CN111968162A - Medical image registration method and system based on Conformal Geometric Algebra (CGA) - Google Patents

Medical image registration method and system based on Conformal Geometric Algebra (CGA) Download PDF

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CN111968162A
CN111968162A CN202010770241.XA CN202010770241A CN111968162A CN 111968162 A CN111968162 A CN 111968162A CN 202010770241 A CN202010770241 A CN 202010770241A CN 111968162 A CN111968162 A CN 111968162A
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CN111968162B (en
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曹文明
钟建奇
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Shenzhen University
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Abstract

The invention discloses a medical image registration method and system based on Conformal Geometric Algebra (CGA). CGA feature point extraction is respectively carried out on a reference image and a floating image based on a CGA Gauss Laplace transformation algorithm to obtain reference image feature points and floating image feature points, a reference image feature sphere and a floating image feature sphere are respectively constructed by utilizing the reference image feature sphere and the floating image feature sphere according to a CGA sphere construction algorithm, a transformation relation is determined by utilizing the reference image feature sphere and the floating image feature sphere in a conformal geometric algebra space, and the reference image and the floating sphere image are registered based on the conformal transformation relation. The conformal geometric algebra has rich and uniform calculation modes, so that complex geometric operation and matrix operation can be simplified, registration data parameters are reduced, geometric transformation complexity is reduced, calculation amount is simplified, calculation speed is increased, meanwhile, the conformal geometric algebra can directly process high-dimensional information, dimension information of medical images is not lost, and the registration precision of the medical images is higher.

Description

Medical image registration method and system based on Conformal Geometric Algebra (CGA)
Technical Field
The invention relates to the field of medical image registration, in particular to a medical image registration method and system based on Geometric algebraic (CGA).
Background
In the prior art, medical image registration is mostly directed at two-dimensional image registration, because 2D/2D medical image registration (registration of a reference image representing 2D and a floating image representing 2D) is easy to implement, fast and low in cost. However, the registration of the two-dimensional images does not take the situation of using high dimensional information into consideration, and under the condition of higher dimensional information, the 3D/3D medical image registration (the registration of a reference image representing 3D and a floating image representing 3D) can better meet the requirements in clinical medicine and surgical navigation. At present, the problems of multiple data parameters, high complexity of geometric transformation and large calculation amount exist in 3D/3D image registration.
Disclosure of Invention
The invention mainly aims to provide a medical image registration method and system based on conformal geometric algebra, which can solve the technical problems of more parameters, high geometric transformation complexity and large calculation amount of 3D/3D image registration data.
In order to achieve the above object, a first aspect of the present invention provides a medical image registration method based on conformal geometric algebra, which is characterized in that the method includes:
conformal geometric algebra CGA feature point extraction is respectively carried out on a reference image and a floating image based on a CGA Gauss Laplace transform algorithm to obtain reference image feature points and floating image feature points, wherein the reference image and the floating image are medical images;
according to a CGA sphere construction algorithm, constructing a reference image feature sphere and a floating image feature sphere by respectively using the reference image feature points and the floating image feature points;
in a conformal geometric algebraic space, determining a transformation relationship using the reference image feature sphere and the floating image feature sphere, registering the reference image and the floating image based on the transformation relationship, the transformation relationship including rotation, translation, and scaling.
To achieve the above object, a second aspect of the present invention provides a medical image registration system based on conformal geometric algebra, which is characterized in that the system comprises:
the extraction module is used for respectively extracting geometric algebraic CGA characteristic points of a reference image and a floating image based on a CGA Gaussian Laplace transform algorithm to obtain the characteristic points of the reference image and the characteristic points of the floating image, wherein the reference image and the floating image are medical images;
the construction module is used for respectively constructing a reference image feature sphere and a floating image feature sphere by using the reference image feature points and the floating image feature points according to a CGA sphere construction algorithm;
and the determining and registering module is used for determining a transformation relation by utilizing the reference image feature sphere and the floating image feature sphere in a conformal geometric algebraic space, and registering the reference image and the floating image based on the transformation relation, wherein the transformation relation comprises rotation, translation and scaling.
The invention provides a medical image registration method and system based on conformal geometric algebra. Because the invention utilizes conformal geometric algebra and conformal geometric algebra in the geometric algebra, both have rich and unified calculation modes, can simplify complex linear operation and matrix operation, provide simpler and more direct expression for geometric transformation, can reduce registration data parameters, reduce geometric transformation complexity, simplify calculation amount and accelerate calculation speed, and simultaneously utilize the advantage that the geometric algebra can directly process high-dimensional information without losing the dimensional information of medical images, so that the registration precision of the medical images is higher.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flowchart illustrating a conformal geometric algebra-based medical image registration method according to a first embodiment of the present invention;
FIG. 2 is a flow chart illustrating a detailed step and a subsequent step of step 101 according to a first embodiment of the present invention;
FIG. 3 is a schematic diagram of a first embodiment of the present invention for constructing a CGA feature sphere using CGA feature points;
FIG. 4 is a schematic flow chart illustrating a refinement step of step 103 in the first embodiment of the present invention;
FIG. 5 is a schematic diagram illustrating a transformation relationship between a reference image feature sphere and a floating image feature sphere according to a first embodiment of the present invention;
FIG. 6 is a schematic structural diagram of a medical image registration system based on conformal geometric algebra according to a second embodiment of the present invention;
FIG. 7 is a schematic structural diagram of a refinement module of the extraction module 201 in the second embodiment of the present invention;
FIG. 8 is a schematic diagram of a refinement module of the construction module 202 according to a second embodiment of the present invention;
fig. 9 is a schematic structural diagram of a refinement module of the registration determining module 203 in the second embodiment of the present invention.
Detailed Description
In order to make the objects, features and advantages of the present invention more obvious and understandable, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The technical problems of multiple 3D/3D image registration data parameters, high geometric transformation complexity and large calculation amount exist in the prior art.
In order to solve the technical problem, the invention provides a medical image registration method and system based on conformal geometric algebra. The invention uses conformal geometric algebra, has rich and uniform calculation modes, can simplify complex linear operation and matrix operation, provides simpler and more direct expression for geometric transformation, can reduce registration data parameters, reduce the complexity of geometric transformation, simplify calculation amount and accelerate calculation speed, and simultaneously uses the advantage that geometric algebra can directly process high-dimensional information without losing the dimensional information of medical images, so that the registration precision of the medical images is higher.
Fig. 1 is a flowchart illustrating a medical image registration method based on conformal geometric algebra according to a first embodiment of the present invention. Specifically, the method comprises the following steps:
step 101, respectively extracting CGA characteristic points of a reference image and a floating image based on a CGA Gauss Laplace transform algorithm to obtain the characteristic points of the reference image and the characteristic points of the floating image, wherein the reference image and the floating image are medical images;
it should be noted that, the CGA gaussian Laplace transform algorithm is to extend the classic Geometric gaussian Laplace transform algorithm into a Conformal Geometric Algebraic (CGA) space, and the algorithm not only has the advantages of translational invariance, rotational invariance, stability and strong robustness, but also directly processes high-dimensional information by using the Geometric algebra and simplifies the calculation amount. For an N-dimensional image
Figure BSA0000215713520000041
Figure BSA0000215713520000042
ei 2＝-1，i＝1，2，...，N，IΣ(a, b) denotes the sum of all pixels in a super-box region from a to b, where a and b are multiple vectors, i.e. a ═ a1e1+ a2e2+....，+aNeN，b＝b1e1+b2e2+....，+bNeNIt is possible to deduce IΣ(a, b) the conformal geometric algebraic representation may be expressed as:
Figure BSA0000215713520000043
further, please refer to fig. 2, which is a flowchart illustrating a step 101 and the following steps in the first embodiment of the present invention. Specifically, the method comprises the following steps:
step 1011, respectively obtaining a CGA integral image of the reference image and a CGA integral image of the floating image according to the reference image and the floating image;
the formula of the CGA integral image is as follows:
Figure BSA0000215713520000044
Figure BSA0000215713520000051
Figure BSA0000215713520000052
Figure BSA0000215713520000053
m＝1，2，3
wherein, IΣ(X) a GA integral image, proj (X, e), representing the reference image or the floating imagem) Denotes the point X at emA projection in a direction, I (x) being a parameter characterizing the reference image or the floating image,
Figure BSA0000215713520000054
representing the medical image at emComponent in the direction, imIs with emFor direction-related labeling, the value of m is 1, 2 or 3; conformal geometric algebra is expanded based on the traditional three-dimensional Euclidean space, and the three-dimensional space has three basis vectors
Figure BSA0000215713520000055
m is 1, 2, 3, and a base vector representing an origin and a base vector of an infinity point
Figure BSA0000215713520000056
e0.e∞＝-1。
Or 3;
step 1012, based on CGA gaussian Laplace transform algorithm, convolving the CGA integral image of the reference image and the CGA integral image of the floating image with a cuboid filter to obtain an image scale space of the reference image and an image scale space of the floating image, respectively on each layer of image in the image scale space of the reference image and the image scale space of the floating image,
obtaining reference image characteristic points and floating image characteristic points according to extreme points of an approximate Gaussian Laplace transform detection image, wherein the Gaussian Laplace transform of the reference image or the floating image is as follows:
Figure BSA0000215713520000057
wherein the content of the first and second substances,
Figure BSA0000215713520000058
and representing the f-Gaussian Laplace transform value of the reference image or the floating image.
Since the medical image is three-dimensional and the CGA integral image is also three-dimensional, the convolution template convolved with the CGA integral image is a rectangular parallelepiped filter. If the medical image has other dimensions, step 1012 may be performed, based on a CGA gaussian Laplace transform algorithm, to convolve the CGA integral image of the reference image and the CGA integral image of the floating image with a rectangular parallelepiped filter to obtain a rectangular parallelepiped filter in the image scale space of the reference image and the image scale space of the floating image, and to change the rectangular parallelepiped filter into a corresponding convolution template. In addition, the gaussian Laplace transform of the reference image or the floating image is approximate to a rectangular filter, and the gaussian kernel of the gaussian Laplace transform of the reference image or the floating image is three-dimensional.
Step 1013, respectively selecting the reference image feature point and the floating image feature point as centers, constructing a preset first cube neighborhood by a registered multi-mode, dividing the first cube neighborhood into three sub-regions in each dimension, and calculating the sum of gaussian response values and gaussian response value absolute values of all pixel points for each sub-region to obtain a conformal geometric algebraic descriptor corresponding to the sub-region, wherein the calculation formula of the conformal geometric algebraic descriptor is as follows:
v＝∑d1e1+∑d2e2+∑d3e3+∑|d1|e1+∑|d2|e2+∑|d3|e3
Figure BSA0000215713520000061
where Cv represents the conformal geometric algebraic descriptor, Σ d, corresponding to the sub-regionmemIs shown at emSummation of haar wavelet response values for all pixel points in the direction, Σ | dm|emIs shown at emAnd (3) summing the absolute values of the haar wavelet response values of all the pixel points in the direction, wherein the value of m is 1, 2 or 3.
It should be noted that, the cube neighborhood with the reference image feature point and the floating image feature point as the center is respectively selected, and the cube neighborhood is divided into three sub-regions in each dimension, and there are nine sub-regions in total (three dimensions, and there are three sub-regions in each dimension). The vector combination of all sub-regions is recorded as a descriptor of the feature point.
102, constructing a reference image feature sphere and a floating image feature sphere by respectively utilizing the reference image feature points and the floating image feature points according to a CGA sphere construction algorithm;
further, please refer to fig. 3, which is a schematic diagram of a first embodiment of the present invention for constructing a CGA feature sphere by using CGA feature points. The invention provides the CGA sphere construction algorithm which is easy to implement and small in calculation amount, and the algorithm is low in complexity, small in calculation amount, simple and easy to implement.
Specifically, in the step 102 of refining, the CGA feature points are reference image feature points or floating image feature points, the CGA feature spheres are reference image feature spheres corresponding to the reference image feature points or floating image feature spheres corresponding to the floating image feature points, and the step 102 of refining includes:
selecting four points adjacent to construct a CGA characteristic ball A ^ B ^ C ^ D as a ball shown in a graph (a) in fig. 3;
judging whether a CGA characteristic point E exists in or on the ball, if E ∈ A ^ B ^ C ^ D, as shown in a graph (B) in fig. 3, then reconstructing the ball A ^ B ^ C ^ E, A ^ B ^ E ^ D, A ^ E ^ C ^ D, E ^ B ^ C ^ D;
if there is a CGA feature point that is not within the sphere constructed by the other four CGA feature points, assume
Figure BSA0000215713520000073
Then the minimum sphere E ^ B ^ C ^ D adjacent to five points, including four points, can be determined as shown in fig. 3 (C).
It should be noted that, when "determining whether there is a CGA feature point E inside or outside the sphere", if there is a CGA feature point E inside or on the sphere (as shown in fig. 3, the diagram pointed to by the directional arrow 1) and there is a CGA feature point that is not inside the sphere constructed by the other four CGA feature points, it is assumed that
Figure BSA0000215713520000071
Then the minimum sphere E ^ B ^ C ^ D adjacent to five points, including four points, can be determined as shown in fig. 3 (C). In FIG. 3, the diagram pointing to arrow three is exemplary; when the CGA characteristic point E does not exist in or on the ball, such as the graph pointed by the pointing arrow 2 in FIG. 3, the search range is gradually enlarged and reduced,
and 103, determining a transformation relation by using the reference image feature ball and the floating image feature ball in the conformal geometric algebraic space, and registering the reference image and the floating image based on the transformation relation, wherein the transformation relation comprises rotation, translation and scaling.
Please refer to fig. 4, which is a flowchart illustrating a step 103 of the first embodiment of the present invention.
Step 1031, respectively determining the sphere centers and the radii of the reference image characteristic sphere and the floating image characteristic sphere, and determining a transformation line and a transformation direction according to the sphere centers and the radii;
wherein, the calculation formula of the transformation line is as follows:
L＝rIE+e∞mIE
wherein L represents the transformation line, and r represents the center c of the reference image feature sphere1M represents a sphere center c1To the center c of the floating image feature sphere2Distance, e∞Represents an infinite point;
step 1032, calculating a translation operator, a scaling factor and a scaling operator according to the transformation line and the transformation direction, and registering the reference image and the floating image according to the translation operator, the scaling factor and the scaling operator;
the calculation formula of the translation operator is as follows:
Figure BSA0000215713520000072
the scaling factor is calculated as:
λ＝r2/r1
the calculation formula of the scaling operator is as follows:
Figure BSA0000215713520000081
the registration formula is:
Figure BSA0000215713520000082
wherein n isLIndicates the direction of transformation, r2Radius of a sphere representing the characteristic of the floating image, r1Denotes the radius of the reference image feature sphere, E denotes the plane vector, S2For characterizing the parameters of the floating image, T denotes a translation operator, S1Are parameters characterizing the reference image.
Please refer to fig. 5, which is a schematic diagram illustrating a transformation relationship between a reference image feature sphere and a floating image feature sphere according to a first embodiment of the present invention. The transformation relationship between the reference image feature ball and the floating image feature ball is determined using the relevant contents involved in steps 1031 and 1032, and mainly includes rotation, translation and scaling. After the transformation relation between the reference image characteristic sphere and the floating image characteristic sphere is obtained, the registration of the reference image and the floating image can be completed according to the relation.
In the embodiment of the invention, because conformal geometric algebra is utilized, the invention has rich and uniform calculation modes, can simplify complex linear operation and matrix operation, provides simpler and direct expression for geometric transformation, can reduce registration data parameters, reduce the complexity of geometric transformation, simplify calculation amount and accelerate calculation speed, and simultaneously utilizes the advantage that conformal geometric algebra can directly process high-dimensional information without losing the dimensional information of medical images, so that the registration precision of the medical images is higher.
Fig. 6 is a schematic structural diagram of a medical image registration system based on geometric algebra according to a second embodiment of the present invention. Specifically, the system comprises:
the extraction module 201 is configured to perform geometric algebraic CGA feature point extraction on the reference image and the floating image respectively based on a CGA gaussian Laplace transform algorithm to obtain a reference image feature point and a floating image feature point, where the reference image and the floating image are both medical images;
the building module 202 is configured to respectively build a reference image feature sphere and a floating image feature sphere by using the reference image feature points and the floating image feature points according to a CGA sphere building algorithm;
and a determining and registering module 203, configured to determine a transformation relation using the reference image feature sphere and the floating image feature sphere in the conformal geometric algebraic space, and register the reference image and the floating image based on the transformation relation, where the transformation relation includes rotation, translation, and scaling.
Further, please refer to fig. 7, which is a schematic structural diagram of a refinement module of the extraction module 201 according to a second embodiment of the present invention;
the obtaining module 2011 is configured to obtain the CGA integral image of the reference image and the CGA integral image of the floating image according to the reference image and the floating image, where the CGA integral image has a formula:
Figure BSA0000215713520000091
Figure BSA0000215713520000092
Figure BSA0000215713520000093
Figure BSA0000215713520000094
m＝1，2，3
wherein, IΣ(X) represents a GA integral image of the reference image or the floating image,
Figure BSA0000215713520000095
denotes the point X at emA projection in a direction, I (x) being a parameter characterizing the reference image or the floating image,
Figure BSA0000215713520000096
representing the medical image at emComponent in the direction, imIs with emFor direction-related labeling, the value of m is 1, 2 or 3; conformal geometric algebra is expanded based on the traditional three-dimensional Euclidean space, and the three-dimensional space has three basis vectors
Figure BSA0000215713520000097
m is 1, 2, 3, and a base vector representing an origin and a base vector of an infinity point
Figure BSA0000215713520000098
e0.e∞＝-1
A convolution detection module 2012, configured to convolve the CGA integral image of the reference image and the CGA integral image of the floating image with a rectangular filter to obtain an image scale space of the reference image and an image scale space of the floating image based on a CGA gaussian Laplace transform algorithm, where the image scale space of the reference image and the image scale space of the floating image are on each layer of image,
obtaining reference image characteristic points and floating image characteristic points according to extreme points of an approximate Gaussian Laplace transform detection image, wherein the Gaussian Laplace transform of the reference image or the floating image is as follows:
Figure BSA0000215713520000099
wherein the content of the first and second substances,
Figure BSA0000215713520000101
and representing the f-Gaussian Laplace transform value of the reference image or the floating image.
Since the medical image is three-dimensional and the CGA integral image is also three-dimensional, the convolution template convolved with the CGA integral image is a rectangular parallelepiped filter. If the medical image has other dimensions, step 1012 may be performed, based on a CGA gaussian Laplace transform algorithm, to convolve the CGA integral image of the reference image and the CGA integral image of the floating image with a rectangular parallelepiped filter to obtain a rectangular parallelepiped filter in the image scale space of the reference image and the image scale space of the floating image, and to change the rectangular parallelepiped filter into a corresponding convolution template. In addition, the gaussian Laplace transform of the reference image or the floating image is approximate to a rectangular filter, and the gaussian kernel of the gaussian Laplace transform of the reference image or the floating image is three-dimensional.
Further, the detecting module 2012 includes:
a calculation module for calculating the time-of-flight,
the method is used for respectively selecting the reference image feature point and the floating image feature point as centers, constructing a preset first cube neighborhood by a registered multi-mode, dividing the first cube neighborhood into three subregions in each dimension, and calculating the sum of Gaussian response values and the absolute values of the Gaussian response values of all pixel points for each subregion to obtain a conformal geometric algebraic descriptor corresponding to the subregion, wherein the calculation formula of the conformal geometric algebraic descriptor is as follows:
v＝∑d1e1+∑d2e2+∑d3e3+∑|d1|e1+∑|d2|e2+∑|d3|e3
Figure BSA0000215713520000102
where Cv represents a conformal geometric algebraic descriptor, Σ d, corresponding to a sub-regionmemIs shown at emSummation of haar wavelet response values for all pixel points in the direction, Σ | dm|emIs shown at emAnd (3) summing the absolute values of the haar wavelet response values of all the pixel points in the direction, wherein the value of m is 1, 2 or 3.
Further, please refer to fig. 8, which is a schematic structural diagram of a refinement module of the construction module 202 according to the second embodiment of the present invention. Specifically, the building module 202 includes:
the first processing module 2021 selects four adjacent CGA characteristic points to construct a CGA characteristic ball a Λ B ^ C ^ D;
a second processing module 2022, for determining whether there is a characteristic point E of CGA inside or outside the ball, if E ∈ a ^ B ^ C ^ D, as shown in the diagram (B) in fig. 3, then reconstructing the ball a ^ B ^ C ^ E, a ^ B ^ E ^ D, a ^ E ^ C ^ D, E ^ B ^ C ^ D.
A third processing module 2023 for assuming a minimum feature sphere based on CGA
Figure BSA0000215713520000114
Then the minimum sphere E Λ B ^ C ^ D adjacent to five points, including four points, can be determined.
Further, please refer to fig. 9, which is a schematic structural diagram of a refining module for determining the registration module 203 according to a second embodiment of the present invention. Specifically, determining the registration module 203 includes:
a determining module 2031, configured to determine a sphere center and a radius of the reference image feature sphere and the floating image feature sphere, respectively, and determine a transformation line and a transformation direction according to the sphere center and the radius;
wherein, the calculation formula of the transformation line is as follows:
L＝rIE+e∞mIE
wherein L represents the transformation line, and r represents the center c of the reference image feature sphere1M represents a sphere center c1To the center c of the floating image feature sphere2Distance, e∞Represents an infinite point;
a calculation registration module 2032 for calculating translation operators based on the transformation lines and the transformation directions
Figure BSA0000215713520000111
Scaling factor λ r2/r1And scaling operator
Figure BSA0000215713520000112
And registering the reference image and the floating image according to the translation operator, the scaling factor and the scaling operator, wherein the registration formula is as follows:
Figure BSA0000215713520000113
wherein n isLIndicates the direction of transformation, r2Radius of a sphere representing the characteristic of the floating image, r1Denotes the radius of the reference image feature sphere, E denotes the plane vector, S2For characterizing the parameters of the floating image, T denotes a translation operator, S1Are parameters characterizing the reference image.
It should be noted that the calculation module may be used as a refinement module of the extraction module 201, or may not be used as a refinement module of the extraction module 201.
For the description of the embodiments of the present invention, please refer to the description of the first embodiment of the present invention, which is not repeated herein.
In the embodiment of the invention, because conformal geometric algebra is utilized, the invention has rich and uniform calculation modes, can simplify complex linear operation and matrix operation, provides simpler and direct expression for geometric transformation, can reduce registration data parameters, reduce the complexity of geometric transformation, simplify calculation amount and accelerate calculation speed, and simultaneously utilizes the advantage that geometric algebra can directly process high-dimensional information without losing the dimension information of medical images, so that the registration precision of the medical images is higher.
In the several embodiments provided in the present application, it should be understood that the disclosed apparatus and method may be implemented in other ways. For example, the above-described apparatus embodiments are merely illustrative, and for example, the division of the modules is merely a logical division, and in actual implementation, there may be other divisions, for example, multiple modules or components may be combined or integrated into another system, or some features may be omitted, or not implemented.
It should be noted that, for the sake of simplicity, the above-mentioned method embodiments are described as a series of acts or combinations, but those skilled in the art should understand that the present invention is not limited by the described order of acts, as some steps may be performed in other orders or simultaneously according to the present invention. Further, those skilled in the art will appreciate that the embodiments described in the specification are presently preferred and that no acts or modules are necessarily required of the invention.
In the above embodiments, the descriptions of the respective embodiments have respective emphasis, and for parts that are not described in detail in a certain embodiment, reference may be made to related descriptions of other embodiments.
The above is a description of a medical image registration method and system based on geometric algebra provided by the present invention, and for those skilled in the art, there may be variations in the specific implementation and application scope according to the idea of the embodiment of the present invention, and in summary, the content of the present specification should not be construed as a limitation to the present invention.

Claims (10)

1. A medical image registration method based on conformal geometric algebra, which is characterized by comprising the following steps:
performing conformal geometric algebraic CGA feature sphere extraction on a reference image and a floating image respectively based on a CGA Gauss Laplace transform algorithm to obtain reference image feature points and floating image feature spheres, wherein the reference image and the floating image are medical images;
according to a CGA sphere construction algorithm, constructing a reference image feature sphere and a floating image feature sphere by respectively using the reference image feature points and the floating image feature sphere;
in a conformal geometric algebraic space, determining a transformation relationship using the reference image feature sphere and the floating image feature sphere, registering the reference image and the floating image based on the transformation relationship, the transformation relationship including rotation, translation, and scaling.
2. The method of claim 1, wherein the step of performing CGA feature point extraction on the reference image and the floating image respectively based on the CGA gaussian Laplace transform algorithm to obtain the reference image feature point and the floating image feature point specifically comprises:
respectively solving a CGA integral image of the reference image and a CGA integral image of the floating image according to the reference image and the floating image, wherein the formula of the CGA integral image is as follows:
Figure FSA0000215713510000011
Figure FSA0000215713510000012
Figure FSA0000215713510000013
Figure FSA0000215713510000014
m＝1，2，3
wherein, I∑(X) a GA integral image, proj (X, e), representing the reference image or the floating imagem) Denotes the point X at emA projection in a direction, I (x) being a parameter characterizing the reference image or the floating image,
Figure FSA0000215713510000015
representing the medical image at emComponent in the direction, imIs with emFor direction-related labeling, the value of m is 1, 2 or 3; conformal geometric algebra is expanded based on the traditional three-dimensional Euclidean space, and the three-dimensional space has three basis vectors
Figure FSA0000215713510000016
With the basis vector representing the origin and the basis vector of the point at infinity
Figure FSA0000215713510000017
e0.e∞＝-1
And on the basis of a CGA Gauss Laplace transform algorithm, respectively convolving the CGA integral image of the reference image and the CGA integral image of the floating image with a cuboid filter to obtain an image scale space of the reference image and an image scale space of the floating image, wherein the image scale space of the reference image and the image scale space of the floating image are respectively on each layer of image.
Obtaining the reference image characteristic point and the floating image characteristic point according to the extreme point of the approximate Gaussian Laplace transform detection image, wherein the Gaussian Laplace transform of the reference image or the floating image is as follows:
Figure FSA0000215713510000021
wherein the content of the first and second substances,
Figure FSA0000215713510000022
representing said reference image orThe floating image f Gauss Laplace transform value.
3. The method of claim 2, wherein the step of obtaining the reference image feature points and the floating image feature points according to an approximate gaussian Laplace transform for detecting extreme points of an image further comprises:
respectively selecting the reference image feature point and the floating image feature point as centers, constructing a preset first cube neighborhood by a registered multi-mode, dividing the first cube neighborhood into three subregions in each dimension, and calculating the sum of the haar wavelet response values and the absolute values of the haar wavelet response values of all pixel points for each subregion to obtain a descriptor corresponding to the subregion, wherein the calculation formula of the descriptor is as follows:
v＝∑d1e1+∑d2e2+∑d3e3+∑|d1|e1+∑|d2|e2+∑|d3|e3
Figure FSA0000215713510000023
where Cv represents the conformal geometric algebraic descriptor, Σ d, corresponding to the sub-regionmemIs shown at emSummation of haar wavelet response values for all pixel points in the direction, Σ | dm|emIs shown at emAnd (3) summing the absolute values of the haar wavelet response values of all the pixel points in the direction, wherein the value of m is 1, 2 or 3.
4. The method according to claim 1, wherein the step of constructing a reference image feature sphere and a floating image feature sphere by using the reference image feature points and the floating image feature points respectively according to a CGA sphere construction algorithm specifically comprises:
and selecting any adjacent four CGA characteristic points to construct a CGA characteristic ball A ^ B ^ C ^ D. If the characteristic point D of the CGA exists, then constructing a ball A ^ B ^ C ^ E, A ^ B ^ E ^ D, A ^ E ^ C ^ D, E ^ B ^ C ^ D and E ^ B ^ C ^ D, if the characteristic point A of the CGA does not exist in the characteristic ball E ^ B ^ C ^ D, the characteristic point C of the CGA, the characteristic point D of the CGA and the characteristic point D of the CGA, the characteristic point E ^ B ^ C ^ D constructed by the characteristic point A of the CGA, and the minimum ball E ^ B ^ C ^ D containing four points in the five adjacent characteristic points of the CGA can be determined.
5. The method according to claim 1, wherein a transformation relation is determined in the conformal geometric algebraic space using a reference image feature sphere and a floating image feature sphere, and the step of registering the reference image and the floating image based on the transformation relation comprises:
respectively determining the sphere center and the radius of the reference image characteristic sphere and the floating image characteristic sphere, and determining a transformation line and a transformation direction according to the sphere center and the radius, wherein the calculation formula of the transformation line is as follows:
L＝rIE+e∞mIE
wherein L represents the transformation line, and r represents the center c of the reference image feature sphere1M represents a sphere center c1To the center c of the floating image feature sphere2Distance, e∞Represents an infinite point;
calculating a translation operator from said transformation line and said transformation direction
Figure FSA0000215713510000031
Scaling factor λ r2/r1And scaling operator
Figure FSA0000215713510000032
And registering the reference image and the floating image according to the translation operator, the scaling factor and the scaling operator, wherein the registration formula is as follows:
wherein n isLRepresenting said transformation direction, r2Radius of a sphere representing the characteristic of the floating image, r1Representing the radius of the reference image feature sphere, E representing a plane vector, S2For characterizing the parameters of the floating image, T represents a translation operator, S1Are parameters characterizing the reference image.
6. A medical image registration system based on geometric algebra, the system comprising:
the extraction module is used for respectively extracting geometric algebraic CGA characteristic points of a reference image and a floating image based on a CGA Gaussian Laplace transform algorithm to obtain the characteristic points of the reference image and the characteristic points of the floating image, wherein the reference image and the floating image are medical images;
the construction module is used for respectively constructing a reference image feature sphere and a floating image feature sphere by using the reference image feature points and the floating image feature points according to a CGA sphere construction algorithm;
and the determining and registering module is used for determining a transformation relation by utilizing the reference image feature sphere and the floating image feature sphere in a conformal geometric algebraic space, and registering the reference image and the floating image based on the transformation relation, wherein the transformation relation comprises rotation, translation and scaling.
7. The system of claim 6, wherein the extraction module specifically comprises:
the calculating module is used for calculating a CGA integral image of the reference image and a CGA integral image of the floating image according to the reference image and the floating image respectively, and the formula of the CGA integral image is as follows:
Figure FSA0000215713510000041
Figure FSA0000215713510000042
Figure FSA0000215713510000043
Figure FSA0000215713510000044
m＝1，2，3
wherein, I∑(X) a GA integral image, proj (X, e), representing the reference image or the floating imagem) Denotes the point X at emA projection in a direction, I (x) being a parameter characterizing the reference image or the floating image,
Figure FSA0000215713510000045
representing the medical image at emComponent in the direction, imIs with emFor direction-related labeling, the value of m is 1, 2 or 3; the three-dimensional European space based on the traditional method has three basis vectors
Figure FSA0000215713510000046
With the basis vector representing the origin and the basis vector of the point at infinity
Figure FSA0000215713510000047
Figure FSA0000215713510000048
e0.e∞＝-1。
And the convolution detection module is used for convolving the CGA integral image of the reference image and the CGA integral image of the floating image with a cuboid filter respectively based on a CGA Gaussian Laplace transform algorithm to obtain an image scale space of the reference image and an image scale space of the floating image, and the image scale space of the reference image and the image scale space of the floating image are respectively positioned on each layer of image.
Obtaining reference image characteristic points and floating image characteristic points according to extreme points of an approximate Gaussian Laplace transform detection image, wherein the Gaussian Laplace transform of the reference image or the floating image is as follows:
Figure FSA0000215713510000049
wherein the content of the first and second substances,
Figure FSA00002157135100000410
and representing the f-Gaussian Laplace transform value of the reference image or the floating image.
8. The system of claim 7, wherein the convolution detection module is followed by:
the calculation module is used for respectively selecting the reference image feature point and the floating image feature point as centers, constructing a preset first cube neighborhood by a registered multi-mode, dividing the first cube neighborhood into three subregions in each dimension, and calculating the sum of the haar wavelet response values and the absolute values of the haar wavelet response values of all pixel points for each subregion to obtain a descriptor corresponding to the subregion, wherein the calculation formula of the descriptor is as follows:
v＝∑d1e1+∑d2e2+∑d3e3+∑|d1|e1+∑|d2|e2+∑|d3|e3
Figure FSA0000215713510000051
where Cv represents the conformal geometric algebraic descriptor, Σ d, corresponding to the sub-regionmemIs shown at emThe sum of the haar wavelet response values for all pixel points in the direction,∑|dm|emis shown at emAnd (3) summing the absolute values of the haar wavelet response values of all the pixel points in the direction, wherein the value of m is 1, 2 or 3.
9. The system according to claim 6, wherein the building module specifically comprises:
the first processing module is used for selecting a CGA characteristic ball, selecting adjacent four points to construct a CGA characteristic ball A ^ B ^ C ^ D, wherein the CGA characteristic ball is the reference image characteristic ball corresponding to the reference image characteristic point or the floating image characteristic ball corresponding to the floating image characteristic point;
the second processing module is used for judging whether a CGA characteristic point E exists in the ball or outside the ball, and if the E is within the range of A, B, C and D, the second processing module is used for further constructing the ball A, B, C and D, A, E, C and D:
a third processing module for assuming a sphere that is not formed at four other points based on the CGA feature smallest sphere
Figure FSA0000215713510000052
Then the minimum sphere E Λ B ^ C ^ D adjacent to five points, including four points, can be determined.
10. The system according to claim 6, characterized in that said determining a registration module comprises in particular:
the determining module is used for respectively determining the sphere centers and the radiuses of the reference image characteristic sphere and the floating image characteristic sphere, and determining a transformation line and a transformation direction according to the sphere centers and the radiuses, wherein the calculation formula of the transformation line is as follows:
L＝rIE+e∞mIE
wherein L represents the transformation line, and r represents the center c of the reference image feature sphere1M represents a sphere center c1To the center c of the floating image feature sphere2Distance, e∞Represents an infinite point;
calculating a registration module forCalculating a translation operator from said transformation line and said transformation direction
Figure FSA0000215713510000061
Scaling factor λ r2/r1And scaling operator
Figure FSA0000215713510000062
And registering the reference image and the floating image according to the translation operator, the scaling factor and the scaling operator, wherein the registration formula is as follows:
Figure FSA0000215713510000063
wherein n isLRepresenting said transformation direction, r2Radius of a sphere representing the characteristic of the floating image, r1Representing the radius of the reference image feature sphere, E representing a plane vector, S2To characterize the parameters of the floating image, T denotes S1Are parameters characterizing the reference image.
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