CN113538539B - Liver CT image registration method based on cuckoo search algorithm and computer-readable storage medium - Google Patents
Liver CT image registration method based on cuckoo search algorithm and computer-readable storage medium Download PDFInfo
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Abstract
The invention provides a liver CT image registration method and a computer-readable storage medium based on a cuckoo search algorithm, wherein the image registration method comprises the following steps: acquiring an image to be registered comprising a reference image and a floating image, and performing two-dimensional discrete wavelet transformation to obtain a preprocessed image; taking normalized mutual information of the preprocessed image as similarity measure, solving by taking an affine transformation model as search space based on a cuckoo search algorithm to obtain a first mapping parameter, and obtaining a result image through cubic convolution interpolation operation; and taking the local normalized mutual information of the result image and the reference image in the image to be registered as similarity measure, establishing a functional extremum problem by combining an optical flow field constraint equation, solving the functional extremum problem based on a cuckoo search algorithm to obtain a second mapping parameter, and obtaining a registration result through cubic convolution interpolation operation. By adopting the technical scheme, the high-precision registration of the liver single-stage or multi-stage CT images can be realized.
Description
Technical Field
The invention relates to the field of medical image analysis, in particular to a liver CT image registration method based on a cuckoo search algorithm and a computer-readable storage medium.
Background
Hepatitis, cirrhosis, liver cancer and the like are clinically high-rise liver diseases. CT is the first imaging examination means for realizing accurate diagnosis of liver diseases, has been widely used in hospitals at all levels, and has high popularity. The CT imaging device is utilized to carry out plain scan (namely non-enhanced common scan) and dynamic enhanced scan of injecting iodine-containing contrast agent, single-phase or multi-phase CT images can be obtained with high quality, and the CT imaging device has the advantages of high sensitivity and specificity, short scanning time and queuing waiting time and low cost.
In clinical research and application, accurate diagnosis of liver diseases based on CT images is realized, and comprehensive processing and analysis of single-stage or multi-stage CT images of the liver are needed by means of a computer. The registration of the liver CT images is an important processing link, and has important significance in the accurate diagnosis of liver diseases. In addition, with the rapid development of AI theory and technology, the development of a liver intelligent auxiliary diagnosis system becomes an important component of intelligent medical treatment. Liver CT image fusion is an important development direction of an intelligent auxiliary diagnosis system for the liver. And this is a prerequisite for fusion, among other things, for liver CT image registration.
Image registration aims to find some kind of mapping between the two images so that the geometric information in the two images is as consistent as possible in spatial position. Since the liver is a large-volume organ, it is easily deformed in motility due to the influence of respiratory gases, physiological peristalsis, and the like. Furthermore, uptake and metabolism of the iodine-containing contrast agent during dynamic enhanced scanning can cause significant changes in pixel values and distribution in the multi-phase CT image of the liver. These factors present a significant challenge for liver CT image registration.
The existing image registration method is mainly oriented to liver single-stage CT images (mainly in a flat scanning period), belongs to single-mode registration, and is low in difficulty. The multi-modal registration is difficult for registration of liver multi-stage CT images (mainly a flat scanning period, an arterial period and a balance period (also called a delay period)). The existing liver multi-stage CT image registration method often needs to manually mark characteristic points, and automation is difficult to realize. The registration method based on the deep learning is sensitive to the change condition of the pixel values and the distribution of the multi-stage CT image, has weak robustness and has no interpretability.
Therefore, a novel liver CT image registration method is needed, no matter for single-phase or multi-phase CT images, a cuckoo search algorithm is used as a core, and an image processing and analyzing technology is used as a support, so that full-automatic liver CT image registration is realized, and a high-quality registration result is obtained.
Disclosure of Invention
In order to overcome the technical defects, the invention aims to provide a liver CT image registration method and a computer-readable storage medium based on a cuckoo search algorithm, which can realize high-precision registration of liver single-stage or multi-stage CT images and have important scientific significance and clinical value for accurate analysis of medical images and accurate diagnosis of liver diseases based on CT images.
The invention discloses a liver CT image registration method based on a cuckoo search algorithm, which comprises the following steps:
acquiring an image to be registered comprising a reference image and a floating image, and performing two-dimensional discrete wavelet transformation on the image to be registered to obtain a preprocessed image comprising image significance characteristics;
taking normalized mutual information of the preprocessed image as similarity measure, solving to obtain a first mapping parameter by taking an affine transformation model as search space based on a cuckoo search algorithm, and obtaining a result image through cubic convolution interpolation operation after the mapping parameter acts on the preprocessed image;
and taking local normalized mutual information of the result image and the reference image in the image to be registered as similarity measure, taking the optical flow field model as search space, combining an optical flow field constraint equation and the local normalized mutual information to establish a functional extremum problem, solving the functional extremum problem based on a cuckoo search algorithm to obtain a second mapping parameter, and obtaining a registration result through cubic convolution interpolation operation.
Preferably, the step of acquiring an image to be registered and performing two-dimensional discrete wavelet transform on the image to be registered to obtain a preprocessed image with image features comprises:
acquiring an image to be registered recorded with liver CT modal information, and performing Daubechiest=2 two-dimensional discrete wavelet transform on the image to be registered;
reserving a coefficient matrix of a high-frequency subband obtained after Daubechiest=2 two-dimensional discrete wavelet transformation, and setting a coefficient matrix of a low-frequency subband;
performing two-dimensional discrete wavelet inverse transformation on the coefficient matrix of the high-frequency sub-band to obtain a preprocessed image IH with image significance characteristics 1 and IH2 。
Preferably, the step of acquiring an image to be registered, in which liver CT modality information is recorded, and performing daubechiesp=2 two-dimensional discrete wavelet transform on the image to be registered includes:
taking the first image as a reference image I 1 The second image is a floating image I 2 ；
The reference image I is respectively based on the following formulas 1 And floating image I 2 Performing two-dimensional discrete wavelet transform;
wherein f (x, y) represents the reference image I 1 Or floating image I 2 M and N represent reference image I 1 Or floating image I 2 Is defined by the row and column widths of (1), and />For the transformed coefficient matrix +.>As a scale function +.>Wavelet functions in horizontal, vertical and diagonal directions respectively, and the wavelet functions are separable functions, and the expression is as follows:
wherein , and />Is a real function of one-dimensional square integrable; ψ (x) and ψ (y) are daubechiesp=2 wavelet functions.
Preferably, the step of obtaining a result image through cubic convolution interpolation operation after taking normalized mutual information of the preprocessed image as similarity measure and taking an affine transformation model as search space to solve and obtain a first mapping parameter based on a cuckoo search algorithm, wherein the mapping parameter acts on the preprocessed image comprises the following steps:
the normalized mutual information of the preprocessed image is represented based on the following expression:
wherein ,p1 (x, y) and p 2 (x, y) are the pre-processed images IH, respectively 1 and IH2 Edge probability distribution, p 12 (x, y) is the pre-processed image IH 1 and IH2 Is IH, omega 1 and IH2 Is set, and takes M x N;
solving the preprocessed images IH based on the following formulas, respectively 1 and IH2 Edge information entropy of (2):
so that it is pre-arrangedProcessing an image IH 1 and IH2 Is expressed as:
preferably, the expression of the affine transformation model is as follows:
wherein [ xy ]]And [ x 'y ]']Respectively pre-processing the image IH 1 Reference coordinates of (c) and the pre-processed image IH 2 A) floating coordinates of a 11 ,a 12 ,a 21 ,a 22 ,b 1 ,b 2 Is a parameter of the affine transformation model.
Preferably, the cuckoo search algorithm comprises the steps of:
initializing parameters of the cuckoo search algorithm, including generating normal distributed random numbers as initial positions x of N bird nests of the cuckoo search algorithm i (i=1, … N) and calculating the initial position x using the similarity measure as an objective function i (i=1, … N) corresponding initial fitness value;
the following parameters were set: dimension d, discovery probability p a Maximum Iteration number Iteration;
the position of the bird nest is updated by Levy flight based on the following formula:
wherein , and />The position of the ith bird nest during the t +1 th and t-th iterations respectively,/>representing point-to-point multiplication, α represents a step size parameter, levy (β) represents a random step size following Levy flight, β is a control factor for Levy flight, and a random search path formula for Levy flight is expressed as:
wherein u and v are random variables obeying standard normal distribution, and the calculation formula of phi is as follows:
wherein Γ represents a Gamma function;
after the bird nest position is updated, calculating the corresponding fitness value again to obtain an updated fitness value;
comparing the updated fitness value with the initial fitness value, and replacing the updated fitness value with the initial fitness value when the updated fitness value is better than the initial fitness value, otherwise, keeping unchanged;
generating a random number r E [0,1 ] subject to uniform distribution]When r < P a When the bird nest is in the nest position, the current bird nest position is reserved and no operation is performed; and when r > P a For the ith nest position in the t+1th iteration processThe new bird nest position is generated using the following formula:
wherein , and />The bird nest positions selected randomly for two times in the t-th iteration process;
repeating the steps until the maximum Iteration number Iteration is reached.
Preferably, the step size parameter α is defined based on a monotonically increasing/decreasing adjustment mechanism, wherein the adjustment mechanism is expressed as follows:
wherein ,α0 Being constant, iter is the current number of iterations.
Preferably, the step of obtaining the registration result through cubic convolution interpolation operation includes the steps of:
the reference image I is represented based on the following expression 1 And resulting imageImage block I of (2) P1 and />Is a normalized mutual information of:
wherein, image block I P1 Andfrom I by using sliding window technique 1 and />Traversing from the upper left corner to the lower right corner of (1), and image block (I) P1 and />Is 8 x 8, the sliding step is 2 +.> and />The following are expressed and solved respectively:
wherein ,p1 (x, y) and p 2 (x, y) respectively represent image block I P1 Andedge probability distribution, p 12 (x, y) represents image block I P1 and />W is the joint probability distribution of image block I P1 and />Is defined in the above-described specification.
Preferably, the step of obtaining the registration result through cubic convolution interpolation operation further comprises the steps of:
based on image block I at t time P1 The intensity E (x (t), y (t), t) at coordinates (x, y), and at time t+Δt for image block I P1 The light intensity E (x (t+Δt), y (t+Δt), t+Δt) at the coordinates (x+Δt, y+Δy) is established as follows:
E(x(t),y(t),t)＝E(x(t+Δt),y(t+Δt),t+Δt)；
block I of the picture P1 Andgray value f of (2) P1 (x, y) and->The light intensity of the light flow field model at the time t+delta t and t is defined as:
and its optical flow field constraint equation:
order theWill->The gradients over the three variables x, y, t are respectively noted asLet the optical flow field constraint equation be abbreviated as:
f x u+f y v+f t ＝0
thereby constructing the following functional extremum problem:
the invention also discloses a computer readable storage medium having stored thereon a computer program which when executed by a processor realizes the steps as described above.
After the technical scheme is adopted, compared with the prior art, the method has the following beneficial effects:
1. full-automatic liver CT image registration can be realized, and a high-quality registration result is obtained;
2. based on the improved cuckoo searching algorithm, the global searching capability is enhanced through monotonic increment of step length parameters in an initial searching stage, and the local searching capability is enhanced through monotonic decrement of step length parameters in a later searching stage, so that the cuckoo searching algorithm is prevented from sinking into a local optimal position, and the searching precision and speed are improved.
Drawings
FIG. 1 is a flow chart of an image registration method according to a preferred embodiment of the present invention;
FIG. 2 is a flow chart illustrating a first stage registration process in accordance with a preferred embodiment of the present invention;
FIG. 3 is a flow chart illustrating a second stage registration process in accordance with a preferred embodiment of the present invention;
FIG. 4 (a) is a schematic view of an arterial phase CT image (reference image) according to a preferred embodiment of the present invention;
FIG. 4 (b) is a schematic view of a pan-scan CT image (floating image) according to a preferred embodiment of the present invention;
FIG. 4 (c) is a schematic view of a balance phase CT image (floating image) according to a preferred embodiment of the present invention;
FIG. 4 (d) is an effect diagram of the boundary extraction and merging of the liver organ and the liver cancer focus in FIG. 4 (a), FIG. 4 (b) and FIG. 4 (c) by using the sketching software according to a preferred embodiment of the present invention, wherein the lower right corner of FIG. 4 (d) is a schematic diagram of the enlarged effect of the liver cancer focus boundary;
FIG. 4 (e) is a schematic illustration of the registration results of FIG. 4 (b) with reference to FIG. 4 (a) in accordance with a preferred embodiment of the present invention;
FIG. 4 (f) is a schematic illustration of the registration results of FIG. 4 (c) with reference to FIG. 4 (a) in accordance with a preferred embodiment of the present invention;
fig. 4 (g) is an effect diagram of the boundary extraction and merging of the liver organ and the liver cancer focus in fig. 4 (a), fig. 4 (e) and fig. 4 (f) by using the sketching software according to a preferred embodiment of the present invention, wherein the lower right corner of fig. 4 (g) is a schematic diagram of the amplifying effect of the liver cancer focus boundary.
Detailed Description
Advantages of the invention are further illustrated in the following description, taken in conjunction with the accompanying drawings and detailed description.
Reference will now be made in detail to exemplary embodiments, examples of which are illustrated in the accompanying drawings. When the following description refers to the accompanying drawings, the same numbers in different drawings refer to the same or similar elements, unless otherwise indicated. The implementations described in the following exemplary examples are not representative of all implementations consistent with the present disclosure. Rather, they are merely examples of apparatus and methods consistent with some aspects of the present disclosure as detailed in the accompanying claims.
The terminology used in the present disclosure is for the purpose of describing particular embodiments only and is not intended to be limiting of the disclosure. As used in this disclosure and the appended claims, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It should also be understood that the term "and/or" as used herein refers to and encompasses any or all possible combinations of one or more of the associated listed items.
It should be understood that although the terms first, second, third, etc. may be used in this disclosure to describe various information, these information should not be limited to these terms. These terms are only used to distinguish one type of information from another. For example, first information may also be referred to as second information, and similarly, second information may also be referred to as first information, without departing from the scope of the present disclosure. The word "if" as used herein may be interpreted as "at … …" or "at … …" or "responsive to a determination", depending on the context.
In the description of the present invention, it should be understood that the terms "longitudinal," "transverse," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," and the like indicate orientations or positional relationships based on the orientation or positional relationships shown in the drawings, merely to facilitate describing the present invention and simplify the description, and do not indicate or imply that the devices or elements referred to must have a specific orientation, be configured and operated in a specific orientation, and therefore should not be construed as limiting the present invention.
In the description of the present invention, unless otherwise specified and defined, it should be noted that the terms "mounted," "connected," and "coupled" are to be construed broadly, and may be, for example, mechanical or electrical, or may be in communication with each other between two elements, directly or indirectly through intermediaries, as would be understood by those skilled in the art, in view of the specific meaning of the terms described above.
In the following description, suffixes such as "module", "component", or "unit" for representing elements are used only for facilitating the description of the present invention, and are not of specific significance per se. Thus, "module" and "component" may be used in combination.
Referring to fig. 1, a flowchart of an image registration method according to a preferred embodiment of the present invention is shown. The invention provides a method for registering liver single-stage or multi-stage CT images (particularly liver multi-stage CT images) in a full-automatic and high-quality manner based on an improved cuckoo searching algorithm, which aims to overcome the defects of the existing liver CT image registration method.
In a preferred embodiment, the liver CT image registration method comprises three main steps of preprocessing, first-stage registration and second-stage registration, and specifically comprises the following steps:
s100: acquiring an image to be registered (comprising a reference image and a floating image), and performing two-dimensional discrete wavelet transformation on the image to be registered to obtain a preprocessed image containing image significance characteristics;
discrete wavelet transform is the discretization of the scale and translation of the basic wavelet. In image processing, a binary wavelet is often employed as a wavelet transform function, i.e., division is performed using the integer power of 2.
In yet another preferred embodiment, the step S100 of acquiring an image to be registered and performing two-dimensional discrete wavelet transform on the image to be registered to obtain a preprocessed image containing significant features of the image includes:
s110: acquiring an image to be registered recorded with liver CT modal information, and performing Daubechies p=2 two-dimensional discrete wavelet transform on the image to be registered;
s120: reserving a coefficient matrix of a high-frequency sub-band obtained after Daubechies p=2 two-dimensional discrete wavelet transformation, and setting a coefficient matrix of a zero low-frequency sub-band, namely discarding the coefficient matrix of the zero low-frequency sub-band;
s130: performing two-dimensional discrete wavelet inverse transformation on the coefficient matrix of the high-frequency sub-band to obtain a preprocessed image IH containing image significance characteristics 1 and IH2 。
Specifically, considering that the registration of the plurality of images is performed by a pairwise registration manner, and that the clinical registration of the liver CT image involves only the registration of two images, the step S110 of acquiring the image to be registered, which is recorded with the liver CT modality information, and performing Daubechies p=2 two-dimensional discrete wavelet transform on the image to be registered includes:
s111: taking a first image (taking a liver arterial phase CT image as an example) as a reference image I 1 The second image (without loss of generality, taking a liver balance phase CT image as an example) is a floating image I 2 ；
S112: the reference image I is respectively based on the following formulas 1 And floating image I 2 Performing two-dimensional discrete wavelet transform;
wherein f (x, y) represents the reference image I 1 Or floating image I 2 M and N represent reference image I 1 Or floating image I 2 Is defined by the row and column widths of (1), and />For the transformed coefficient matrix +.>As a scale function +.>i= { H, V, D } is a wavelet function in the horizontal, vertical, diagonal directions, respectively, and the wavelet function is a separable function, expressed as follows:
wherein , and />Is a real function of one-dimensional square integrable; ψ (x) and ψ (y) are Daubechies p=2 wavelet functions.
Through the steps, the coefficient matrix of the high-frequency sub-band obtained by the two-dimensional discrete wavelet transformation can be reserved, the coefficient matrix of the low-frequency sub-band is set to zero, and then the two-dimensional discrete wavelet inverse transformation is carried out, so that the matrix only comprises I 1 and I2 Image IH of salient features such as middle edges and textures 1 and IH2 . It is emphasized that the number of decomposition layers of daubechiesp=2 two-dimensional discrete wavelet transform in this step is round (M, N)/64.
S200: and taking normalized mutual information (normalized mutual information, NMI) of the preprocessed image as a similarity measure, solving to obtain a first mapping parameter of the first stage by taking an affine transformation model as a search space (also called a mapping model) based on a cuckoo search algorithm, and obtaining a result image of the first stage through cubic convolution interpolation operation after the mapping parameter acts on the preprocessed image. In this step, the similarity measure of the normalized mutual information is taken as the fitness, i.e. the objective function, in the cuckoo search algorithm.
Referring to fig. 2, step S200, as a first stage registration step, specifically includes:
s210: the normalized mutual information of the preprocessed image is represented based on the following expression:
wherein ,p1 (x, y) and p 2 (x, y) are the pre-processed images IH, respectively 1 and IH2 Edge probability distribution, p 12 (x, y) is the pre-processed image IH 1 and IH2 Is a joint summary of (1)Rate distribution, Ω is IH 1 and IH2 Is set, and takes M x N;
s220: solving the preprocessed images IH based on the following formulas, respectively 1 and IH2 Edge information entropy of (2):
so that the image IH is preprocessed 1 and IH2 Is expressed as:
further, the expression of the affine transformation model is as follows:
wherein [ x y ]]And [ x 'y ]']Respectively pre-processing the image IH 1 Reference coordinates of (c) and the pre-processed image IH 2 A) floating coordinates of a 11 ,a 12 ,a 21 ,a 22 ,b 1 ,b 2 Is a parameter of the affine transformation model.Is the parameter matrix of the affine transformation model.
In the above steps, improvements are proposed for the cuckoo search algorithm common in the industry, and three rules are assumed in terms of the principle of the cuckoo search algorithm: (1) each cuckoo only produced one egg at a time, and randomly selected one host bird nest to place; (2) among randomly selected host bird nests, the optimal host bird nest is reserved to the next generation; (3) number of selectable host bird nestsThe probability of the cuckoo egg being found by the host bird is defined as P a ∈[0,1]Once the host bird finds the cuckoo's eggs, the old nest is discarded and the nest is re-built. Based on the above principle, the cuckoo algorithm in a preferred embodiment of the present invention is improved, and specifically includes the following steps:
parameters of a cuckoo search algorithm are initialized. Comprises generating random numbers with normal distribution by MATLAB software and random (& gt) function, and using the random numbers as initial positions x of N bird nests i (i=1, … N) and calculating the initial position x using the similarity measure of the normalized mutual information as an objective function i (i=1, … N) corresponding initial fitness value. The method also comprises the following steps of manually setting: dimension d, discovery probability p a Maximum Iteration number Iteration;
the position update of the bird nest is performed by Levy flight, named as vero-lewy, a french mathematical, based on the following formula, wherein the probability distribution of step sizes refers to random walk of heavy-tail distribution, that is, a relatively high probability of large stride occurs during random walk:
wherein , and />Represents the position of the ith bird nest, < >/during the t+1st and t iterations, respectively>Representing a point-to-point multiplication, α represents a step size parameter, levy (β) represents a random step size following Levy flight, and β is a control factor for Levy flight, which may be set to 1.5, for example. And the random search path formula for Levy flight is expressed as:
wherein u and v are random variables obeying standard normal distribution, and the calculation formula of phi is as follows:
wherein Γ represents a Gamma function;
after the bird nest position is updated, the corresponding fitness is calculated again, and then an updated fitness value is obtained. Comparing the updated fitness value with the initial fitness value, and replacing the updated fitness value with the initial fitness value when the updated fitness value is better than the initial fitness value, otherwise, keeping unchanged;
generating a random number r E [0,1 ] subject to uniform distribution]When r < P a And when the bird nest is positioned, the current bird nest position is reserved, and no operation is performed. And when r > P a For the ith nest position in the t+1th iteration processThe new bird nest position is generated using the following formula:
wherein , and />The bird nest positions selected randomly for two times in the t-th iteration process;
repeating the steps until the maximum Iteration number Iteration is reached.
For a typical cuckoo algorithm, the step size parameter α takes a fixed value of 0.01. Thus, the optimum search performance of the cuckoo search algorithm is primarily dependent on Levy flights. The change of the flight path has the characteristic of heavy tail probability distribution (namely, short step length occurs frequently and long step length occurs occasionally in the searching process), so that local searching and global searching are realized. However, as the search scale increases (i.e., the N value increases), the algorithm tends to sink into a locally optimal location (solution) and the search speed drops significantly. To improve the algorithm, to improve its performance, the step size parameter α is defined based on a monotonically increasing/decreasing adjustment mechanism expressed as follows:
wherein ,α0 Is constant and may be, for example, 0.5.Iter is the current iteration number. Thus, in the initial search phase, global search capability is enhanced by monotonically increasing the step size parameter, and in the later search phase, local search capability is enhanced by monotonically decreasing the step size parameter. Thereby avoiding the search algorithm from sinking into a local optimal position (solution) and improving the search precision and speed. In this step, d=10, p is preferably set a ＝0.8、Iteration＝200。
S300: and taking local normalized mutual information of the result image and a reference image in the image to be registered as similarity measure, taking an optical flow field model as search space (also called mapping model), combining an optical flow field constraint equation and the local normalized mutual information to establish a functional extremum problem, solving the functional extremum problem based on a cuckoo search algorithm to obtain a second mapping parameter of a second stage, and obtaining a final registration result through cubic convolution interpolation operation.
Referring to fig. 3, step S300, as a step of coarse registration, specifically includes:
s310: the reference image I is represented based on the following expression 1 And resulting imageImage block I of (2) P1 and />Is a normalized mutual information of:
wherein, image block I P1 Andfrom I by using sliding window technique 1 and />Traversing from the upper left corner to the lower right corner of (1), and image block (I) P1 and />Is 8 x 8, the sliding step is 2 +.> and />The following are expressed and solved respectively:
wherein ,p1 (x, y) and p 2 (x, y) respectively represent image block I P1 Andedge probability distribution, p 12 (x, y) represents image block I P1 and />W is the joint probability distribution of image block I P1 and />Is defined in the above-described specification.
Further, the step S300 of using the local normalized mutual information of the result image and the reference image in the image to be registered as a similarity measure, using the optical flow field model as a search space (also referred to as a mapping model), combining the optical flow field constraint equation and the local normalized mutual information to establish a functional extremum problem, solving the functional extremum problem based on a cuckoo search algorithm to obtain a second mapping parameter of the second stage, and obtaining a final registration result through a cubic convolution interpolation operation further includes:
s320: based on image block I at t time P1 The intensity E (x (t), y (t), t) at coordinates (x, y), and at time t+Δt for image block I P1 The light intensity E (x (t+Δt), y (t+Δt), t+Δt) at the coordinates (x+Δt, y+Δy) is established as follows (in this embodiment, Δt is small enough to be considered as the light intensity being unchanged):
E(x(t),y(t),t)＝E(x(t+Δt),y(t+Δt),t+Δt)；
s330: reference image I 1 And "coarse registration" of the resulting imageImage block I of (2) P1 and />Consider two frames in the motion process of the image I, and consider the image block I P1 and />Gray value f of (2) P1 (x, y) and->Defined as the optical flow field model at times t+Deltat and tAnd (3) solving the light intensity to obtain:
performing taylor expansion on the right side of the model, omitting higher order terms above second order, and obtaining an optical flow field constraint equation under the assumption that the light intensity is unchanged:
order theThen u= (u, v) is the velocity field describing the motion of the image and will +.>The gradients over the three variables x, y, t are denoted as +.>Let the optical flow field constraint equation be abbreviated as:
f x u+f y v+f t ＝0
in general, the optical flow field model needs to introduce smooth continuous constraint conditions and then be converted into functional extremum solving problems. This conventional approach is only applicable in cases where the difference in pixel values between the images to be registered is small. In the embodiment of the invention, the similarity measure of the optical flow field constraint equation and the local normalization mutual information is combined, so that the following functional extremum problem is constructed:
in the link, the formula is used as fitness, and an improved cuckoo search algorithm is adopted to solve an optimal value, so that mapping parameters in the second-stage registration step are obtained. In this embodiment, the parameter setting for improving the cuckoo search algorithm is improvedSet to d=8, p a =0.8, iteration=100. And finally, the second mapping parameter of the second stage is acted on the result image, and a final registration result is obtained through cubic convolution interpolation operation.
Referring to fig. 4 (a) - (g), an example of registering a set of liver multi-phase CT images using the liver CT registration method of the present invention is shown. Fig. 4 (a) is a schematic diagram of an arterial phase CT image (reference image) according to a preferred embodiment of the present invention, fig. 4 (b) is a schematic diagram of a pan phase CT image (floating image) according to a preferred embodiment of the present invention, fig. 4 (c) is a schematic diagram of a balance phase CT image (floating image) according to a preferred embodiment of the present invention, fig. 4 (d) is an effect diagram of drawing and merging the boundary of a liver organ and a liver cancer lesion together by using a drawing software according to a preferred embodiment of the present invention, wherein the lower right corner of fig. 4 (d) is a schematic diagram of an enlarged effect of a liver cancer lesion boundary according to a preferred embodiment of the present invention, fig. 4 (e) is a schematic diagram of registration results of fig. 4 (b) according to a preferred embodiment of the present invention, fig. 4 (f) is a reference image according to a preferred embodiment of the present invention, and fig. 4 (c) is a schematic diagram of registration results of fig. 4 (g) is a schematic diagram of a liver cancer lesion drawn by using a drawing software according to a preferred embodiment of the present invention, and the lower right corner of fig. 4 (f) is a liver cancer lesion drawn boundary of the liver cancer lesion is a preferred embodiment of the present invention. The difference between before and after registration of the images is evident from fig. 4 (a) - (g).
The invention also discloses a computer readable storage medium having stored thereon a computer program which when executed by a processor realizes the steps as described above.
It should be noted that the embodiments of the present invention are preferred and not limited in any way, and any person skilled in the art may make use of the above-disclosed technical content to change or modify the same into equivalent effective embodiments without departing from the technical scope of the present invention, and any modification or equivalent change and modification of the above-described embodiments according to the technical substance of the present invention still falls within the scope of the technical scope of the present invention.
Claims (8)
1. The liver CT image registration method based on the cuckoo search algorithm is characterized by comprising the following steps of: acquiring an image to be registered comprising a reference image and a floating image, and performing two-dimensional discrete wavelet transformation on the image to be registered to obtain a preprocessed image comprising image significance characteristics;
taking normalized mutual information of the preprocessed image as similarity measure, solving to obtain a first mapping parameter by taking an affine transformation model as search space based on a cuckoo search algorithm, and obtaining a result image through cubic convolution interpolation operation after the mapping parameter acts on the preprocessed image;
taking local normalized mutual information of a result image and a reference image in an image to be registered as similarity measure, taking an optical flow field model as search space, combining an optical flow field constraint equation and the local normalized mutual information to establish a functional extremum problem, solving the functional extremum problem based on a cuckoo search algorithm to obtain a second mapping parameter, and obtaining a registration result through cubic convolution interpolation operation, wherein the method comprises the steps of
The method comprises the steps of taking local normalized mutual information of a result image and a reference image in an image to be registered as similarity measure, taking an optical flow field model as search space, combining an optical flow field constraint equation and the local normalized mutual information to establish a functional extremum problem, solving the functional extremum problem based on a cuckoo search algorithm to obtain a second mapping parameter, and obtaining a registration result through cubic convolution interpolation operation, wherein the steps comprise:
the reference image I is represented based on the following expression 1 And resulting imageImage block I of (2) P1 and />Is a normalized mutual information of:
wherein, image block I P1 Andfrom I by using sliding window technique 1 and />Traversing from the upper left corner to the lower right corner of (1), and image block (I) P1 and />Is 8 x 8, the sliding step is 2 +.> and />The following are expressed and solved respectively:
wherein ,p1 (x, y) and p 2 (x, y) respectively represent image block I P1 Andedge probability distribution, p 12 (x, y) represents image block I P1 and />Is a joint summary of (1)The rate distribution, w is the image block I P1 and />Is defined by the area coverage of (a);
the method comprises the steps of taking local normalized mutual information of a result image and a reference image in an image to be registered as similarity measure, taking an optical flow field model as search space, combining an optical flow field constraint equation and the local normalized mutual information to establish a functional extremum problem, solving the functional extremum problem based on a cuckoo search algorithm to obtain a second mapping parameter, and obtaining a registration result through cubic convolution interpolation operation, wherein the method further comprises the following steps:
based on image block I at t time P1 The intensity E (x (t), y (t), t) at coordinates (x, y), and at time t+Δt for image block I P1 The light intensity E (x (t+Δt), y (t+Δt), t+Δt) at the coordinates (x+Δt, y+Δy) is established as follows:
E(x(t),y(t),t)＝E(x(t+Δt),y(t+Δt),t+Δt)；
block I of the picture P1 Andgray value f of (2) P1 (x, y) and->The light intensity of the light flow field model at the time t+delta t and t is defined as:
and its optical flow field constraint equation:
order theWill->The gradients over the three variables x, y, t are denoted as +.> Let the optical flow field constraint equation be abbreviated as:
f x u+f y v+f t ＝0
thereby constructing the following functional extremum problem:
2. the image registration method according to claim 1, wherein the steps of acquiring an image to be registered and performing two-dimensional discrete wavelet transform on the image to be registered to obtain a preprocessed image having image features include:
acquiring an image to be registered recorded with liver CT modal information, and performing Daubechies p=2 two-dimensional discrete wavelet transform on the image to be registered;
reserving a coefficient matrix of a high-frequency subband obtained after Daubechies p=2 two-dimensional discrete wavelet transformation, and setting a coefficient matrix of a low-frequency subband;
performing two-dimensional discrete wavelet inverse transformation on the coefficient matrix of the high-frequency sub-band to obtain a preprocessed image IH with image significance characteristics 1 and IH2 。
3. The image registration method according to claim 2, wherein the steps of acquiring an image to be registered, which is recorded with liver CT modality information, and performing Daubechies p=2 two-dimensional discrete wavelet transform on the image to be registered, include:
taking the first image as a reference image I 1 The second image is a floating image I 2 ；
Respectively are provided withThe reference image I is based on the following formula 1 And floating image I 2 Performing two-dimensional discrete wavelet transform;
wherein f (x, y) represents the reference image I 1 Or floating image I 2 M and N represent reference image I 1 Or floating image I 2 Is defined by the row and column widths of (1), and />For the transformed coefficient matrix +.>As a scale function +.>Wavelet functions in horizontal, vertical and diagonal directions respectively, and the wavelet functions are separable functions, and the expression is as follows:
wherein , and />Is a real function of one-dimensional square integrable; ψ (x) and ψ (y) are Daubechies p=2 wavelet functions.
4. The image registration method according to claim 2, wherein the step of obtaining the result image through cubic convolution interpolation operation after taking normalized mutual information of the preprocessed image as a similarity measure and taking an affine transformation model as a search space to solve for the first mapping parameter based on a cuckoo search algorithm, so that the mapping parameter acts on the preprocessed image comprises:
the normalized mutual information of the preprocessed image is represented based on the following expression:
wherein ,p1 (x, y) and p 2 (x, y) are the pre-processed images IH, respectively 1 and IH2 Edge probability distribution, p 12 (x, y) is the pre-processed image IH 1 and IH2 Is IH, omega 1 and IH2 Is set, and takes M x N;
solving the preprocessed images IH based on the following formulas, respectively 1 and IH2 Edge information entropy of (2):
so that the image IH is preprocessed 1 and IH2 Is expressed as:
5. the image registration method according to claim 4, wherein an expression of the affine transformation model is as follows:
wherein [ x y ]]And [ x 'y ]']Respectively pre-processing the image IH 1 Reference coordinates of (c) and the pre-processed image IH 2 A) floating coordinates of a 11 ,a 12 ,a 21 ,a 22 ,b 1 ,b 2 Is a parameter of the affine transformation model.
6. The image registration method of claim 4, wherein the cuckoo search algorithm comprises the steps of: initializing parameters of the cuckoo search algorithm, including generating normal distributed random numbers as initial positions x of N bird nests of the cuckoo search algorithm i (i=1, … N) and calculating the initial position x using the similarity measure as an objective function i (i=1, … N) corresponding initial fitness value;
the following parameters were set: dimension d, discovery probability p a Maximum Iteration number Iteration;
the position of the bird nest is updated by Levy flight based on the following formula:
wherein , and />Represents the position of the ith bird nest, < >/during the t+1st and t iterations, respectively>Representing point-to-point multiplication, α represents a step size parameter, levy (β) represents a random step size following Levy flight, β is a control factor for Levy flight, and a random search path formula for Levy flight is expressed as:
wherein u and v are random variables obeying standard normal distribution, and the calculation formula of phi is as follows:
wherein Γ represents a Gamma function;
after the bird nest position is updated, calculating the corresponding fitness value again to obtain an updated fitness value;
comparing the updated fitness value with the initial fitness value, and replacing the updated fitness value with the initial fitness value when the updated fitness value is better than the initial fitness value, otherwise, keeping unchanged;
generating a random number r E [0,1 ] subject to uniform distribution]When r < P a When the bird nest is in the nest position, the current bird nest position is reserved and no operation is performed; and when r > P a For the ith nest position in the t+1th iteration processThe new bird nest position is generated using the following formula:
wherein , and />The bird nest positions selected randomly for two times in the t-th iteration process;
repeating the steps until the maximum Iteration number Iteration is reached.
7. The image registration method according to claim 6, wherein the step size parameter α is defined based on a monotonically increasing/decreasing adjustment mechanism, wherein the adjustment mechanism is expressed as follows:
wherein ,α0 Being constant, iter is the current number of iterations.
8. A computer readable storage medium, on which a computer program is stored, which computer program, when being executed by a processor, carries out the steps of any of claims 1-7.
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| CN105447882A (en) * | 2015-12-16 | 2016-03-30 | 上海联影医疗科技有限公司 | Image registration method and system |
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| CN105447882A (en) * | 2015-12-16 | 2016-03-30 | 上海联影医疗科技有限公司 | Image registration method and system |
| CN110264503A (en) * | 2019-06-18 | 2019-09-20 | 上海理工大学 | A kind of method for registering images based on CS search |
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