CN109242759B - Graph contraction grouping registration method based on density clustering - Google Patents
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Abstract
The invention discloses a graph contraction grouping and registering method based on density clustering. The invention comprises the following steps: step 1, carrying out affine registration; step 2, obtaining a global central image I according to a formula O (ii) a Clustering the data set I by using an improved density clustering DBSCAN algorithm, and dividing the data set I into omega small groups G α Step 3, constructing an NxN symmetrical connection matrix E, wherein an element E in the symmetrical connection matrix E i,j ＝0,
j belongs to {1, \8230;, N }; step 5, registering is carried out through continuously iterating the graph contraction process until convergence; the invention reduces the computational complexity of the grouping registration algorithm of hierarchical unbiased graph contraction; the two parameter methods are set to be related to the global central image, so that the subsequent graph contraction process is easier, and the registration iteration times are reduced. The method is very suitable for processing the data set with large and complex structural change, and improves the registration accuracy to a certain extent.
Description
Technical Field
The invention belongs to the field of three-dimensional medical image registration, is applied to large-scale medical brain image registration, and particularly relates to a hierarchical unbiased graph contraction grouping registration algorithm based on density clustering.
Technical background
Since the advent of Magnetic Resonance Imaging (MRI), many imaging-based studies have begun investigating structural changes within a population, between populations, and at different times within the same population. In these studies, image registration is critical to eliminate population differences, including differences in individual presses directly or structural variation changes in one experimenter (e.g., variations associated with brain disease). In particular, subtle changes may be difficult to discern if the image registration is performed inaccurately enough.
There are many pairwise registration methods to register a set of images to a template image. However, template selection is not a trivial task and, if done improperly, will affect subsequent statistical analysis. To address this problem, a group registration method has recently been proposed to align all images together onto a common space without explicitly specifying a template. The objective function in the group registration aims to minimize the overall gray level difference or entropy of the joint gray level distribution over all images. In order to optimize a large-scale objective function in group registration, an effective gradient-based Gaussian-Newton optimization algorithm is proposed. The hierarchical group registration principle is also used by selecting key points in the image and letting only key points drive the whole group registration.
Many existing packet registration methods require well-defined registration targets. For example, an effective group registration algorithm, which alternates the following two steps all the time:
(1) Averaging all the images to obtain an initialized registration template, and then registering each image with the template in pairs.
(2) And averaging all the images registered in the previous step to obtain a new registration template. The group matching method is suitable for data sets with small structural change.
However, for large data sets and widely varying structures, this method may produce a blurred group mean image, thereby reducing registration accuracy. To solve this problem, a sharp-mean based group registration method using a block-based weighted average method has been proposed. However, a common limitation of these methods is that registration of the group mean image is required regardless of whether the structure of the individual image is significantly different from the group mean image. Thus, these methods are limited in processing data sets with large and complex structural variations.
On the other hand, the accuracy of group registration can be improved by using image distribution information. Improved registration accuracy may be obtained by clustering the images in a population into several subgroups and then registering each subgroup by group registration. Since the images in the subgroups are similar in appearance, accurate registration can be obtained relatively easily. After intra-subgroup registration, the representative image of each subgroup can be used for inter-subgroup registration. However, one drawback of this approach is that the intra-subgroup distribution information is not dedicated to group registration.
One method is called HUGS (layered unbiased graph shrinkage). In HUGS, the image distribution of the entire data set is characterized by using a graph, where nodes represent images and edges represent similarities between images. Only similar images are connected to the diagram. Registering all images to a hidden common space is expressed as a dynamic graph contraction problem, where all nodes are close to each other along the edges. Since both global and local image distribution information is available in the map, the topology of the entire image manifold can be more accurately preserved throughout the registration process. Although more accurate, the HUGS is still limited in processing different types of data sets because a single simple graph is often insufficient in complex image distribution modeling. The HUGS uses a simple threshold-based approach to construct the graph, i.e., by connecting two images at a distance less than a given threshold, given a heterogeneous dataset, the threshold must be relaxed significantly to ensure that all images are connected on the graph, which tends to result in an overly connected and inefficient graph. This also leads to many unnecessary registrations between different image pairs, which not only significantly increases the computation time, but also leads to considerable registration errors.
The existing cohort registration HUGS method is described as follows:
it is assumed that the deformation of a single image is a dynamic process that varies with the time variable t. I is i (t) represents the deformed image I at time t i . The map defined in the brain image manifold is then used as follows. Suppose that
Is a graph node, E = { E = i,j I, j = 1.. N } is an edge between two nodes in the graph. e.g. of a cylinder i,j =1 denotes I i (t) and I j (t) there is a connection between, otherwise, I in the figure i (t) and I j (t) there is no direct connection between them. In addition, an N weighted adjacency matrix is defined, in which each element exp (v) i,j (t)) description of twoGeodesic paths between pictures, if e i,j =1 and v i,j (t) = ∞ then v i,j (t)>0。
v i,j (t) represents the velocity vector of the geodetic path, which represents I i (t) and I j (t) distance between (t). Registering deformable images to estimate each velocity vector v i,j (t) and by exp (v) i,j (t)) calculating I i (t) and I j (t) where 'exp' is an exponential mapping. The goal of graph-based group registration is to minimize the velocity vectors on all graph edges, as defined below:
the principle of F (t) is shown in FIG. 3. First, it is assumed that all images are located in a high-dimensional manifold. The topology of the image distribution is then described using a graph, where edges represent local connections between nodes. Velocity vector v i,j (t) is associated with each edge, where along v i,j The integral of (t) is from I i (t) to I j (t) geodesic distance.
The minimization of F (t) can be viewed as a dynamic image reduction process that reduces each image from I i (t) deformation to I i (t + Δ t), the overall geodesic distance is reduced while the topology of the entire map is maintained. With increasing time t, all I i (t) final registration to the central image, and rational determination of the velocity vector v i,j (t) and a time increment Δ t.
As the map shrinks dynamically, it is critical that the group registration compare to determine each image I i (t) how to deform at time t such that the energy function F (t) is minimized. Suppose that each image is from I i (t 0 ) Is changed into I i (t k ) Where { t } k Is time t (K =0, \8230;, K, t) 0 ＝0,t k → ∞) discretization. According to its connecting node to connect I i (t k ) Moving in the average direction, so each node I in the graph i (t k ) Is locally connected toThe consistency is reasonable.
Since the velocity vector lies on the manifold I i (t k ) In the tangential space of (A), is calculated by linear averaging
Wherein
Is a 1 i (t k ) The number of connections of (c). Given at a point in time t k If each node I i (t k ) From t in the direction of the velocity vector k Move to t k +Δt k The entire energy function F (t) then decreases strictly monotonically, with a time increment Δ t k Is obtained by the following formula:
finally, from t by a connection 0 To t k To obtain each image I i Geodesic path to the center
Namely, it is
Wherein
The deformation composition is shown. During graph contraction, all images are gradually deformed into a hidden common space, and the topology of the graph is preserved. Using t based on interval Δ t k (k =0,1,2, \ 8230;, where t is 0 =0 and t when k → ∞ time t k → ∞) to discretize t. Use of
As time t k A new deformed image will
Expressed as time t k Image of the department
The resultant deformation field of (a).
A novel group registration method (eHUGS) has a hierarchical graph with each node representing a single image. The layered image captures an image distribution manifold to obtain image distribution information, so that the image distribution information can be utilized. More specifically, the lower level graph describes the distribution of images in each subgroup, and the upper level graph represents the relationship between representative images in the subgroup. In one particular graph representation model, we can register all images to a common space by dynamically reducing the graph on the image manifold. The topology of the overall image distribution remains unchanged throughout the graph contraction. However, this method has the defect that the eHUGS method adopts a neighbor propagation clustering method (AP clustering), which requires setting a reference degree in advance, and the size of the reference degree is positively correlated with the number of clustering centers. Because the AP algorithm needs to update the attraction value and the attribution value of each data point for each iteration, the algorithm complexity is high, and the running time is long under the condition of large data volume. Not only does this happen, the eHUGS method selects a global central image, and then selects a sub-image representative image according to the image, and the selection of the global image has a great effect on the whole registration process, and influences the final registration result to a great extent.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: and the cluster-based graph contraction grouping registration algorithm improves the group registration accuracy and the running speed.
The invention is based on the graph contraction grouping registration algorithm of clustering, utilizes the improved density clustering DBSCAN algorithm, is beneficial to processing the data set with large and complex structural change, improves the registration precision, naturally reduces the complexity of the algorithm to some extent and accelerates the group registration speed.
The technical scheme adopted by the invention for solving the technical problem comprises the following steps:
step 2, according to the formula
Obtaining a global central image I O (ii) a Clustering the data set I by using an improved density clustering DBSCAN algorithm, and dividing the data set I into omega small groups G α = (α ∈ {1, \8230;, Ω } and
step 3, constructing an NxN symmetrical connection matrix E, wherein elements in the symmetrical connection matrix E
If image I i And image I j Are connected, setting the elements E of the symmetric connection matrix E i,j =1 otherwise e i,j =0; all diagonal elements in the symmetric connection matrix E are set to 0; determining each group G α Closest to the global center image I o And taking the image as a representative image
Step 4, constructing the group G α An internal linking system;
setting a threshold value, and representing the image
Image I with high similarity i {I i ∈G α ,i≠ i α There is a connection, otherwise all are set to 0; construction of groups of subgroupsEach representative image
All the images are connected with the global central image, and any two representative images are not connected and are set as 0;
step 5, registering is carried out through continuously iterating the graph contraction process until convergence; the goal of graph-based group registration is to minimize the velocity vectors on all graph edges, as defined below:
the minimization of F (t) is considered as a dynamic image reduction process, which reduces each image from I i (t) deformation to I i (t + Δ t), reducing the overall geodesic distance while maintaining the topology of the entire map; with increasing time t, all I i (t) final registration to the central image.
Step 2, the density clustering algorithm DBSCAN is characterized in that the sample distribution compactness is described based on a group of neighborhood parameters (epsilon, minPts), the two parameters need to be set in advance by a user, and the parameters are kept unchanged in the continuous iteration process, so that the DBSCAN algorithm cannot process samples with variable densities. And the selection of the two parameters greatly influences the clustering result so as to influence the final registration result, so that the method for setting the two parameters related to the global central image is used, the image is easier to shrink, and the registration iteration times are reduced. The improved density clustering DBSCAN algorithm is described as follows:
2-1. Determining the global central image I of the closest hidden common space among the data sets O ；
Data set I = { I) composed of N images i I = 1.. N }, first applying affine registration to align all images into a common space, and then filling in an N × N similarity matrix S, the elements S of which are ij Is defined as negative SSD, i.e. s ij ＝d ij ＝||I i -I j || 2 ；
2-2, determining a neighborhood radius epsilon;
removing the self-similarity value of the N × N similarity matrix S, i.e. removing d ii Removing the previous Num with the number of Nx (N-1)/2, and obtaining the previous Num by using KD tree nearest neighbor algorithm rough Minimum number of data, num rough ＝k*N×(N-1)/2；
Introducing a parameter beta limits the neighborhood radius epsilon to obtain a value of k:
∈ rough is the preliminary neighborhood radius, dis i Denotes d as small as the ith ordering ij ，
Num ∈ Satisfy the requirement of
The number of o ≠ j, and the final neighborhood radius belongs to the following:
2-3, determining the number MinPts of the images contained in the neighborhood radius epsilon of the representative image sample,
Num Pts (o, j) denotes a global center image I o And image I j Whether the distance of (c) is within e neighborhood of the origin point
Setting a parameter alpha to adjust MinPts,0< alpha ≦ 1
2-4. Dividing the global central map I O As a seed, finding all representative image samples with the density of which can be reached, wherein the representative image samples form a current group, and points contained in the current group are removed from the data set I, and the group number c = c +1;
2-5, repeating steps 2-1 to 2-4 until the data set I is empty.
The step 4 is realized as follows:
4-1. Determining the global central image I of the closest hidden common space among the data sets O (ii) a For N images I = { I i I = 1.. N } is clustered, and the omega subgroup G is obtained by using the improved density clustering DBSCAN algorithm described in step 2 α = (alpha epsilon {1, \8230;, omega } and
4-2. In each subgroup G α In the method, the core object obtained by the first clustering is the global central image I O (ii) a Omega images of omega subgroups
Thus having a global central image
The benefit of choosing representative images in a group based on the global center image is that other images in the group can be more easily deformed toward the global center; for the rest omega-1 subgroups, selecting each point in each subgroup and the global central image I according to the similarity matrix S O The point with the smallest distance is taken as a representative image of the small group;
4-3. For each subgroup G α Representative image I iα And all other images are connected in a group; for any pair of images I i And image I j ∈G α Where j ≠ i, if i = i α Or j = i α Has e i,j =1, otherwise e i,j ＝0；
4-4. For high level connections between subgroups, global center image I O Connecting all other representative images
For any pair of images I i And
in other words, if i = o or j = o, then there is e i,j =1, otherwise e i,j ＝0。
The step 5 is realized as follows:
as the map shrinks dynamically, it is critical that the group registration compare to determine each image I i (t) how to deform at time t such that the energy function F (t) is minimized; suppose that each image is from I i (t 0 ) Is changed into I i (t k ) Where { t } k Is time t (K =0, \8230;, K, t) 0 ＝0,t k Discretization to ∞); according to its connecting node to connect I i (t k ) Moving in the average direction, so each node I in the graph i (t k ) Local connectivity of (a) is reasonable;
since the velocity vector lies on the manifold I i (t k ) On the tangent space of (2), by linear averaging
Wherein
Is I i (t k ) The number of connections of (c); given at a point in time t k If each node I i (t k ) From t in the direction of the velocity vector k Move to t k +Δt k The entire energy function F (t) then decreases strictly monotonically, with time increments Δ t k Is obtained by the following formula:
finally, from t by a connection 0 To t k To obtain each image I i Geodesic path to the center
Namely, it is
Wherein
Represents a deformation composition; during graph contraction, all images are gradually deformed to a hidden common space, and the topology of the graph is preserved; using t based on interval Δ t k (k =0,1,2, \ 8230;, where t is 0 =0 and t when k → ∞ time t k → ∞) to discretize t; use of
As time t k A new deformed image will
Expressed as time t k Image of the department
The resultant deformation field of (a).
The method of the invention has the advantages and beneficial results that:
(1) The calculation complexity of the neighbor propagation clustering algorithm is O (N) 3 ) And the calculation complexity of the density clustering algorithm DBSCAN is O (N) 2 ) With the improved DBSCAN method, the KD tree established when searching for the nearest neighbor can reduce the computational complexity to O (NlogN). Therefore, the computational complexity of a grouping registration algorithm of hierarchical unbiased graph contraction can be reduced;
(2) The parameter preference value set by the neighbor propagation algorithm is irrelevant to the global central graph, and the clustering result is greatly influenced, so that the final registration result is influenced. The density clustering algorithm inspects the connectivity between samples from the perspective of sample density, the two parameters in the improved DBSCAN algorithm have little influence on the clustering result, and most importantly, the method for setting the two parameters is related to the global central image, so that the subsequent graph contraction process is easier, and the registration iteration times are reduced.
(3) The method is suitable for processing the data sets with large and complex structural changes, and improves the registration accuracy to a certain extent.
Drawings
FIG. 1 is a schematic diagram of the image, geodesic path connections on a high dimensional manifold of the present invention.
FIG. 2 is a graph of image clustering results obtained according to the modified density clustering DBSCAN algorithm;
fig. 3 is a schematic diagram of a group registration method based on hierarchical unbiased graph contraction of density clustering.
Detailed Description
The invention will be further described with reference to the accompanying drawings.
As shown in fig. 1-3, the graph contraction grouping registration method based on density clustering specifically comprises the following steps:
step 2, according to the formula
Obtaining a global central image I O . Clustering the data set I by using an improved density clustering DBSCAN algorithm, and dividing the data set I into omega small groups G α = (α ∈ {1, \8230;, Ω } and
the improved density clustering DBSCAN algorithm is described as follows:
2-1. Determining the global central image I of the closest hidden common space among the data sets O . Data set I = { I) composed of N images i I = 1.. N }, first applying affine registration to align all images into a common space, and then filling in an N × N similarity matrix S, the elements S of which are ij Is defined as negative SSD, i.e. s ij ＝d ij ＝||I i -I j || 2 。
2-2, determining the neighborhood radius epsilon.
Removing the self-similarity value of the N × N similarity matrix S, i.e. removing d ii Removing the previous Num to leave Nx (N-1)/2, and obtaining the previous Num by using a KD tree nearest neighbor algorithm rough Minimum number of data, num rough ＝k*N×(N-1)/2；
Introducing a parameter beta limits the neighborhood radius epsilon to obtain a value k:
∈ rough is the preliminary neighborhood radius, dis i Represents the ith smallest of the ranks ij ，
Num ∈ Satisfy | | I o -I j || 2 ≤∈ rough The number of o ≠ j, and the final neighborhood radius belongs to the following range:
2-3, determining the number MinPts, num of images contained in the neighborhood radius epsilon of the representative image sample Pts (o, j) denotes a global center image I o And image I j Whether the distance of (c) is within e neighborhood of the origin point
Setting a parameter alpha to adjust MinPts,0< alpha ≦ 1
2-4. Dividing the global central map I O As a seed, finding all representative image samples with the density of which can be reached, wherein the representative image samples form a current group, and points contained in the current group are removed from the data set I, and the group number c = c +1;
2-5, repeating steps 2-1 to 2-4 until the data set I is empty.
Step 3, constructing an NxN symmetrical connection matrix E, wherein elements in the symmetrical connection matrix E
If image I i And image I j Are connected, elements E of a symmetrical connection matrix E are set i,j =1 otherwise e i,j =0. All diagonal elements in the symmetric connection matrix E are set to 0; determining each group G α Closest to the global center image I O And taking the image as a representative image
Step 4, constructing the group G α An internal linking system;
setting a threshold value, and representing the image
Image I with high similarity i {I i ∈G α ,i≠ i α There are connections, otherwise all are set to 0. Constructing a connected system between the groups of cells, each representative image
All the images are connected with the global central image, and any two representative images are not connected and are set to be 0; the specific construction process is as follows:
4-1. Determining the global central image I in the dataset closest to the hidden public space O . For N images I = { I = i I = 1.. N } for clustering, and the improved density clustering DBSCAN algorithm described in step 2 is used to form Ω subgroups G α = (α ∈ {1, \8230;, Ω } and
4-2 in each subgroup G α In the method, the core object obtained by the first clustering is the global central image I o . Omega small groups have omega representative images
Thus having a global central image
The benefit of choosing representative images in a group based on the global center image is that other images in the group can be more easily deformed toward the global center. For the rest omega-1 subgroups, selecting each point in each subgroup and the global central image I according to the similarity matrix S O The point with the smallest distance is taken as a representative image of the group;
4-3. For each subgroup G α, representative image I iα And all other images. For any pair of image Ii and image I j ∈G α Where j ≠ i, if i = i α Or j = i α Has e i,j =1, otherwise e i,j ＝0。
4-4. For high level connections between subgroups, global center image I O Connecting all other representative images
For any pair of images I i And
in other words, if i = o or j = o, then there is e i,j =1, otherwise e i,j ＝0。
And 5, continuously iterating the graph contraction process to carry out registration until convergence. The goal of graph-based group registration is to minimize the velocity vectors on all graph edges, as defined below:
minimization of F (t) is considered as a dynamic image reduction process that reduces each image from I i (t) deformation to I i (t + Δ t), the overall geodesic distance is reduced while the topology of the entire map is maintained. With increasing time t, all I i (t) final registration to the center image, and rational determination of the velocity vector v i , j (t) and a time increment Δ t. The concrete implementation is as follows:
as the map shrinks dynamically, it is critical that the group registration compare to determine each image I i (t) how to deform at time t such that the energy function F (t) is minimized. Suppose that each image is from I i (t 0 ) Is changed into I i (t k ) Where { t k Is time t (K =0, \8230;, K, t) 0 ＝0,t k → ∞) discretization. According to its connecting node i (t k ) Moving in the average direction, so each node I in the graph i (t k ) Local connectivity ofIs reasonable.
Since the velocity vector lies on the manifold I i (t k ) On the tangent space of (2), by linear averaging
Wherein
Is I i (t k ) The number of connections. Given at a point in time t k If each node I i (t k ) From t in the direction of the velocity vector k Move to t k +Δt k The entire energy function F (t) then decreases strictly monotonically, with a time increment Δ t k Is obtained by the following formula:
finally, from t by a connection 0 To t k To obtain each image I i Geodesic path to the center
Namely that
Wherein
The deformation composition is shown. During graph contraction, all images are gradually deformed into a hidden common space, and the topology of the graph is preserved. Using t based on interval Δ t k (k =0,1,2, \ 8230;, where t is 0 =0 and t when k → ∞ time t k → infinity) to discretize t. Use of
As time t k A new deformed image will
Is shown as time t k Image of the department
The resultant deformation field of (a).
Claims (4)
1. The graph contraction grouping and registering method based on density clustering is characterized by comprising the following steps of:
step 1, carrying out affine registration to obtain N image data sets I, I = { I) with affine alignment i I =1, ·, N }; calculate all distances with SSD
Obtaining a distance matrix D;
step 2, according to the formula
Obtaining a global central image I O (ii) a Clustering the data set I by using an improved density clustering DBSCAN algorithm, and dividing the data set I into omega small groups G α = (α ∈ { 1.,. Omega } and
)；
step 3, constructing an NxN symmetrical connection matrix E, wherein elements in the symmetrical connection matrix E
If the image I i And image I j Are connected, elements E of a symmetrical connection matrix E are set i，j =1 otherwise e i，j =0; all diagonal elements in the symmetric connection matrix E are set to 0; determining each subgroup G α Closest to the global center image I O And taking the image as a representative image
Step 4, constructing the group G α An internal linking system;
setting a threshold value, and representing the image
Image I with high similarity i {I i ∈G α ，i≠i α There is a connection, otherwise all are set to 0; constructing a connected system between the groups of cells, each representative image
All the images are connected with the global central image, and any two representative images are not connected and are set as 0;
step 5, registering is carried out through continuously iterating the graph contraction process until convergence; the goal of graph-based group registration is to minimize the velocity vectors on all graph edges, as defined below:
minimization of F (t) is considered as a dynamic image reduction process that reduces each image from I i (t) deformation to I i (t + Δ t), reducing the overall geodesic distance while maintaining the topology of the entire map; with increasing time t, all I i (t) final registration to the central image.
2. The graph shrinkage grouping registration method based on density clustering according to claim 1, wherein the improved density clustering DBSCAN algorithm of step 2 is described as follows:
2-1. Determining the global central image I of the closest hidden common space among the data sets O ；
Data set I = { I) composed of N images i I = 1.... N }, first apply affine registration to align all images into a common space, and then fill in nxn similarity momentsArray S, elements S of the similarity matrix S ij Is defined as negative SSD, i.e. s ij ＝d ij ＝||I i -I j || 2 ；
2-2, determining the radius of the neighborhood as an element;
removing the self-similarity value of the N × N similarity matrix S, i.e. removing d ii Removing the previous Num with the number of Nx (N-1)/2, and obtaining the previous Num by using KD tree nearest neighbor algorithm rough Minimum number of data, num rough ＝k*N×(N-1)/2；
Introducing a parameter beta limits the neighborhood radius epsilon to obtain a value of k:
∈ rough is the preliminary neighborhood radius, dis i Denotes d as small as the ith ordering ij ，
Num ∈ Satisfy | | I o -I j || 2 ≤∈ rough The number of o ≠ j, and the final neighborhood radius belongs to the following:
2-3, determining the number MinPts of the images contained in the neighborhood radius epsilon of the representative image sample,
Num Pts (o, j) denotes a global center image I o And image I j Whether the distance of (c) is within e neighborhood of the initial point
Setting a parameter alpha to adjust MinPts,0< alpha ≦ 1
2-4. Dividing the global central map I O As a seed, finding all representative image samples with the density of which can be reached, wherein the representative image samples form a current group, and points contained in the current group are removed from the data set I, and the group number c = c +1;1-5;
2-5, repeating steps 2-1 to 2-4 until the data set I is empty.
3. The graph contraction grouping registration method based on density clustering according to claim 2, wherein the step 4 is implemented as follows:
4-1. Determining the global central image I of the closest hidden common space among the data sets O (ii) a For N images I = { I i I = 1.. N } for clustering, and the improved density clustering DBSCAN algorithm described in step 2 is used to form Ω subgroups G α = (α ∈ { 1.,. Omega } and
)；
4-2. In each subgroup G α In the method, the core object obtained by the first clustering is the global central image I O (ii) a Omega images of omega subgroups
Thus having a global central image
The advantage of choosing representative images in the subgroup based on the global center image is that other images in the subgroup can be madeCan be deformed more easily towards the global center; for the rest omega-1 subgroups, selecting each point in each subgroup and the global central image I according to the similarity matrix S O The point with the smallest distance is taken as a representative image of the group;
4-3. For each subgroup G α Representative image
And all other images are connected in a group; for any pair of images I i And image I j ∈G α Where j ≠ i, if i = i α Or j = i α Has e i，j =1, otherwise e i，j ＝0；
4-4. For high level connections between subgroups, global center image I O Connecting all other representative images
For any pair of images I i And
in other words, if i = o or j = o, then there is e i，j =1, otherwise e i，j ＝0。
4. The graph contraction grouping registration method based on density clustering according to claim 3, wherein the step 5 is implemented as follows:
as the map shrinks dynamically, it is critical that group registration be more accurate to determine each image I i (t) how to deform at time t such that the energy function F (t) is minimized; suppose that each image is from I i (t 0 ) Is changed into I i (t k ) Where { t } k Is time t (K =0, K, t) 0 ＝0，t k Discretization of → ∞); according to its connecting node to connect I i (t k ) Moving in the average direction, so each node I in the graph i (t k ) Local connectivity of (a) is reasonable;
since the velocity vector lies on the manifold I i (t k ) On the tangent space of (2), by linear averaging
Wherein
Is I i (t k ) The number of connections of (a); given at a point in time t k If each node I i (t k ) From t in the direction of the velocity vector k Move to t k +Δt k The entire energy function F (t) then decreases strictly monotonically, with time increments Δ t k Is obtained by the following formula:
finally, from t by a connection 0 To t k To obtain each image I i Geodesic path to the center
Namely that
Wherein
Represents a deformation composition; during graph contraction, all images gradually deform to a hidden common space, and the topology of the graph is preserved; using t based on interval Δ t k (k =0,1,2., where t 0 =0 and t when k → ∞ time t k → ∞) to discretize t; use of
As time t k A new deformed image will
Is shown as time t k Image of the department
The resultant deformation field of (a).
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