CN108765472B - Image set registration method based on sparse directed graph - Google Patents

Image set registration method based on sparse directed graph Download PDF

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CN108765472B
CN108765472B CN201810477230.5A CN201810477230A CN108765472B CN 108765472 B CN108765472 B CN 108765472B CN 201810477230 A CN201810477230 A CN 201810477230A CN 108765472 B CN108765472 B CN 108765472B
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赵海峰
刘烨敏
汤振宇
张少杰
罗斌
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Anhui University
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Abstract

The invention discloses an image set registration method based on a sparse directed graph, which comprises the following steps: step 1, inputting a group of image sets { I) containing n images i |i=1,…,n};Step 2, calculating the image similarity of the image set by using a sparse manifold coding method based on the image set global information and the image distribution manifold; step 3, establishing a directed graph which takes the image as a node and the reciprocal of the image similarity as weight according to the similarity calculation result; step 4, determining the shortest path between every two nodes and a root node image based on the directed graph, and further determining the shortest path from the non-root node image to the root node image, namely a registration path; and 5, sequentially registering all non-root node images and the result images registered according to the registration path to the direct father node images until the root node images are registered according to the determined registration path. The invention effectively improves the precision of image set registration.

Description

Image set registration method based on sparse directed graph
Technical Field
The invention relates to the field of image processing, in particular to an image set registration method based on a sparse directed graph.
Background
Image registration can be divided into two major categories depending on the number of images to be registered: two-by-two image registration and image set registration. Registering every two images refers to aligning one image to be registered with a target image space; whereas image set registration is the alignment of a set (number greater than 2) of images into a uniform space, the images that serve as a uniform space are generally referred to as the center images. The image set registration plays an important role in medical image processing and computer vision, such as detecting structural or functional differences of brain images (brain image information is analyzed by registering images of different ages, health and diseases), monitoring lesion development, establishing a more reasonable face model and the like.
Due to the wide application of the two-by-two image registration method, in the early stage of the study of the image set registration method, all images to be registered are generally directly registered to the central image by using the existing two-by-two image registration method, and this simple image set registration is called direct image set registration. Such methods have significant disadvantages: when images with larger difference between the image set and the central image are aligned, larger deformation is generated, and the registration effect is poor. Due to the problems of the direct image set registration method, in recent years, an indirect image set registration strategy capable of obtaining a better registration result is receiving wide attention. The image set registration method based on the graph becomes a research hotspot due to the characteristics of high operation efficiency and accurate registration.
The basic steps of the map-based image set registration method include four parts: (1) calculating the similarity between images of the image set; (2) establishing a graph according to the similarity; (3) Determining a root node image (generally used as a central image) in the image, and then determining the shortest path from a non-root node image to the root node image; and (4) registering two images. To illustrate the general flow of this type of method, a two-dimensional composite image set is used here for registration, as shown in fig. 1. FIG. 1 (a) shows a set of images comprising 6 two-dimensional composite images; FIG. 1 (b) is a graph established based on the similarity between images, where image 2 is the root node determined according to equation (1),
Figure BDA0001664784470000011
d (I) in the formula j ,I i ) Representing an image I j To I i N represents the number of images. In fig. 1b, the edge between two images represents the shortest path, and the shortest path from each image to the root node image forms the registration path from the image to the root node. Taking the example of registering image 1 to root node image 2, FIG. 1 (c) shows the shortest path of image 1, where each image in the path is registered to its parent node, i.e. image 1 is registered to image 3 to obtain deformation field D 13 And registering the image 3 to the root node image 2 to obtain a deformation field D 32 . The deformation field of the image 1 registered to the root node can be obtained through deformation field integration
Figure BDA0001664784470000012
Finally, the deformation field D 12 Acting on image 1, a resulting image 7 is obtained, the image 1 being registered to the image 2. Wherein the symbol
Figure BDA0001664784470000021
Representing a complex of functions, i.e.
Figure BDA0001664784470000022
Corresponding to g 1 (g 2 (x) ). The comparison image 2 and the registration image 7 are almost the same, and the registration effect is good. Compared with a direct image set registration method, the method has the obvious advantage that the registration of large deformation is divided into a series of integrations of small deformation registration so as to improve the registration accuracy.
The above is a general idea of most image set registration methods based on images at present, in these methods, when calculating the similarity between images, local image information such as gray difference between two images or spatial euclidean distance is generally used, and global information of an image set and internal manifold of an image are ignored, so that a large error exists when estimating the overall distribution manifold of an image in an image set. The currently popular method for calculating the similarity between one image and all images in an image set based on local image information mainly comprises the steps of firstly determining the number of adjacent points of the image, then calculating the similarity of the image and the other image in the image set according to the gray difference between the image and the other image in the image set until the similarity calculation between the image and all images in the image set is completed, and finally selecting the image with the maximum similarity of the determined number as the adjacent points of the image. The graph is built by generally using a K neighbor graph or a minimum spanning tree method; the deformation field fusion method mentioned above has obvious error accumulation, because there may be a large difference between the deformation fields obtained by two-by-two image registration on the shortest path. These problems ultimately affect the registration accuracy of the image set.
It is therefore desirable to provide a new image set registration method to solve the above problems.
Disclosure of Invention
The invention aims to solve the technical problem of providing an image set registration method based on a sparse directed graph, which uses a sparse manifold coding method based on image set global information and image distribution manifold to calculate the similarity between images, establishes the directed graph and combines with a continuous result image registration method to achieve the aim of accurate registration.
In order to solve the technical problems, the invention adopts a technical scheme that: the image set registration method based on the sparse directed graph comprises the following steps:
s1: inputting a set of images containing n images I i |i=1,…,n};
S2: calculating the image similarity of the image set by using a sparse manifold coding method based on the global information of the image set and the image distribution manifold;
s3: establishing a directed graph with the image as a node and the reciprocal of the image similarity as a weight according to the similarity calculation result;
s4: determining a shortest path between every two nodes and a root node image based on the directed graph, and further determining a shortest path from a non-root node image to the root node image, namely a registration path;
s5: and according to the determined registration path, sequentially registering all non-root node images and result images obtained by registering according to the registration path to the direct father node images until the root node images are registered, fusing the obtained deformation field and acting on the non-root node images to finish the registration from the non-root node images to the root node images.
In a preferred embodiment of the invention, in step S2, a sparse representation is computed for each image in the set of images, and all neighboring images used to represent the image are in the same manifold as the image.
Further, a formula for calculating the sparse representation of each image in the image set is as follows:
Figure BDA0001664784470000031
wherein | · | charging 1 Represents the L1 norm, which is to get a sparse solution; parameter lambda>0, acting to balance the sparsity and represent errors; coefficient of sparseness
Figure BDA0001664784470000032
In, s ij Not equal to 0, represents the image I j And image I i In the same manifold; parameter Q i Is a positive definite diagonal matrix whose elements take on values of
Figure BDA0001664784470000033
Figure BDA0001664784470000034
Is { I j -I i } j≠i The normalized vector of (a); constraint 1 T S i =1 representing a sparse coefficient vector S i The sum of the elements in (1); sparse coefficient vector S i Is the result of the computation of the sparse manifold coding method.
Further, the specific steps of step S3 include:
for the
Figure BDA0001664784470000035
The images corresponding to the elements with the middle being not zero are connected by using directed edges if the element s ij Not equal to 0, a slave image I is created i Pointing to an image I j Has a weight value of s ij Is the reciprocal of (1/s) ij
In a preferred embodiment of the present invention, in step S4, according to the weight values of the directed edges in the directed graph established in step S3, the Dijkstra algorithm is used to calculate the shortest path between the nodes, and the root node is calculated according to the following formula:
Figure BDA0001664784470000036
d (I) in the formula j ,I i ) Representing an image I j To I i N represents the number of images, and after the root node is determined, the shortest path from the non-root node to the root node is the registration path from the non-root node to the root node image.
The beneficial effects of the invention are:
(1) The method adopts a sparse manifold coding method to adaptively select the nearest neighbor images in the same manifold, realizes the global similarity calculation of the images, and can better estimate the image distribution manifold of the image set according to the directed graph established by the similarity result;
(2) According to the method, all the non-root node images and the result images obtained by registering according to the registration path are sequentially registered to the direct father node images until the root node images are registered, and the intermediate result images on the registration path are used for participating in registration, so that the error accumulation during deformation field fusion is reduced, and the registration accuracy of the image set is improved.
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FIG. 1 is a detailed implementation of most prior art map-based image set registration methods, where (a) is an image set containing 6 two-dimensional composite images; (b) Is a graph established according to the similarity between images, and (c) shows the shortest path of the image 1 and the image of the registration result;
FIG. 2 is a flow chart of an image set registration method of the present invention;
FIG. 3 is a diagram of an example of an image set registration method according to the present invention;
FIG. 4 is an exemplary diagram of selecting neighboring points for an image according to the similarity measurement method of the present invention;
FIG. 5 is a graphical representation of the accuracy of 54 brain regions calculated using the Jaccard method for the registration of LPBA40 image sets using the kNN, kNN + MST, ABSORB and the four image set registration methods of the present invention;
FIG. 6 is a schematic diagram of the accuracy of 32 brain regions in the registration result of the NIREP-NA0 image set obtained by using the Jaccard method to calculate the registration result of the four image sets, i.e., kNN + MST, ABSORB and the method of the present invention;
FIG. 7 is a schematic diagram of the accuracy of the whole brain region of the image in the registration result of LPBA40 image set obtained by using the method of Jaccard to calculate the registration result of the four image sets of kNN, kNN + MST, ABSORB and the method of the invention;
FIG. 8 is a schematic diagram of the accuracy of the whole brain region of the image in the registration result of the NIREP-NA0 image set obtained by using the four image set registration methods of kNN, kNN + MST, ABSORB and the method of the present invention by using the Jaccard method.
Detailed Description
The following detailed description of the preferred embodiments of the present invention, taken in conjunction with the accompanying drawings, will make the advantages and features of the present invention more comprehensible to those skilled in the art, and will thus provide a clear and concise definition of the scope of the present invention.
Referring to fig. 2, an embodiment of the invention includes:
a sparse directed graph-based image set registration method comprises the following steps:
s1: inputting n (n > 2) two-dimensional or three-dimensional gray scale images.
S2: and calculating the global similarity of the input images according to the global information of the image set and the manifold of the image distribution.
In this step, the formula for simultaneously calculating the similarity of each image to all images is:
Figure BDA0001664784470000051
wherein | · | charging 1 Represents the L1 norm, which is to get a sparse solution; parameter lambda>The effect of 0 is to balance the sparse solution and represent the error; coefficient of sparseness
Figure BDA0001664784470000052
In, if s ij Not equal to 0, representing image I j And image I i The images are in the same manifold, otherwise, the two images belong to different manifolds, and n represents the number of the input images; parameter Q i Is a positive definite diagonal matrix whose elements take on values of
Figure BDA0001664784470000053
I.e. if the other images in the image set are distant from the image I i The closer the value of the corresponding element is, the smaller the non-zero coefficient should be assigned to the image, if it is from the image I i Far away, the larger the value of the corresponding element is, the coefficient with the value of zero should be allocated to the image;
Figure BDA0001664784470000054
is { I j -I i } j≠i The normalized vector of (2). Affine constraint 1 T S i =1 tableSparse coefficient vector S i The sum of the elements in (1) is equal to 1.
Figure BDA0001664784470000055
S representing the right expression reaches a minimum value i The value is obtained.
In the formula (2), the sparse coefficient
Figure BDA0001664784470000056
Each element value of (a) represents the corresponding image in the representation image I i The larger each element value is, the larger the occupied proportion is; the element value is zero, indicating that the picture does not participate in representing the picture I i . Thus can convert S into i Viewed as an image I i Similarity to corresponding other images in the image set. For and image I i Images I in the same manifold j S corresponding thereto i Element s in (1) ij (representing image I) i And image I j Similarity of) is greater than zero, and the higher the similarity, s ij The larger the value of (a). If image I k And image I i In different manifolds, the similarity s between two images ik The assignment is zero.
Further, the formula (2) can be understood as: is an image I i Solving an optimal linear expression
Figure BDA0001664784470000057
So as to represent the image I i The number of images of (1) is as small as possible and the image I can be expressed to the maximum i . This is an optimization problem, which differs from the LASSO optimization problem in that there is an affine constraint 1 T S i =1, the solution of equation (2) is similar to the solution process of the LASSO algorithm. Compared with the popular method for calculating the similarity between one image and all images in the image set based on the local image information, the method can simultaneously complete two processes of determining the number of the adjacent points and calculating the similarity between the image and all images in the image set. To beWhen the image selects the adjacent points, the method utilizes the distribution manifold of the image to obtain the adjacent images in the same manifold, and the number of the determined adjacent images is different because the number of the images in the same manifold as that of each image is different. Therefore, the method has the greatest advantage that the adjacent images which are in the same manifold and span the same affine subspace can be selected for the images in an adaptive mode.
As shown in FIG. 3, it is the process of the method to select the neighboring image for the image, M in the image 1 And M 2 Is two different image local manifolds, namely image I 1 When selecting neighboring points, assume image I 4 ,I 5 And I 6 Distance image I 1 Comparison image I 2 And I 3 More recently. Image I calculated by formula (2) 1 In the sparse representation of (2), only the image I in the same manifold 2 And I 3 Has a coefficient of non-zero value, I 2 And I 3 Through I 1 Spanning the same low-dimensional affine subspace, the same as I can be obtained 1 Belong to the same manifold M 1 Of neighboring images I 2 And I 3
S3: and establishing a directed graph according to the image similarity result calculated in the step S2.
In this step, when a directed graph is created, the image is represented by a node, and the image I is subjected to the process i I =1,2, \8230n, n, image I calculated according to step S2 i And establishing the relation between the images with the result of the similarity of all the images. In a specific manner, for
Figure BDA0001664784470000061
Images corresponding to elements other than zero in the image are connected using directed edges, e.g. element s ij Not zero, a slave image I is established i Pointing to the image I j Is a directed edge, the weight of the edge is s ij Is the reciprocal of (1/s) ij . By operating on all the images according to the method, a directed graph containing all the input images can be established.
S4: and calculating the shortest path and the root node image based on the weight of the directed edge in the directed graph, and further determining the shortest path from the non-root node image to the root node image, namely the registration path. In the step, the Dijkstra algorithm is adopted for calculating the shortest path, and a formula (1) is adopted for determining the root node.
S5: according to the determined registration path of the non-root node images, sequentially registering all the non-root node images and the result images obtained by registration to the next node image in the path until the root node images are registered; and fusing the obtained deformation field and acting on the non-root node image to complete the registration from the non-root node image to the root node image.
In this step, the current Diffemoraphic Demons method is used for registration between the two images. When the non-root node image is registered according to the registration path, firstly registering to a direct father node image to obtain a deformation field and a registration result image, then registering the result image with a next node image in the path, and sequentially registering the result image obtained by previous registration with the next node image in the path according to the method until the root node image is registered.
Fig. 4 is a directed graph created by using 5 images as an image set to be registered by using the method of the present invention, and the way of registering a non-root node image to a root node image is specifically explained by taking this as an example. In the figure, the nodes v, w, x, y, z represent the input image, the gray node x 1 And x 2 Intermediate registration result images representing image x, directed edges representing shortest paths, values on edges representing registration deformation fields, e.g. D xz Representing the deformation field resulting from the registration of image x to image z, and node y is the root node. Taking the registration of image x to root node y as an example, its registration path P x→y = x, z, y, x, z, y being nodes in the path, the registration process being x registering to z resulting in a deformation field D xz And registering the resulting image x 1 ,x 1 Registering to y to obtain a deformation field D x1y And registering the resulting image x 2 Fusing the deformation field D xz And D x1y Obtaining the final deformation field
Figure BDA0001664784470000071
And (5) acting the final deformation field on the image x to obtain a final registration image, so as to finish the registration of the image x to y. All non-root node graphsAnd performing registration according to the mode to complete the registration process from all images in the image set to the root node.
The method of the invention was tested using 2 common nmr image datasets LPBA40 and NIREP-NA 0. The LPBA40 dataset contains 40 three-dimensional brain images (T1-weighted) from different individuals, each image corresponding to a manually segmented label image containing 54 brain regions; the NIREP-NA0 dataset contains 16 three-dimensional brain images (T1-weighted) from different individuals, each corresponding to a manually segmented tag image containing 32 brain regions. The method of the invention is compared with classical map-based image set registration methods including K-nearest neighbor map method (KNN) and K-nearest neighbor combined minimum spanning tree method (KNN + MST), popular ABSORB method.
For the two LPBA40 and NIREP-NA0 datasets, there are 780 image pairs for the LPBA40 dataset and 120 image pairs for the NIREP-NA0 dataset. Fig. 5 and fig. 6 show the average value of the coverage rate of each brain region in the images obtained by registration of the method of the present invention and 3 comparison methods, and the larger the value is, the higher the coverage rate is, the better the registration effect is. Fig. 7 and 8 show the registration accuracy of 4 methods, i.e. the average value of the sum of the coverage of the whole brain region between two images. In addition, the T-test method is also used for detecting the significance of the result, compared with the comparison method, the p value of the method is far less than 0.05, and the result shows that the result of the method is superior to the results of the other three methods and has significance.
The above description is only an embodiment of the present invention, and not intended to limit the scope of the present invention, and all modifications of equivalent structures and equivalent processes performed by the present specification and drawings, or directly or indirectly applied to other related technical fields, are included in the scope of the present invention.

Claims (3)

1. A sparse directed graph-based image set registration method comprises the following steps:
s1: inputting a set of images I comprising n images i |i=1,L,n};
S2: calculating the image similarity of the image set by using a sparse manifold coding method based on the global information of the image set and the image distribution manifold;
calculating a sparse representation result for each image in the image set, wherein all adjacent images used for representing the image are in the same manifold with the image; the formula for calculating the sparse representation of each image in the image set is as follows:
Figure FDA0003794119630000011
wherein | · | purple 1 Represents the L1 norm, which is to get a sparse solution; the parameter lambda is more than 0 and is used for balancing sparse solution and representing errors; coefficient of sparseness
Figure FDA0003794119630000012
In, s ij Not equal to 0, represents the image I j And image I i Are in the same manifold; the parameter Qi is a positive definite diagonal matrix whose elements take on values of
Figure FDA0003794119630000013
Figure FDA0003794119630000014
Is { I j -I i } j≠i The normalized vector of (a); constraint 1 T S i =1 represents a sparse coefficient vector S i The sum of the elements in (1); sparse coefficient vector S i Is the calculation result of the sparse manifold coding method;
s3: establishing a directed graph with the image as a node and the reciprocal of the image similarity as a weight according to the similarity calculation result;
s4: determining a shortest path between every two nodes and a root node image based on the directed graph, and further determining a shortest path from a non-root node image to the root node image, namely a registration path;
s5: and according to the determined registration path, sequentially registering all non-root node images and result images obtained by registering according to the registration path to the direct father node images until the root node images are registered, fusing the obtained deformation field and acting on the non-root node images to finish the registration from the non-root node images to the root node images.
2. The sparse directed graph-based image set registration method according to claim 1, wherein the specific steps of step S3 comprise:
for the
Figure FDA0003794119630000015
Figure FDA0003794119630000016
The images corresponding to the elements with the middle being not zero are connected by using directed edges if the element s ij Not equal to 0, a slave image I is created i Pointing to an image I j And the weight value of the edge is s ij Is the reciprocal of (1/s) ij
3. The sparse directed graph-based image set registration method according to claim 1, wherein in step S4, according to the weight values of the directed edges in the directed graph established in step S3, the Dijkstra algorithm is used to calculate the shortest path between nodes, and the root node is calculated according to the following formula:
Figure FDA0003794119630000021
d (I) in the formula j ,I i ) Representing an image I j To I i N represents the number of images, and after the root node is determined, the shortest path from the non-root node to the root node is the registration path registered to the root node image.
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