CN110517299B - Elastic image registration algorithm based on local feature entropy - Google Patents
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Abstract
An elastic image registration algorithm based on local feature entropy analyzes the defects of local boundary entropy and causes of the defects, improves the defects in a targeted manner, achieves the purpose of detecting more image feature textures, can be used in a multi-mode image elastic registration task, obtains relatively high registration precision, and can provide important theoretical support for target space positioning and multi-mode information fusion.
Description
Technical Field
The invention particularly relates to the technical field of image processing, in particular to elastic registration processing aiming at the phenomena of low tissue contrast, serious uniform gray scale and the like of an image, and the elastic registration processing can assist the spatial positioning of an interest target in a clinical medical image and the fusion of multi-modal image information.
Background
Image registration is a processing technology for finding optimal spatial transformation, which quantifies information difference between images to be registered through similarity measurement, minimizes the difference by utilizing an optimization algorithm so as to find optimal spatial transformation parameters, and realizes full alignment of image positions and morphological information. The image processing technology can assist clinical tasks such as image understanding and analysis, multi-modal image information fusion, target positioning, morphology detection and the like, so that the method has very important clinical diagnosis value and research significance. Currently, there are a large number of image elastic registration algorithms, which are generally classified into intensity based registration (intensity based methods) and feature based registration (feature based methods). The gray-based registration method mainly evaluates the information difference between the images to be registered by developing a suitable similarity measure. The information quantization performance of the similarity measure directly determines the accuracy of the image registration. The existing similarity measure often cannot effectively quantify the information difference in the local fuzzy area, thereby causing a larger local registration error. Such a disadvantage is mainly caused by a local region having a low tissue contrast and a severe gray unevenness phenomenon, and the influence of the above phenomenon cannot be sufficiently reduced by using only the pixel gray. To reduce the effects of weak tissue contrast and gray scale non-uniformity, feature-based registration methods have been proposed and extensively studied. The method does not directly use the pixel gray information to carry out the registration of the image, but utilizes a characteristic description operator to convert the image gray into the characteristic texture with unique attributes, and realizes the quantification of the image information to be registered through the characteristic texture. The better the feature operator has image information detection capability, the less the weak contrast and gray scale non-uniformity phenomena have on image registration. Therefore, how to design a proper feature descriptor becomes an important research direction. This not only relates to the extraction of different feature textures in the image, but also determines the registration accuracy of the global and local regions of the image.
In order to design a proper feature descriptor to extract potential texture information in an image, it is necessary to analyze the relative information difference of each pixel and its neighboring pixels in the local neighborhood in terms of gray scale and position, and convert the information difference into an easily-distinguished feature value through a selected function (such as a gaussian function). The information transformation of the feature operator has the following characteristics:
(1) different image information is converted to correspond to different characteristic values, and the distribution of the characteristic values is in a relatively reasonable value range; (2) the texture features of the image can be well stored after conversion, and the loss of other information caused by detection of certain information is prevented. There are many image feature operators satisfying the two characteristics, wherein the local boundary entropy can extract the image boundary information to some extent and is used in the image segmentation task. However, the operator has an obvious disadvantage that the calculation of the boundary entropy uses a modulus operator, and the operator cannot distinguish pixels with gray values smaller than a local mean value, so that the influence of weak tissue contrast and uneven gray values cannot be effectively reduced. Therefore, reasonably improving the calculation of the local boundary entropy can effectively inhibit the influence of the above adverse factors, and assist and improve the image registration accuracy of the local region.
After the feature description operator is proposed, the image to be registered can be converted into a feature texture map (feature map), and how to evaluate the information difference between the feature texture maps needs to design a registration similarity measure. Common similarity measures are sum of squared differences (sum of squared differences), cross-correlations (cross correlations), and mutual information (mutual information). Of these measures, the sum of squares of the differences has the characteristics of simple calculation and rapid convergence, and is widely used. To this end, the present invention uses the sum of the squares of the differences to quantify the information difference between the feature texture maps and minimizes such feature information difference to achieve registration of the original grayscale images.
Disclosure of Invention
In order to solve the defects in the prior art, the invention provides an elastic image registration algorithm based on local feature entropy, potential texture information in an image fuzzy region is detected by designing two new feature entropy operators, the feature textures are used for image registration, information difference between the feature textures is evaluated by using the sum of squares of differences, quantification of information between images to be registered is executed, and then elastic registration of the images is realized.
The main calculation thought of the invention is as follows: by analyzing the defects of the local boundary entropy and the reasons for the defects, the defects are improved and processed in a targeted manner, so that the aim of detecting more image characteristic textures is fulfilled. The method comprises the following specific steps:
(1) integrating the difference value between the pixel gray level and the local gray level mean value into a local boundary entropy operator, thereby leading out two new local structure description operators, namely local non-uniform entropy and local structure entropy, and realizing the extraction of different image characteristic textures in a local area;
(2) three different characteristic entropy images can be obtained after an image is processed by three characteristic operators, namely local boundary entropy, local non-uniform entropy and local structure entropy, and the characteristic entropy images are used for describing the texture of the image from different aspects and are integrated to form a characteristic entropy vector to be used in an image registration task, so that the conversion from a gray level image to the characteristic entropy vector is realized; by utilizing the conversion relation, two images to be registered, namely a reference image and a floating image are converted into a reference vector and a floating vector, the information difference between the original images to be registered can be quantified by calculating the square sum of the difference between the two characteristic entropy vectors, and the space position alignment between the images can be realized by minimizing the square sum measure of the difference by using an optimization algorithm;
(3) the free deformation registration frame is characterized in that when an optimization algorithm is utilized to minimize the information difference between images to be registered, namely the square sum of the difference between characteristic entropy vectors, a floating image needs to be gradually transformed and is close to a reference image step by step until the reference image and the floating image are completely overlapped, the spatial transformation of the floating image is generally realized in the registration of an elastic image through the free deformation registration frame which is developed based on a cubic spline function, the position deviation of each pixel point in the floating image is interpolated and calculated through a plurality of spline functions, the position transformation of the floating image is realized, because the cubic spline function is continuous in second order, the spatial transformation based on the free deformation can analytically simulate the position change of pixels in the global and local ranges of the image, and after the position of the pixels is changed, the corresponding gray scale also needs to be updated by using an interpolation technology, and after the position and the gray scale of each pixel in the image are updated, obtaining a new floating image, restarting the next round of calculation of the new floating image and the original reference image, and circulating the process until the information difference between the images is not changed any more, namely the image registration is finished.
The development steps of the local characteristic entropy operator in the step (1) are as follows: the local boundary entropy can be expressed as:
where m is the mean value of the gray levels (mean) in the local image area)，ΠXIs a three-dimensional square area with the center at X and the side length r, I (y) is the pixel gray scale at the coordinate position y, p (y) is the probability distribution corresponding to the gray scale I (y), log (-) is the natural logarithm operator, mod (-) is the modulus operator, because the modulus operator can not effectively detect the gray scale value smaller than the local mean value (i.e. I<m) pixels, thereby causing the local boundary entropy operator to have limited boundary detection capability, and in order to improve the defects of the modulus operator, the difference between the pixel gray level and the gray level mean value is introduced into the calculation of p (y) to obtain a new probability p1(y) is specifically represented as follows:
where, |, represents an absolute value operator. The probability can relieve the defects of a modulus operator to a certain extent and enhance the information change between the pixel gray level and the local gray level mean value. Based on this new probability distribution, a local non-uniform entropy can be obtained, which can be expressed as:
according to the two probability distributions, the information difference between the images can be effectively detected by using the modulus operator and the local gray average value. Thus, two new images can be derived from the two probability distributions, which are respectively represented as:
these two new images can be regarded as intensity variations of the original image, which illustrate the grey scale variation between adjacent pixels in the original image from different aspects. From the original image and its two gray variants, another gray variant can be constructed, specifically represented as:
I3(y)＝|(I1(y)+I2(y)-I(y))I(y)|
using this gray variant, a new gray probability distribution and a new local feature operator can be designed, which can be expressed as:
this feature operator is called local structural entropy (STR);
from the above-mentioned local boundary entropy, local non-uniform entropy, and local structure entropy operators (i.e. lee (X), inh (X), and str (X)), it can be seen that three different characteristic entropy information will correspond at any coordinate position X in the image, and thus they can be used simultaneously in image registration to assist in the quantization of the image information to be registered.
The step (2) is that the similarity measure construction step in the similarity measure based on the local feature entropy is as follows:
three characteristic entropy operators LEE (X), INH (X) and STR (X) are utilized to convert a reference image and a floating image to be registered into a reference characteristic entropy vector diagram and a floating characteristic entropy vector diagram respectively by VRAnd VFThe concrete calculation formula is as follows:
wherein, the result of processing the reference image by the three characteristic entropy operators is LEER(X),INHR(X),STRR(X)，
The result of the processing of the floating image is LEEF(X),INHF(X),STRF(X)；
In the registration process, when the characteristic entropy vector VRAnd VFWhen the difference of each corresponding vector component is minimum, the image to be registered is in a complete alignment state in space, namely the registration is completed;
to evaluate a characteristic entropy vector VRAnd VFThe invention uses the sum of the squares of the differences as a similarity measure to quantify the inconsistency between the differences, and the specific calculation formula can be expressed as:
wherein Ω is the global image region, and T (X, Φ) is a spatial transformation with Φ as a parameter.
The construction steps of the image elasticity space transformation in the free deformation registration frame in the step (3) are as follows: (3a) in the spatial transformation T (X, phi), its corresponding transformation parameter phi can be used as Nx×Ny×NzThe grid of (a) represents that the grid intervals adjacent to each other are available in the three image coordinate axis directions as s ═ s(s)x,sy,sz) It is shown that the corresponding position offset of each grid intersection (i.e., grid nodule) at coordinates (i, j, k) is di,j,kFor any pixel point X in the floating image (X, y, z), the corresponding spatial transformation T (X, Φ) is:
wherein the content of the first and second substances,
u＝x/sx-i-1,v＝y/sy-i-1,w＝z/sz-i-1,
for the round-down operator, LlRepresents the ith basis function in the spline function, which can be represented as L0(t)＝(1-t)3/6，L1(t)＝(3t3-6t2+4)/6，L2(t)＝(-3t3+3t2+3t +1)/6 and L3(t)＝t3/6, where 0. ltoreq. t<1；
(3b) In image registration, in order to ensure the smoothness of the spatial deformation field and avoid the non-conformity with the actual image deformation, a constraint term of applying irregular deformation to the deformation field in the calculation of the similarity measure is required, and the constraint term is called bending energy (bending energy) and has the calculation formula:
where B (-) is the bending energy and N is the number of pixels involved in the operation. Integrating this constraint term into the similarity measure, the final image registration quantization function can be obtained, i.e., (1- λ) S (Φ) + λ B (Φ), where λ is the weighting factor.
The invention has the beneficial effects that: the invention provides an elastic image registration algorithm based on local feature entropy, which aims to improve and process the defects by analyzing the defects of local boundary entropy and the reasons causing the defects, thereby achieving the purpose of detecting more image feature textures, being capable of being used in a multi-mode image elastic registration task, obtaining relatively high registration precision and providing important theoretical support for target space positioning and fusion of multi-mode information.
Drawings
FIG. 1 is a flow chart of the present invention.
Fig. 2 is a simulation experiment performed on the artificially synthesized mr image disclosed in the present invention, in which the first column is a reference image and a corresponding manual label, the second column is a floating image and a label thereof, and the third column is a difference between the reference label and the floating label before and after registration.
FIG. 3 is a simulation experiment performed on clinical MRI images according to the present invention, wherein the first column is a reference image and a corresponding manual label, the second column is a floating image and a label thereof, and the third column is a difference between the reference label and the floating label before and after registration;
FIG. 4 is a simulation experiment performed on clinical MRI images according to the present invention, wherein the first column is a reference image and a corresponding manual label, the second column is a floating image and a label thereof, and the third column is a difference between the reference label and the floating label before and after registration;
fig. 5 is a comparison of the results of the algorithm of the present invention with several existing image registration algorithms.
Detailed Description
The general idea of the invention is as follows:
(1) the probability distribution corresponding to the local boundary entropy operator is calculated by a modulus operator, and the operator is used for storing pixels with the gray scale smaller than the local mean value and pixels with the truncated gray scale value larger than the local mean value, so that the enhancement of the gray scale difference in the local area is selectively realized. This selective operation results in the boundary entropy operator not being able to efficiently detect image texture information in certain regions. In order to overcome the defects of the local boundary entropy, the difference value of pixel gray scale and the squared local mean value can be introduced into the corresponding probability distribution calculation, so that the defects of a modulus operator are alleviated; or the modulus operator is used on the gray of the original image to obtain two different gray variants. By effectively integrating the original gray scale and two variants thereof, new characteristic entropy operators (namely local non-uniform entropy and local structure entropy) can be constructed.
(2) Three different feature texture maps (feature maps) corresponding to one image can be obtained by using the feature entropy operators (local boundary entropy, local non-uniform entropy and local structure entropy). These texture maps depict the latent feature information that an image has from different aspects, and these feature information are interrelated and complementary to each other. Using these feature information alone to perform image registration would likely result in registration results with limited accuracy. To this end, the present invention simultaneously uses these feature information in image registration to obtain better registration accuracy, and uses the sum of the squares of the differences to quantify the information difference between them.
(3) Image elastic registration requires a key spatial transform (space transform) in addition to similarity measurement to perform the transformation of each pixel location information. The elastic spatial transform is usually constructed based on a cubic spline function (cube B-spline function), i.e., Free Form Deformation (FFD). Under the deformation frame, the position offset of each pixel point is obtained through the common interpolation calculation of three spline functions.
The following describes the elastic image registration algorithm based on the local structure operator with reference to the accompanying drawings;
referring to fig. 1, the elastic image registration algorithm based on local feature entropy of the present invention includes the following steps:
step 1, constructing a local characteristic entropy operator capable of effectively enhancing local gray variation and extracting potential texture information
(1a) According to the defects existing in the calculation of the probability distribution corresponding to the local boundary entropy operator, a rectangular region (r is the side length of the local region) with the size of r multiplied by r is taken from the image, the gray level of the pixels in the region is normalized, and the pixel gray level in the region is normalized through a formula
And p (y) mod (I (y), m)/m, and p1(y)＝mod(|I2(y)-m2And (4) calculating two different probability distributions in the ratio of I, m to m, and applying the probability distributions to the calculation of the image entropy to obtain two different characteristic entropy information (namely local boundary entropy and local non-uniform entropy). To further detect feature texture in the image, a corresponding variation of the original gray level (i.e., I) is constructed based on the two probability distributions1(y) mod (I (y), m) and I2(y)＝mod(|I2(y)-m2I, m)), and then integrating the original gray scale and its two gray scale variants to design a new gray scale variant (i.e. I)3(y)＝|(I1(y)+I2(y) -I (y)) is used for extracting the image texture features. Specifically, the calculation formula of p (y) is applied to I3A new probability distribution (i.e. p) available on (y)2(y)＝mod(I3(y, m)/m) and the local structure entropy characteristics can be obtained by utilizing the probability distribution.
(1b) Three different feature textures can be obtained by processing an image by using the feature entropy operators (namely local boundary entropy, local non-uniform entropy and local structure entropy). The feature textures describe the target object in the image from different aspects, and the feature textures can complement each other, so that the feature textures are simultaneously used for image registration, the similarity measure in the registration process and the updating of an optimization algorithm are jointly restricted, and high-quality registration is realized.
Step 2, similarity measure based on local characteristic entropy
The three local characteristic entropy operators are integrated to form a characteristic entropy vector (entropy vector) corresponding to the pixel gray level. The feature entropy operator is used for image registration, and better registration accuracy can be obtained than single feature entropy registration. Based on the method, the reference images and the floating images to be registered can be converted into reference and floating characteristic entropy vector diagrams, the difference between the two characteristic entropy vector diagrams in size and direction can be calculated by using sum of squares (sum of squared differences), and the evaluation of the information difference between the original images to be registered is assisted.
In image registration, the spatial transformation searched by the optimization algorithm is used for transforming the floating image, and the minimization of the information difference (namely, the minimization of the similarity measure) between the floating image and the reference image is realized. A common elastic space transformation is a free deformation model based on cubic spline functions; these models have a second order differential and are therefore able to smoothly model the image deformation of local and global regions. And when the optimal space transformation parameters are searched by the optimization algorithm, the image to be registered is in a space alignment state, and the registration is completed.
1. Simulation conditions are as follows:
the invention carries out simulation on MATLAB 2013a software on a Windows 1064 bit Intel (R) core (TM) i7-6700HQ CPU @2.60GHz RAM 16GB platform, the simulation data selects public magnetic resonance image data to carry out an elastic registration experiment, and the websites of experimental data sources are https:// woven web.bic.mni.mcgill.ca/woven web/http:// www.loni.ucla.edu/atlas/LPBA 40/.
2. Simulation content and results
1) Simulation experiment 1:
the simulation experiment uses an artificially synthesized multi-mode magnetic resonance image to carry out a registration experiment, the effectiveness of the algorithm is verified, and the experimental result is shown in figure 2:
from the comparison before and after image registration it can be seen that: the two multi-mode images to be registered before the registration have larger difference in gray scale, position and morphology; but the disparity between the two images after registration is significantly reduced.
In fig. 2, the first column is a reference mr image and its corresponding manual labeling, which respectively labels three different brain tissues, namely white brain (WM), gray brain (GM) and cerebrospinal fluid (CSF), the second column is a floating image and its corresponding manual labeling, and the third column is the difference between the reference and floating manual labeling before and after registration. As can be seen from the figure, the algorithm can effectively reduce the morphological difference between the manually marked images.
2) Simulation experiment 2:
the simulation experiment uses clinical magnetic resonance images of the same modality to perform an elastic registration experiment, the registration performance of an algorithm to clinical actual images is verified, and the registration result is presented in fig. 3:
in fig. 3, the first column is a reference magnetic resonance image of the same modality and a corresponding manual labeling image thereof, the labeling interest areas are white matter, gray matter and cerebrospinal fluid, respectively, the second column is a floating image and a corresponding manual labeling image thereof, respectively, and the third column is a difference between the two manual labeling images before and after registration. As can be seen from the figure, the two images before registration have larger position errors, and the position and morphology difference between the images after registration is obviously reduced.
3) Simulation experiment 3:
the simulation experiment uses clinical magnetic resonance images of the same modality to perform an elastic registration experiment, the registration performance of the algorithm on clinical actual images is verified, and the registration result is shown in fig. 4:
in fig. 4, the first column is a reference magnetic resonance image and a floating magnetic resonance image of the same modality, the second column is manual labeling corresponding to 54 regions of interest in the reference image and the floating image, respectively, and the third column is a difference map between the two manually labeled images before and after registration. As can be seen from the figure, the two images before registration have larger position errors, and the position and morphology difference between the images after registration is obviously reduced.
3) Simulation experiment 4:
in the simulation experiment, the image registration effectiveness of the method is verified by comparing the performance difference between the algorithm and the existing registration algorithms (namely eSD algorithm, NMI algorithm and MIND algorithm).
Contrast experiments registration performance comparisons using multi-modal clinical magnetic resonance images, the experimental results quantify the coincidence ratio between three regions of interest (i.e. white brain matter, gray matter, cerebrospinal fluid) by means of the overlay accuracy (DSC), which can be expressed as follows:
wherein, A represents the manual labeling result of the reference image, B represents the result after algorithm registration, N represents the intersection operational character, N (-) is the solving function of the pixel number in the given area, the value range of DSC is between 0 and 1, and the larger the DSC is, the more accurate the algorithm registration is.
The comparison result of the simulation experiment refers to fig. 5, from which it can be observed relatively directly that the MIND algorithm obtains the highest DSC values on two regions of interest, and thus has the best registration accuracy; the algorithm herein is slightly weaker than the MIND algorithm, but has significantly better registration performance than the eSSD and NMI algorithms.
The comparison result shows that the algorithm disclosed by the invention can have similar registration precision to the existing registration algorithm (such as MIND) in the registration performance in the global image range, and is superior to the eSD and NMI algorithms.
The skilled person should understand that: although the invention has been described in terms of the above specific embodiments, the inventive concept is not limited thereto and any modification applying the inventive concept is intended to be included within the scope of the patent claims.
The above description is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above embodiments, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention. It should be noted that modifications and embellishments within the scope of the invention may occur to those skilled in the art without departing from the principle of the invention, and are considered to be within the scope of the invention.
Claims (3)
1. An elastic image registration algorithm based on local feature entropy is characterized by comprising the following steps:
(1) integrating the difference value between the pixel gray level and the local gray level mean value into a local boundary entropy operator, thereby leading out two new local structure description operators, namely local non-uniform entropy and local structure entropy, and realizing the extraction of different image characteristic textures in a local area, wherein the development steps of the local characteristic entropy operator are as follows: the local boundary entropy can be expressed as:
wherein m is the mean value of the gray levels (mean), Π in the local image areaXThe method is characterized in that the method is a three-dimensional square area with the center at X and the side length of r, I (y) is pixel gray at a coordinate position y, p (y) is probability distribution corresponding to the gray I (y), log (-) is a natural logarithm operator, mod (-) is a modulus operator, pixels with gray values smaller than a local mean value (i.e. I < m) cannot be effectively detected by the modulus operator, so that a local boundary entropy operator has limited boundary detection capability, and in order to improve the defects of the modulus operator, the difference between the pixel gray value and the gray mean value is introduced into the calculation of p (y) to obtain a new probability p (y)1(y) is specifically represented as follows:
wherein, |, represents the absolute value operator, and this probability can alleviate the not enough that the operator exists of taking the modulus to a certain extent, strengthens the information change between pixel grey scale and local grey scale mean, based on this new probability distribution, can obtain a local uneven entropy, can express as:
as can be seen from the two probability distributions, the difference in information between the images can be effectively detected by using the modulo operator and the local gray-scale mean, so that two new images can be extracted from the two probability distributions, which are respectively represented as:
the two new images can be used as gray-scale variants of the original image, which illustrate the gray-scale variation between adjacent pixels in the original image from different aspects, and from the original image and its two gray-scale variants, another gray-scale variant can be constructed, specifically expressed as:
I3(y)＝|(I1(y)+I2(y)-I(y))I(y)|
using this gray variant, a new gray probability distribution and a new local feature operator can be designed, which can be expressed as:
this feature operator is called local structural entropy;
according to the local boundary entropy, the local non-uniform entropy and the local structure entropy operators LEE (X), INH (X) and STR (X) mentioned above, it can be seen that three different characteristic entropy information will correspond to any coordinate position X in the image, so that they can be simultaneously used in image registration to assist the quantification of the image information to be registered;
(2) three different characteristic entropy images can be obtained after an image is processed by three characteristic operators, namely local boundary entropy, local non-uniform entropy and local structure entropy, and the characteristic entropy images are used for describing the texture of the image from different aspects and are integrated to form a characteristic entropy vector to be used in an image registration task, so that the conversion from a gray level image to the characteristic entropy vector is realized; by utilizing the conversion relation, two images to be registered, namely a reference image and a floating image are converted into a reference vector and a floating vector, the information difference between the original images to be registered can be quantified by calculating the square sum of the difference between the two characteristic entropy vectors, and the space position alignment between the images can be realized by minimizing the square sum measure of the difference by using an optimization algorithm;
(3) a free deformation registration frame, which is to gradually transform a floating image and make the floating image approach to a reference image step by step when an optimization algorithm is utilized to minimize the information difference between images to be registered, namely the square sum of the difference between characteristic entropy vectors, until the reference image and the floating image are completely overlapped together, the space transformation of the floating image is generally realized by the free deformation registration frame in the elastic image registration, the registration frame is developed based on a cubic spline function, the position offset of each pixel point in the floating image is interpolated and calculated by a plurality of spline functions, the position transformation of the floating image is realized, because the cubic spline function is continuous in second order derivation, the space transformation based on the free deformation can analytically simulate the position change of pixels in the global and local ranges of the image, and after the position of the pixels is changed, the corresponding gray scale also needs to be updated by using an interpolation technology, and after the position and the gray scale of each pixel in the image are updated, obtaining a new floating image, restarting the next round of calculation of the new floating image and the original reference image, and circulating the process until the information difference between the images is not changed any more, namely the image registration is finished.
2. The local feature entropy-based elastic image registration algorithm according to claim 1, wherein the step (2) comprises the following steps of constructing the similarity measure of the local feature entropy-based similarity measure:
three characteristic entropy operators LEE (X), INH (X) and STR (X) are utilized to convert a reference image and a floating image to be registered into a reference characteristic entropy vector diagram and a floating characteristic entropy vector diagram respectively by VRAnd VFThe concrete calculation formula is as follows:
wherein, the result of processing the reference image by the three characteristic entropy operators is LEER(X),INHR(X),STRR(X), LEE as a result of processing the floating imageF(X),INHF(X),STRF(X)；
In the registration process, when the characteristic entropy vector VRAnd VFWhen the difference of each corresponding vector component is minimum, the image to be registered is in a complete alignment state in space, namely the registration is completed;
to evaluate a characteristic entropy vector VRAnd VFThe invention uses the sum of the squares of the differences as a similarity measure to quantify the inconsistency between the differences, and the specific calculation formula can be expressed as:
wherein Ω is the global image region, and T (X, Φ) is a spatial transformation with Φ as a parameter.
3. The local feature entropy-based elastic image registration algorithm according to claim 1, wherein the step (3) of constructing the spatial transformation of the image elasticity in the free deformation registration framework comprises the following steps:
(3a) in the spatial transformation T (X, phi), its corresponding transformation parameter phi can be used as Nx×Ny×NzThe grid of (a) represents that the grid intervals adjacent to each other are available in the three image coordinate axis directions as s ═ s(s)x,sy,sz) It is shown that the corresponding position offset of each grid intersection (i.e., grid nodule) at coordinates (i, j, k) is di,j,kFor any pixel point X in the floating image (X, y, z), the corresponding spatial transformation T (X, Φ) is:
wherein the content of the first and second substances,
for the round-down operator, LlRepresents the ith basis function in the spline function, which can be represented as L0(t)＝(1-t)3/6，L1(t)＝(3t3-6t2+4)/6，L2(t)＝(-3t3+3t2+3t +1)/6 and L3(t)＝t3(iii) t is more than or equal to 0 and less than 1;
(3b) in image registration, in order to ensure the smoothness of the spatial deformation field and avoid the non-conformity with the actual image deformation, a constraint term of applying irregular deformation to the deformation field in the calculation of the similarity measure is required, and the constraint term is called bending energy (bending energy) and has the calculation formula:
where B (·) is the bending energy and N is the number of pixels participating in the operation, and this constraint term is integrated into the similarity measure, a final image registration quantization function can be obtained, i.e., (1- λ) S (Φ) + λ B (Φ), where λ is a weighting factor.
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