diseases with high clinical incidence probability and directly threaten the lives of people. In the treatment of liver cancer, local ablation represented by rf ablation has become the third major treatment means for liver cancer in addition to surgical resection and interventional therapy. Due to the imaging advantages and disadvantages of ultrasound, ultrasound-CT fusion is often used in ablation procedures to guide surgical needle insertion. The key technology is the registration of CT-ultrasonic multi-mode images.
Registration of ultrasound images with CT images remains an international challenge, and automated and accurate real-time registration in practical clinical applications remains difficult. The liver ultrasound-CT registration problem has a plurality of difficulties, which mainly include the following aspects: (1) Because the difference between CT and ultrasound images is very large, and the structure that can be developed in CT may not be clearly seen in ultrasound, it is difficult to set the similarity measure of two modalities, which belongs to the multi-modality registration problem in the registration problem. (2) Because the field of view of the ultrasound is narrow, the liver is the largest organ of the abdomen, and due to the shielding of the abdominal bone, only part of the liver can be displayed in the ultrasound image, but the whole liver cannot be displayed like the CT; (3) influence of respiratory motion on image registration accuracy. The respiratory motion can cause the displacement of the liver and the focus, the size of the displacement is related to the respiratory amplitude, and the individual difference is large. The solution by controlling the breathing state is sometimes not very good. And the probe of the ultrasonic instrument can extrude the human body when acquiring the ultrasonic image, so that the liver tissue is deformed. Accurate registration results are typically obtained by coarse registration first, followed by non-rigid registration. However, the non-rigid registration technology is still immature, and further research is needed to establish a suitable mathematical model to deal with complex liver tissue deformation.
Several liver ultrasound and CT registration methods have been proposed. In the feature-based registration method, features such as liver contours and blood vessels are required to be extracted for registration. Although the speed is high and the robustness is high, the automatic extraction of the liver contour and the blood vessel is a difficult problem; in the image-based registration method, a suitable similarity measure needs to be extracted by overcoming the obstacle of large difference of multi-modal image information. One class of algorithms uses CT simulation of an ultrasound image to register with acquired ultrasound based on the ultrasound imaging principles. Another method combines manually calibrated feature points (points with anatomical significance, such as vessel intersections) and statistical information of the images for registration; some registration methods correct the physical coordinates of the ultrasound and CT images with sensors positioned on the patient and the couch. This registration of the outer marker points, although fast, does not achieve very high accuracy, especially in the case of local deformations. These methods have advantages and disadvantages, and the above problems cannot be completely solved. Therefore, an accurate, automatic and efficient liver CT-ultrasonic deformable registration method is provided, and a practical and feasible scheme which is convenient to operate clinically is very important.
Disclosure of Invention
The invention mainly aims to overcome the defects in the prior art and provide a rapid method for accurately registering three-dimensional CT-ultrasonic liver images by simply selecting feature points. In order to solve the technical problem, the solution of the invention is as follows:
the method for registering the three-dimensional CT and the ultrasonic liver image based on the rapid convex optimization algorithm comprises the following steps:
(1) Adjusting the ultrasonic and CT image resolution to be the same;
(2) Coarse registration of ultrasound and CT images based on rigid body transformations;
(3) Extracting unified feature information of multi-modal image registration;
(4) Constructing a fast convex optimization algorithm, and calculating the gradient fields of D (u) and D (u) in the data items under the current non-rigid deformation field u (x)
(5) Solving each step model of the gradual convex optimization method to obtain the optimal corrected deformation field h (x) of the current deformation field u (x), updating the current value u (x) = u (x) + h (x) of the new deformation field, and repeating the processes (4) and (5) until the L1-mode function of the corrected value of the deformation field is smaller than a certain set threshold value;
(6) Transforming the ultrasonic image according to the solved non-rigid deformation field, and registering the ultrasonic image with the CT image;
the process (1) specifically comprises the steps of:
step A: acquiring three-dimensional ultrasonic image I needing to be registered U (x) And three-dimensional CT image I C (x) Then the three-dimensional ultrasonic image I U (x) And three-dimensional CT image I C (x) Is adjusted to [0, N ] in the image display window level]Then, the three-dimensional CT image I is taken C (x) Is adjusted to follow the three-dimensional ultrasonic image I U (x) The same is true; n is an integer greater than 0, x represents a point in the three-dimensional image, and the definition domain of the image is omega;
the process (2) specifically comprises the following steps:
and B: respectively in a three-dimensional ultrasonic image I U (x) And three-dimensional CT image I C (x) 4 to 6 pairs of (anatomically significant) feature points (1 andmurak) are selected;
step C: according to the characteristic points, the three-dimensional ultrasonic image I is processed U (x) And three-dimensional CT image I C (x) Carrying out rigid registration;
the process (3) specifically comprises the following steps:
step D: extracting a uniform feature description MIND (Modality Independent neighboring neuro Descriptor) Independent of different image modes as a similarity measure for image registration, for a given three-dimensional CT image I C (x) And three-dimensional ultrasonic image I U (x) Calculating MIND characteristics of each point x ∈ omega in the image, and respectively recording the MIND characteristics as a vector function C (x): = (c) 1 (x)，...，c k (x)) T And R (x): = (r) 1 (x)，...，r k (x)) T ；
Wherein, the I C (x) Representing the three-dimensional CT image processed in the step A; said I U (x) Representing the three-dimensional ultrasonic image processed in the step A; the x represents a point in the three-dimensional image, and the definition domain of the image is omega; k is calculating MIND informationThe dimension of the local block is set and represents the dimension of MIND characteristic; c is said k A value representing the kth dimension of MIND feature of the CT image; said r k A value representing the kth dimension of the MIND feature of the ultrasound image; the T represents a vector (c) 1 (x)，...，c k (x)) T ，(r 1 (x)，...，r k (x)) T Transposing the vector in (1); said C (x) represents a three-dimensional CT image I C (x) MIND feature vector function of (1); the R (x) represents a three-dimensional ultrasound image I U (x) MIND feature vector function of (1);
the process (4) specifically comprises the following steps:
step E: the calculation is u (x) = (u) in the current deformation field 1 (x)，u 2 (x)，u 3 (x)) T Time, constants in data itemGradient field
Wherein u is 1 (x)，u 2 (x)，u 3 (x) Respectively representing each point x = (x) in the image 1 ，x 2 ，x 3 ) The deformation amount in the three directions of x, y and z; the T represents a vector transpose; the above-mentionedRepresents summing from i =1.. K; c is mentioned i (x) Representing the image I calculated in Process (3) C (x) The value of the dimension f of the MIND feature of (1); r is i (x + u) denotes the image I U (x) The f-dimension value of the MIND characteristic after the action of a deformation field u (x); x + u represents the ultrasound image I U (x) Applying a deformation field u (x), i.e. applying a deformation to each point x in the x, y, z direction, to obtain the position (x) of the new point 1 (x)+u 1 (x)，x 2 (x)+u 2 (x)，x 3 (x)+u 3 (x) ); the above-mentionedRepresents D (u) (x) scoreSeparately calculating the partial derivatives in the x, y and z directions, wherein the symbolsRepresenting a partial derivative operator;
the process (5) specifically comprises the following steps:
step F: a step-by-step convex optimization method (sequential constant x optimization) is adopted, the current value u (x) of the non-rigid deformation field is fixed in the specific process of each step, and the optimized energy functional is convex (one definition in mathematics), so that a convex model is obtained in the following form:
wherein, the h = (h) 1 (x)，h 2 (x)，h 3 (x)) T Representing the optimal correction deformation field to be solved; first term in convex modelRepresenting a data item, of which D (u) andcalculated from step E; second itemRepresenting a smooth regularization of the deformation field; the parameter alpha is a constant larger than 0 and is used for adjusting the proportion of the data item and the regular item (set by a user);
the symbolRepresenting the gradient with respect to u; symbolRepresenting a gradient operator; symbol min h Represents minimizing with respect to h; the symbol | | | represents solving an absolute value; symbol ^ n Ω Indicating integration within the image region omega(ii) a The symbol dx represents a volume element; h is 1 (x)，h 2 (x)，h 3 (x) Respectively representing the deformation quantity of each point in the image in the three directions of x, y and z; t represents vector transposition; symbol denotes vector multiplication; symbol(s)Represents summing from i =1,2,3;
the convex model of model (1) is transformed by the primitive-dual algorithm into the following form:
wherein, with L c (h, w, q) represents an energy function of the defined model, said w, q = (q) 1 ,q 2 ,q 3 ) Representing dual variables in the model (2); the h represents a Lagrange multiplier, namely an optimal correction distortion field needing to be solved in the model (1); the alpha is a parameter used for adjusting a data item and a regular item in the model (1) and is a constant greater than 0; c is a constant greater than 0; d (u) of a cyclic structure,calculated from step E, u = (u) 1 ，u 2 ，u 3 ) Is a known deformation field current value;
the symbol min h Represents minimizing with respect to h; max of w，q Represents the maximization of w, q; symbol: = means "defined as"; the symbol div represents a divergence operator; symbol(s) integral number of Ω Indicating integration within the image region Ω; the symbol dx represents a volume element; symbol(s)Represents summing from i =1,2,3; symbol(s)<，>, representing to calculate the inner product; symbolRepresents a pair u i Calculating a partial derivative; symbol | | | charging 2 The L2-norm is calculated, and the symbol | | | | is used for calculating an absolute value;
the solution model (1) is equivalent to the solution model (2), so h (x) required by the model (1) can be obtained by optimizing the model (2);
the process (6) specifically comprises the steps of:
step G: updating a non-rigid deformation field current value u (x) = u (x) + h (x), wherein x belongs to omega, and adding the obtained deformation field correction value to the old deformation field current value to obtain a new deformation field value;
step H: according to the solved non-rigid body deformation field, the ultrasonic image I is processed U (x) Is subjected to deformation I U (x + u (x)), and registering the ultrasonic image and the CT image;
I U (x+u)＝I U (x 1 (x)+u 1 (x)，x 2 (x)+u 2 (x)，x 3 (x)+u 3 (x))，(x 1 (x)，x 2 (x)，x 3 (x) Is the coordinate of pixel point x, (u) 1 (x)，u 2 (x)，u 3 (x) Is the deformation of the pixel point x in x, y, z directions.
The working principle of the invention is as follows: through analyzing the difficulty of three-dimensional ultrasonic-CT liver image registration and the defects of the prior art, a reasonable model is provided, and a corresponding fast algorithm is designed for solving.
Compared with the prior art, the invention has the beneficial effects that:
by establishing a reasonable model, a rapid and accurate three-dimensional ultrasonic-CT liver image registration algorithm is designed, so that needle insertion is guided in tumor ablation operation navigation represented by radio frequency ablation, and the accuracy, safety and effectiveness of the ablation operation are improved.
Drawings
FIG. 1 is a flow chart of the operation of the present invention.
Detailed Description
The invention is described in further detail below with reference to the following figures and embodiments:
fig. 1 is a flowchart of registering three-dimensional CT and ultrasound liver images based on a fast convex optimization algorithm, which specifically includes the following processes:
step A: for the input liver CT image I C (x) And ultrasound image I U (x) Adjusting window width window level to make image display value be 0, 255]And (4) inside. I is C (x) Size 512X 58, size of each voxel 0.79mm X3 mm, I is interpolated C (x) The size becomes 1094 × 1094 × 115, and each voxel size is 0.37mm × 0.37mm × 1.5mm. I.C. A U (x) Size 300X 1275, size of each voxel 0.37mm X0.10 mm, by downsampling, I U (x) The size becomes 300 × 300 × 85, each voxel size being 0.37mm × 0.37mm × 1.5mm. The symbols are as defined in the description of the steps of the specification.
And B, step B: for the first step of coarse registration based on rigid body transformation, we can manually select the rough positions of 4 to 6 pairs of feature points (bifurcation points of blood vessels) in the given CT and ultrasound three-dimensional images.
And C: and (3D-slicer software is used for calculating the optimal three-dimensional rigid body transformation matrix T for the characteristic points extracted from CT and ultrasound. Coarse registration is performed for given CT and ultrasound three-dimensional images.
Step D: for a given CT image I C (x) And ultrasound image I U (x) And the MIND characteristic information of each point x ∈ omega in the image is respectively a vector function C (x): = (c) 1 (x)，...，c k (x)) T And R (x): = (r) 1 (x)，...，r k (x)) T In this example, k is 6. The symbols are as defined in the description of the steps of the specification.
And E, step E: the calculation is u (x) = (u) in the current deformation field 1 (x)，u 2 (x)，u 3 (x)) T When the temperature of the water is higher than the set temperature,
gradient fieldThe symbols are as defined in the description of the steps of the specification.
Step F: solving the model (2) by using a convex optimization algorithm
The fast convex optimization algorithm iteration process is as follows:
● Setting an initial value w 0 ，q 0 ，h 0 And k =0, said w 0 ，q 0 ，h 0 The superscript 0 of (a) represents the initialization of w, q, h; circulating the following steps:
● Fixed q k And h k Solving for w k+1 ：
w k+1 ：＝arg max w L c (h k ，w，q k ).
Equivalent to convex optimization problem
Wherein, T i k (x) I =1.. 3, is based on q k And h k A fixed value of (2). Symbol argmax w L c (h k ，w，q k ) Expressing the equation L c (h k ，w，q k ) The maximum w. The symbol s.t. represents the constraint. Symbol q k ，h k ，w k ，T i k The superscript k of the etc. indicates the kth iteration. Other symbols are as defined in the description of the steps of the specification.
This problem can be easily solved by the gradient descent method.
● Fixed w k+1 And h k Solving for q k+1 ；
q k+1 ：＝arg min g L c (h k ，w k+1 ，q)；
Equivalent to the following three convex optimization problems
i =1.. 3; whereini =1.. 3, based on w k+1 And h k A fixed value of (2). arg min q L c (h k ，w k+1 Q) denotes solving c (h k ，w k+1 Q) the smallest q.Is shown with respect to q i And (5) obtaining a minimum value. Other symbols are as defined in the description of the steps of the specification.
This problem can be easily solved by the gradient descent method.
● Update h k+1 ：
Wherein, the symbolRepresents a pair u i The partial derivatives are solved and the sign div represents the divergence operator.
● k = k +1, repeating the above steps until convergence:
where δ is the chosen convergence threshold, which in this example may be taken to be 0.01.Is the L1-modulo function.
G: updating the current value u (x) = u (x) + h (x) of the non-rigid deformation field, wherein x belongs to omega until the change valueLess than a threshold, which in this example takes 0.01.Is the L1-modulo function.
Step H: according to the solved non-rigid deformation field u (x), carrying out ultrasonic image I U (x) Is subjected to deformation I U (x + u (x)), the ultrasound and CT images are registered.
Finally, it should be noted that the above-mentioned list is only a specific embodiment of the present invention. It is obvious that the present invention is not limited to the above embodiments, but many variations are possible. All modifications which can be derived or suggested by a person skilled in the art from the disclosure of the present invention are to be considered within the scope of the invention.
Claims (1)
1. The method for registering the three-dimensional CT and the ultrasonic liver image based on the rapid convex optimization algorithm is characterized by comprising the following steps:
(1) Adjusting the ultrasonic and CT image resolution to be the same;
(2) Coarse registration of ultrasound and CT images based on rigid body transformations;
(3) Extracting unified feature information of multi-modal image registration;
(4) Constructing a fast convex optimization algorithm, solving a mathematical model of three-dimensional non-rigid transformation registration, namely assuming that u (x) is a current value of a non-rigid deformation field, calculating an optimal correction deformation field h (x) for the non-rigid deformation field u (x) in each step, updating the non-rigid deformation field u (x) = u (x) + h (x), and iteratively optimizing the non-rigid deformation field step by step; in the first step of gradual convex optimization, the current non-rigid deformation field current value is a deformation field transformed by the rigid body obtained in the process (2); in this process, the data under the current non-rigid deformation field u (x) is first calculatedGradient fields of D (u) and D (u) in the term
(5) Solving each step model of the gradual convex optimization method to obtain the optimal corrected deformation field h (x) of the current deformation field u (x), updating the current value u (x) = u (x) + h (x) of the new deformation field, and repeating the processes (4) and (5) until the L1-mode function of the corrected value of the deformation field is smaller than a certain set threshold value;
(6) Transforming the ultrasonic image according to the solved non-rigid deformation field, and registering with the CT image;
the process (1) specifically comprises the following steps:
step A: acquiring three-dimensional ultrasonic image I needing to be registered U (x) And three-dimensional CT image I c (x) Then the three-dimensional ultrasonic image I is obtained U (x) And three-dimensional CT image I Ｃ (x) Is adjusted to [0, N ] in the image display window level]Then, three-dimensional CT image I is obtained Ｃ (x) Is adjusted to follow the three-dimensional ultrasonic image I U (x) The same is true; the N is an integer larger than 0, the x represents one point in the three-dimensional image, and the definition domain of the image is omega;
the three-dimensional ultrasonic image and the three-dimensional CT image after the adjustment are still respectively marked as I U (x) And I Ｃ (x) And in the subsequent step, if no special description is added, the three-dimensional ultrasonic image and the three-dimensional CT image both refer to the three-dimensional ultrasonic image I adjusted in the step A U (x) And three-dimensional CT image I c (x)；
The process (2) specifically comprises the following steps:
and B: respectively in a three-dimensional ultrasonic image I U (x) And three-dimensional CT image I Ｃ (x) Selecting 4 to 6 pairs of feature points;
and C: according to the characteristic points, the three-dimensional ultrasonic image I is processed U (x) And three-dimensional CT image I Ｃ (x) Carrying out rigid registration;
the process (3) specifically comprises the following steps:
step D: extracting uniform feature description MIND independent of different image modes as similarity of image registrationMeasuring the performance of the three-dimensional CT image I processed in the step A Ｃ (x) And three-dimensional ultrasonic image I U (x) Calculating MIND characteristics of each point x ∈ omega in the image, and respectively recording the MIND characteristics as a vector function C (x): = (c) 1 (x)，...，c k (x)) T And R (x): = (r) 1 (x)，...，r k (x)) T ；
Wherein, the I c (x) Representing the three-dimensional CT image processed in the step A; said I U (x) Representing the three-dimensional ultrasonic image processed in the step A; the x represents a point in the three-dimensional image, and the definition domain of the image is omega; the k is the dimension of the local area block set during the MIND information calculation and represents the dimension of the MIND characteristic; c is mentioned k A value representing the kth dimension of MIND feature of the CT image; said r k A value representing the kth dimension of the MIND feature of the ultrasound image; the T represents a vector (c) 1 (x)，...，c k (x)) T ，(r 1 (x)，...，r k (x)) T Transposing the vector in (1); said C (x) represents a three-dimensional CT image I Ｃ (x) MIND feature vector function of (1); the R (x) represents a three-dimensional ultrasound image I U (x) MIND feature vector function of (1);
the process (4) specifically comprises the following steps:
step E: the calculation is u (x) = (u) in the current deformation field 1 (x)，u 2 (x)，u 3 (x)) T Time, constant in data itemGradient field
Wherein u is 1 (x)，u 2 (x)，u 3 (x) Respectively representing each point x = (x) in the image 1 ，x 2 ，x 3 ) The deformation amount in the three directions of x, y and z; the T represents a vector transpose; the describedMeans to solve from i =1And; c is said i (x) Representing the image I calculated in Process (3) Ｃ (x) The value of the ith dimension of the MIND feature of (1); said r i (x + u) denotes the image I U (x) The value of the ith dimension of the MIND characteristic after the action of a deformation field u (x); x + u represents the ultrasound image I U (x) Applying a deformation field u (x), i.e. applying a deformation to each point x in the x, y, z direction, to obtain the position (x) of the new point 1 (x)+u 1 (x)，x 2 (x)+u 2 (x)，x 3 (x)+u 3 (x) ); the describedDenotes D (u) (x) which derives the partial derivatives in the three directions x, y and z, respectively, where the symbolsRepresenting a partial derivative operator;
the process (5) specifically comprises the following steps:
step F: a step-by-step convex optimization method is adopted, the non-rigid deformation field current value u (x) is fixed in the specific process of each step, the optimized energy functional is convex, and a convex model is obtained in the following form:
wherein, the h = (h) 1 (x)，h 2 (x)，h 3 (x)) T Representing the optimal corrected deformation field for u (x) to be solved, given the present value of a non-rigid deformation field u (x); first term in convex modelRepresenting a data item, of which D (u) andcalculated from step E; second itemRepresenting a smooth regularization of the deformation field; the parameter alpha is a constant larger than 0 and is used for adjusting the proportion of the data item and the regular item;
the symbolRepresenting the gradient with respect to u; symbolRepresenting a gradient operator; symbol min h Represents minimizing with respect to h; the symbol | | | represents solving an absolute value; symbol(s) integral multiple of Ω Indicating integration within the image region Ω; the notation dx denotes the volume element; h is 1 (x)，h 2 (x)，h 3 (x) Respectively representing the deformation quantity of each point in the image in the three directions of x, y and z; t represents vector transposition; the symbol represents the vector multiplication; symbolRepresents summing from i =1,2,3;
the convex model of model (1) is transformed by the primitive-dual algorithm into the following form:
is constrained to
i＝1，2，3；
Wherein, L is used c (h, w, q) represents an energy function of the defined model, said w, q = (q) 1 ，q 2 ，q 3 ) Representing dual variables in the model (2); the h (x) = (h) 1 (x)，h 2 (x)，h 3 (x)) T Representing the lagrange multiplier, i.e. the optimal corrective deformation field to be solved in the model (1); the alpha is a parameter used for adjusting the specific gravity of the data item and the regular item in the model (1) and is a constant greater than 0; c is a constant greater than 0; d (u) of a cyclic aromatic hydrocarbon,calculated from step E, u = (u) 1 ，u 2 ，u 3 ) Is a known deformation field current value;
the symbol min h Represents minimizing with respect to h; max w，q Represents the maximization of w, q; symbol: = means "defined as"; the symbol div represents the divergence operator; symbol ^ n Ω Indicating integration within the image region Ω; the notation dx denotes the volume element; symbol(s)Represents summing from i =1,2,3; symbol<，>, representing the inner product; symbol(s)Represents a pair u i Calculating a partial derivative; symbol | | | charging 2 The L2-norm is calculated, and the symbol | | | | is used for calculating an absolute value;
the solution model (1) is equivalent to the solution model (2), so h (x) required by the model (1) can be obtained by optimizing the model (2);
the process (6) specifically comprises the steps of:
step G: updating a non-rigid deformation field current value u (x) = u (x) + h (x), wherein x belongs to omega, and adding the obtained deformation field correction value to the old deformation field current value to obtain a new deformation field value;
step H: according to the solved non-rigid body deformation field, the ultrasonic image I is processed U (x) Is subjected to deformation I U (x + u (x)), and registering the ultrasonic image and the CT image;
I U (x+u)＝I U (x 1 (x)+u 1 (x)，x 2 (x)+u 2 (x)，x 3 (x)+u 3 (x))，(x 1 (x)，x 2 (x)，x 3 (x) Is the coordinate of pixel point x, (u) 1 (x)，u 2 (x)，u 3 (x) Is the deformation amount of the pixel point x in x, y, z directions.
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