CN110443785A - The feature extracting method of three-dimensional point cloud under a kind of lasting people having the same aspiration and interest - Google Patents
The feature extracting method of three-dimensional point cloud under a kind of lasting people having the same aspiration and interest Download PDFInfo
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Abstract
The invention discloses a kind of feature extracting methods of three-dimensional point cloud under lasting people having the same aspiration and interest, the present invention attached the feature of a CCAC on the basis of zero dimension Betti number, the subsequent evolution-information of point cloud nesting complex is further estimated, and propose a novel integrated persistence feature IPF and thus condensed single argument topological characteristic SIP out, not only theoretically Betti number is expanded, and it can more completely characterize the spatial evolution process of nested complex, it can be used for measuring the topologies change of complicated point cloud, there is better statistic property than the feature based on graph theory, a kind of very effective method for extracting the potential Imaging biological marker of Alzheimer disease can be become.A kind of wide, strong robustness character representation method that the present invention provides applicabilities, can satisfy the demand of different levels in practical application.
Description
Technical field
The present invention relates to a kind of features of three-dimensional point cloud under feature extracting method technical field more particularly to lasting people having the same aspiration and interest to mention
Take method.
Background technique
Existing three-dimensional point cloud signature analysis is directed to the relatively simple rigid objects of structure mostly, and real-life three
Dimension point cloud change is colourful, influences the factor numerous and complicated of its feature descriptive power.Therefore, study that some applicabilities are wide, robustness
Strong character representation method, meets the needs of different levels in practical application, is the key points and difficulties of three-dimensional point cloud character representation.
Summary of the invention
To solve the disadvantage that the prior art and deficiency, a kind of feature extracting method of three-dimensional point cloud under the lasting people having the same aspiration and interest is provided,
To meet the needs of different levels in practical application.
Provided for achieving the object of the present invention under a kind of lasting people having the same aspiration and interest three-dimensional point cloud feature extracting method,
Include step 1: observation object people having the same aspiration and interest rank of a group distinguishes topology using based on the connectivity of k dimension simplicial complex
Space, it is k-th of people having the same aspiration and interest rank of a group that kth, which ties up Betti number, indicates " hole " quantity in kth dimension；
Step 2: the complex K that a given side right is all positive is rejected after arranging the side right of its minimum spanning tree by ascending order
Repetition values obtain: λ1< ... < λm, thus construct the nested complex of K
Then in filter value λiLocate the 0th dimension Betti number β of complex K0For
Wherein λ0=0；The minimum spanning tree that m is complex K does not repeat the number of side right；
Step 3: calculating connected component and polymerize cost, connected component's polymerization cost is referred to as CCAC, i.e., from current connection point
The sum of side right involved in evolution process of the branch to final full-mesh figure, calculates in filter value λiLocate the polymerization cost of complex K
Wherein, λo=0, CCAC cost are defined as being evolved into the sum of filter value required before being fully connected complex, by
In filter value λm-1Place all nodes all have connected, so when CCAC cost be zero；
Step 4: the CCAC cost tieing up Betti number by integration the 0th and newly defining calculates a kind of novel topology category
Property --- integrated persistence feature, integrated persistence feature are referred to as IPF, and the IPF for defining non-normalization isWithProduct, i.e.,
In order to make IPF can with the complex of the different interstitial contents of processing of consistency by above formula 3 divided by m* (m-1)
The value for obtaining IPF is limited to [0, max (λi)], to obtain the IPF of normalization
Step 5: according to formula, the complex K that a given side right is all positive, by its minimum spanning tree
Side right rejects repetition values after arranging by ascending order, can obtain: λ1< ... < λm, thus construct the nested complex of KThen in filter value λiThe IPF of place complex K is defined as
Wherein, λ0=0；
Step 6: the complex K that a given side right is all positive constructs the nested complex of KProve the IPF of nested complex with filter value λiIn monotone decreasing and receipts
It holds back；
Step 7: minimum two is utilized to all possible filter value in nesting complex defined in step 6 and corresponding IPF
Multiplication carries out linear regression, and the slope-SIP that will be obtained is defined as new topology metric, and a topology as three-dimensional point cloud is special
Sign.
The beneficial effects of the present invention are:
Compared with prior art, the present invention attached the feature of a CCAC on the basis of zero dimension Betti number, into one
Step estimated the subsequent evolution-information of point cloud nesting complex, and propose a novel integrated persistence feature IPF and
Thus condensed single argument topological characteristic SIP out, not only theoretically expands Betti number, and can be more completely
The spatial evolution process for characterizing nested complex can be used for measuring the topologies change of complicated point cloud.The present invention provides
A kind of applicability is wide, strong robustness character representation method, can satisfy the demand of different levels in practical application.
Detailed description of the invention
Below in conjunction with attached drawing, specific embodiments of the present invention will be described in further detail, in which:
Fig. 1 is the feature evolution figure under the lasting people having the same aspiration and interest, and (a) is the continuous variation with filter value λ, Betti number β in figure0With
β1The nested complex image changed correspondingly is (b) bar code image after coding, is (c) the persistence image after visualization；
Fig. 2 is the sample calculation of topological characteristic under the lasting people having the same aspiration and interest；
Fig. 3 is experiment flow figure of the invention；
Fig. 4 is the effect contrast figure for the multiple dimensioned brain structure that the present invention tests, and (a) is the brain knot of AD subject in figure
The effect contrast figure of structure is (b) effect contrast figure of the brain structure of MCI subject, is (c) brain structure of NC subject
Effect contrast figure.
Specific embodiment
Referring to Fig. 3 flow chart, by taking the brain 3-dimensional image signature analysis of Alzheimer disease as an example, to the present invention do into
The elaboration of one step, specific implementation method are as follows:
The brain 3-dimensional image data of Alzheimer disease are pre-processed first, pre-treatment step is as follows:
S1: generating three groups of data at random, and every group includes K=40 subject, and each subject has S=100 width three-dimensional
Scan-image；
S2: M=90 brain area is defined by AAL90 brain map, each brain area is as a node；
It needs to follow the steps below calculating after pretreatment:
Step 1: observing the people having the same aspiration and interest rank of a group of the three-dimensional brain image data after pretreatment, tie up simplicial complex using based on k
Connectivity distinguish manifold, it is k-th of people having the same aspiration and interest rank of a group that kth, which ties up Betti number, indicate " hole " quantity in kth dimension；
Attached drawing 1 (a) is illustrated as the λ of filter value constantly changes, Betti number β0And β1It changes correspondingly, and passes through the bar shaped in Fig. 1 (b)
Persistence figure in code and Fig. 1 (c) is encoded and is visualized.Bar code is the set of limited section composition on real number axis,
Each section indicates the birth and extinction of hole under respective dimensions, is parallel to each other between these sections.In Fig. 1, as λ=7, produce
Hole (the β of 4 zero dimensions is given birth to0=4) and 1 one-dimensional hole (β1=1)；And in λ=9.5, some holes " are filled up "
, while some new holes are produced again, there is 1 zero dimension hole (β at this time0=1) and 2 one-dimensional hole (β1=2).Fig. 1 (c)
In a leftmost blue vertical line be considered as a point of infinite point, represent the topological characteristic never withered away.
Step 2: the complex K that a given side right is all positive is rejected after arranging the side right of its minimum spanning tree by ascending order
Repetition values obtain: λ1< ... < λm, thus construct the nested complex of K
Then in filter value λiLocate the 0th dimension Betti number β of complex K0For
Wherein λ0=0；The minimum spanning tree that m is complex K does not repeat the number of side right；Three-dimensional brain is sought based on minimum spanning tree
The nested complex of image data, solution procedure are as follows:
S2.1: assuming that xijk, yijk, zijkRespectively indicate the i-th width 3-dimensional image data of k-th of subject in three groups of crowds
In j-th of brain area (node) semaphore, with independent standard normal distribution function N (0,1) to they initialize, herein just
State Distribution Function Definition isWherein μ is average value, and σ is standard deviation, in order to enable x and y
It is not exclusively the same, a small amount of noise N (0,0.01~0.1) is added in y.
S2.2: the different connection modes in order to simulate every group of interior joint select node serial number for p=1 in two groups of the past, and 3,
5,7 four nodes, select node serial number for p=1 from third group, 3,5 ..., 15 eight nodes, then selected
Linear regression is carried out with least square method between node and generates linear dependence, this 8 nodes respectively represent defined in AAL90
Sinistrocerebral 8 brain areas: under precentral gyrus, back outside superior frontal gyrus, pars orbitalis superior frontal gyrus, middle frontal gyrus, pars orbitalis middle frontal gyrus, opercular part volume
Return, triangular part gyrus frontalis inferior, pars orbitalis next time.Every group of specific emulation mode of data is as follows:
Wherein, i ∈ { 1,2 ..., S }, j ∈ { 1,2 ..., M } A, k ∈ { 1,2 ..., K }.In addition, every group also added
A small amount of noise N (0,0.01) upsets nodal value.
S2.3: it is based on Pearson correlation
The adjacency matrix of side right is calculated using formula (3).
S2.4: p={ v is set0, v1..., vk∈ P be xiAnd xjBetween path, wherein P is xiAnd xjBetween all possibility
The set in path, and v0=xi, vk=xj.Then the form of Definition of single-stranded distance is as follows,
The single-stranded distance matrix of W is calculated using formula (4), and finds minimum spanning tree using kruskal algorithm,
Method based on minimum spanning tree is that each subject generates a nested complex, and therefore, every group constructs 40 nested complex,
It is as shown in Figure 4 to construct result.
Step 3: calculating connected component and polymerize cost, connected component's polymerization cost is referred to as CCAC, i.e., from current connection point
The sum of side right involved in evolution process of the branch to final full-mesh figure, calculates in filter value λiLocate the polymerization cost of complex K
Wherein, λ0=0, CCAC cost are defined as being evolved into the sum of filter value required before being fully connected complex, by
In filter value λm-1Place all nodes all have connected, so when CCAC cost be zero；
Step 4: the CCAC cost tieing up Betti number by integration the 0th and newly defining calculates a kind of novel topology category
Property --- integrated persistence feature, integrated persistence feature are referred to as IPF, and the IPF for defining non-normalization isWithProduct, i.e.,
In order to make IPF can with the complex of the different interstitial contents of processing of consistency by above formula 3 divided by m* (m-1)
The value for obtaining IPF is limited to [0, max (λi)], to obtain the IPF of normalization
Step 5: according to formula (1), (5), (6), (7), the complex K that a given side right is all positive generates its minimum
The side right of tree rejects repetition values after arranging by ascending order, can obtain: λ1< ... < λm, thus construct the nested complex of KThen in filter value λiThe IPF of place complex K is defined as
Wherein, λ0=0；
Step 6: the complex K that a given side right is all positive constructs the nested complex of KProve the IPF of nested complex with filter value λiIn monotone decreasing and receipts
It holds back；Fig. 2 gives a sample calculation of topological characteristic under the lasting people having the same aspiration and interest, calculates its minimum by the complex K on the left side and generates
The side right set { 0.1,0.2,0.4 } of tree constructs nested complex as scale
Then, the 0th Betti number β is calculated separately out according to formula equation (1), (5), (6), (7)0, connected component polymerize cost, non-rule
One changes this four topological characteristics of IPF and normalization IPF, and calculated result is shown in Fig. 2.
Step 7: minimum two is utilized to all possible filter value in nesting complex defined in step 6 and corresponding IPF
Multiplication carries out linear regression, and the slope-SIP that will be obtained is defined as new topology metric, and a topology as three-dimensional point cloud is special
Sign.
On the basis of step 2 acquires nested complex, by step 3,4,5,6 calculation processing is AD, MCI and NC group
In each subject construct multiple dimensioned brain structure, the corresponding SIP value of each nested complex is asked according to step 7, that is,
Acquire corresponding SIP feature.
In order to verify the validity of the method for the present invention, this method to the SIP feature acquired, further examine by degree of resurveying, inspection
It is as follows to test process:
S1: it is assumed that the feature to two groups of subjects carries out Variant statistical analysis, it is its i-th of subject's structure for the 1st group
Build a multiple dimensioned brain structure and corresponding IPF feature γ1(i, λ)；Equally, j-th of subject in the 2nd group is also counted
Calculate its IPF feature γ2(j, λ).
S2: to the slope of IPF sequence --- SIP feature is tested.It is assumed that i-th of SIP being tested in the 1st group and
The SIP of j-th of subject in 2 groups is expressed asWithThen null hypothesis are as follows:
And it substitutes and assumes are as follows:
" mean " is the average value of all subject SIP in taken group herein.
S3: experiment uses two kinds of nonparametric discrimination methods.Firstly, nonparametric permutation test is commonly used between the group of characteristic value
In pairs relatively, therefore, pass through 10,000 times in experiment about the group difference analysis between AD and MCI, AD and NC and MCI and NC
Available strategy method carry out permutation test.Secondly, the Variant statistical analysis (AD-MCI-NC) between three groups executes Kruskal-
Wallis is examined.
SIP feature is compared with original lasting people having the same aspiration and interest feature BNP in experiment, they are in tri- groups of AD, MCI and NC
The results are shown in Table 1 for Variant statistical analysis on not.The results show that SIP proposed by the present invention can detecte any two groups of (p
< 0.05) and three groups (p=0.002) between significant difference, and BNP can not detect the difference (p=between AD and MCI
0.499), thus SIP obtain more significant group between statistical discrepancy.This method is than calculation amount needed for original method fewer
It is more.In each round permutation test, original method needs are constructed one big using the image data with all subjects of group
Brain structure, the calculating of this wheel about needs 0.84 second in this method experimental situation, and completing all 10,000 wheel calculating about needs 2.3 hours
(10,000*0.84 seconds).And this research is that a brain structure (about 0.48 second) is constructed for each subject, and it can be with
Calculated in advance goes out the SIP value of each subject before permutation test, therefore for 106 subjects, all displacement of 10,000 wheels
Inspection only needs 4.5 minutes or so (106*0.48 seconds, additional additional some calculating times).This method is than former methodical operation
Time about improves 31 times.
Then summarize in brain area signal, SIP feature resurveys under the different schemes such as functional cohesion calculates and brain area divides
Reliability.
Method are as follows: carry out repeating experiment, the height generated at random including one on the brain map of 4 different resolutions
The resolution ratio brain map H1024 (brain map of 1024 brain areas and three low resolution: HOA112 (112 brains), AAL116 (116
A brain area and Crad200 (200 brain areas).Statistic property between the group of all features, system are assessed in all brain region schemes
Meter the results are shown in Table 2.The result shows that the SIP feature that we's hair proposes achieves better statistical power in different schemes, have
There is preferable robustness.
The group difference statistical result of 1 different topology feature of table
Note: (1) brain area is defined by AAL90.
(2) scale problem: scale selection problem is not present in the multiple dimensioned feature of the first two；It needs to delete before 4 feature calculations afterwards
Except the functional cohesion of non-limiting (Bonferroni corrects p >=0.05).
Statistical analysis technique between (3) two groups is 10,000 permutation tests；Statistical analysis technique between three groups is
Kruskal-Wallis is examined, and result (p value) display of all statistics is in the table.
(4)aP < 0.01；b0.01≤p≤0.05；c0.05 < p < 0.1.
3.2 different characteristic of table statistic analysis result between the group on 4 big brain map
Note: (1) scale problem: the problem of scale selection is not present in the first two Analysis On Multi-scale Features；It is needed before 4 feature calculations afterwards
Delete the connection of non-limiting (Bonferroni corrects p >=0.05).
(2) brain map: HOA112: the Harvard-Oxford brain map containing 112 brain areas；AAL116: contain 116 brain areas
Automation anatomical landmarks brain map (automated anatomical labeling)；Crad200: containing 200 brain areas
Craddock brain map；H1024: the brain map containing 1024 brain areas generated at random.
Statistical analysis technique between (3) two groups is 10,000 permutation tests；Statistical analysis technique between three groups is
Kruskal-Wallis is examined, and result (p value) display of all statistics is in the table.
(4)aP < 0.01；b0.01≤p≤0.05；c0.05 < p < 0.1.
The topological characteristic proposed is applied to the brain 3-dimensional image signature analysis of Alzheimer disease by the present invention, is provided
A kind of novel opinion to the analysis of full brain function.The SIP feature proposed can distinguish AD and MCI and healthy control group
Come, there is better statistic property compared with other widely used characteristics of graph theory.Experimental result is AD and MCI patient in full brain
Functional organization's damage in range provides substantial evidence, while showing that SIP is likely to become the potential Imaging biological marker of AD.
Above embodiments are not limited to the technical solution of the embodiment itself, can be incorporated between embodiment new
Embodiment.The above embodiments are merely illustrative of the technical solutions of the present invention and is not intended to limit it, all without departing from the present invention
Any modification of spirit and scope or equivalent replacement, shall fall within the scope of the technical solution of the present invention.
Claims (1)
1. the feature extracting method of three-dimensional point cloud under a kind of lasting people having the same aspiration and interest, it is characterised in that:
Include step 1: observation object people having the same aspiration and interest rank of a group distinguishes manifold using based on the connectivity of k dimension simplicial complex,
It is k-th of people having the same aspiration and interest rank of a group that kth, which ties up Betti number, indicates " hole " quantity in kth dimension；
Step 2: the complex K that a given side right is all positive is repeated the side right of its minimum spanning tree by rejecting after ascending order arrangement
Value, obtains: λ1< ... < λm, thus construct the nested complex of KThen exist
Filter value λiLocate the 0th dimension Betti number β of complex K0For
Wherein λ0=0；The minimum spanning tree that m is complex K does not repeat the number of side right；
Step 3: calculate connected component polymerize cost, connected component polymerization cost be referred to as CCAC, i.e., from current connected component to
The sum of side right involved in the evolution process of final full-mesh figure, calculates in filter value λiLocate the polymerization cost of complex K
Wherein, λ0=0, CCAC cost are defined as being evolved into the sum of filter value required before being fully connected complex, due to filtering
Value λm-1Place all nodes all have connected, so when CCAC cost be zero；
Step 4: the CCAC cost tieing up Betti number by integration the 0th and newly defining calculates a kind of novel topological attribute --- collection
At persistence feature, integrated persistence feature is referred to as IPF, defines non-normalizationForWithProduct, i.e.,
In order to make IPF can with the complex of the different interstitial contents of processing of consistency, by above formula 3 divided by m* (m-1) so that
The value of IPF is limited to [0, max (λi)], to obtain normalization
Step 5: according to formulaConstruct the nested complex of KSeek filter value λiLocate the IPF of complex K
Wherein, λ0=0；
Step 6: proving the nested complex for the K that step 5 acquiresWith filter value λiIn monotone decreasing and convergence；
Step 7: to all possible filter value in the nested complex of K defined in step 6 and correspondingIt utilizes
Least square method carries out linear regression, and the slope S IP that will be obtained is defined as new topology metric, one as three-dimensional point cloud
Topological characteristic.
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