CN101650838A - Point cloud simplification processing method based on resampling method and affine clustering algorithm - Google Patents

Abstract

The invention relates to a point cloud simplification processing method based on a resampling method and an affine clustering algorithm, which comprises the following steps: 1, setting a threshold value of the simplified target point number; 2, uniformly sampling an initial point cloud D to acquire a point subset SD of the initial point cloud D and searching a k nearest neighboring point of each point in the subset SD; 3, calculating the curvature CV of each point in the SD by using the k nearest neighboring point acquired in the step 2; 4, calculating the similarity between the points in theSD to acquire a similarity matrix S; 5, inputting S and CV as an AP algorithm by applying an AP clustering algorithm and calculating a representative degree matrix and an adaptive selecting degree matrix between the points; selecting representing points according to an iteration result; if the number D of the representing points is smaller than the threshold value, namely D=D-SD, turning to the step 2; and adding a representing point label selected each time into the same matrix till a target value is achieved to acquire a final point set FD. The invention simplifies the calculation, reducesthe occupied memory capacity and has favorable effectiveness.

Description

Point cloud simplifying treatment method based on method for resampling and affine clustering algorithm

Technical field

The present invention relates to computer vision, data processing, computer graphics, numerical computation method and reverse-engineering field, especially a kind of point cloud simplifying treatment method.

Background technology

Can obtain large-scale sampled point by images match and scanning real-world object modelling technique and promptly put cloud.The point cloud comprises lot of data point usually and can well express object surfaces.All brought very big difficulty for the drafting of point and editor but put cloud on a large scale, on the other hand, the expression of three-dimensional model does not need so many point usually.For more effective expression and drawing three-dimensional point cloud model, a lot of methods of Ti Chuing are applied to point cloud simplification in recent years.In the early stage in the research to a cloud, most researchs are based on topological net a little, there is the general introduction of four kinds of classical simplified algorithms to see Mark Pauly mark. the article of Pohle: M.Pauly, " EfficientSimplification of Point-Sampled Surfaces ", IEEE Visualization 2002Oct.27-Nov., i.e. mark. effective simplification IEEE vision 2002.10 of Pohle point cloud curved surface; Comprised four kinds: (1) summit removes (2) summit cluster (3) limit and shrinks (4) particle emulation.These several algorithms all are based on a topology and need expend more internal memory.So recently the emphasis of a lot of researchs begin to be placed on directly a cloud is simplified on.Boissonnat introduced a kind of progressively by coarse to meticulous short-cut method, reference literature: J.-D.Boissonnat and F.Cazals. " Coarse-to-fine surface; simplificationwith geometric guarantees " .EUROGRAPHICS 01, Conf.Proc., Manchester, UK, 2001; Be the refinement point cloud simplification Europe graphics conference Britain 2001 of Bai Naite based on method of geometry.11。Method for resampling is a subclass of calculating the initial point cloud by the rule of some customizations, and the implication of cluster is the representative point that data set is divided into subclass and finds each subclass.Most of clustering algorithms all need be at concentrated some cluster centres of selection at random of primary data, and the selection of these initial cluster centers can have influence on the result of the representative point of finally selecting usually.The proposition of affine clustering algorithm has overcome this defective, its main thought is initially each to be put all as initial representative point, and point between send the message have dot information, but equally with other clustering algorithms be not suitable for being applied to dense similar matrix.

In the prior art, mainly based on the mesh topology of a cloud, carry out lattice simplifiedly reaching the purpose of a simplification to the research of point cloud simplification according to the relation of topological net, the defective of this method is a large amount of grid of storage and need bigger internal memory.And present main stream approach mainly is directly a cloud to be simplified.The major advantage of affine clustering algorithm is to send message between points, and has processing speed faster, and application is comparatively extensive, but needs bigger internal memory during for dense data similar matrix.

Summary of the invention

For the calculation of complex of the disposal route that overcomes existing point cloud simplification, need take the deficiency of big internal memory, validity difference, the invention provides a kind of memory size that calculatings, minimizing takies, point cloud simplifying treatment method simplified based on method for resampling and affine clustering algorithm with good validity.

The technical solution adopted for the present invention to solve the technical problems is:

A kind of point cloud simplifying treatment method based on method for resampling and affine clustering algorithm may further comprise the steps:

Step 1: set the threshold value of simplifying the impact point number;

Step 2: initial point cloud D uniform sampling is obtained its sub-point set SD, to each the point search k arest neighbors near point among the subclass SD, i.e. the k of data point q nearest point:

KNN (q)=| p _i-q|≤| p-q|, p _i∈ D}, p _i(i=1 2...k) is the neighbor point of a q;

Step 3: the k arest neighbors near point that utilizes step 2 to obtain calculates the curvature CV of each point among the SD, and the i that sets up an office has k neighbor point p _Ik(k=1,2...k), the coordinate mean value of k+1 point is ap _i, the covariance matrix of some i is C; Mutual relationship is expressed as follows:

ap _i＝(p _i1+p _i2+...p _ik)/(k+1)

$C={\left[\begin{array}{c}{p}_{i1}-{\mathrm{ap}}_i\\ p_{i2}-{\mathrm{ap}}_i\\ ..............\\ p_{\mathrm{ik}}-{\mathrm{ap}}_i\end{array}\right]}^T\left[\begin{array}{c}{p}_{i1}-{\mathrm{ap}}_i\\ p_{i2}-{\mathrm{ap}}_i\\ ..............\\ p_{\mathrm{ik}}-{\mathrm{ap}}_i\end{array}\right]$

C*V＝λ*V

Wherein, C is the positive semidefinite matrix of a symmetry, and eigenwert is real-valued, and V is the proper vector of covariance matrix, λ ₁, λ ₂, λ ₃It is the eigenwert of the character pair vector of C; Get λ _iBe minimal eigenvalue, represent the curved transition value of an i: cv with eigenwert _i=λ ₁/ (λ ₁+ λ ₂+ λ ₃);

Step 4: calculate similarity between points among the SD, obtain similarity matrix S, specifically have: the similarity of some i and some k be labeled as S (i, k), similarity can reflect the close relationship of point-to-point transmission, the similarity value is chosen the negative value of distance between two points square, as

S(i，k)＝-(‖x _i-x _k‖ ²+‖y _i-y _k‖ ²+‖z _i-z _k‖ ²) (1)

(x _i, y _i, z _i) be the D coordinates value of data point i;

Step 5: utilization AP clustering algorithm, S and CV are as the input of AP algorithm, and representative degree matrix between calculation level and suitable degree of choosing matrix specifically have:

For the arbitrfary point, calculate representative degree and grade of fit sum R+A:

R(i，k)+A(i，k)＝S(i，k)+A(i，k)-{A(i，j)+S(i，j)}.

The value representation point of R+A is as the validity of class representative point and can characterize a little selected probability;

A (k, k) and R (k, growth k) and deflection parameter P be S (k, k) relevant; Introduced a decay factor λ and carried out iteration, add this parameter after, R, S, relationship change is as follows between three matrixes of A:

$R^{\left(t\right)}(i,k)=(1-\mathrm{\λ})*\{S(i,k)-\max \underset{j\≠k}{\{A(i,k)+S(i,j)\}}\}+\mathrm{\λ}*R^{(t-1)}(i,k)$

$A^{\left(t\right)}(i,k)=(1-\mathrm{\λ})*\{0,R(k,k)+\underset{j\∉\{i,k\}}{\mathrm{\Σ}}\max \{0,R(j,k)\left\}\right\}\}+\mathrm{\λ}*A^{(t-1)}(i,k)$

$A^{\left(t\right)}(k,k)=(1-\mathrm{\λ})*\left\{\underset{j\≠k}{\mathrm{\Σ}}\max \right\{0,R(j,k)\left\}\right\}+\mathrm{\λ}*A^{(t-1)}(k,k)$

The result selects representative point according to iteration, and less than threshold value, promptly D=D-SD turns back to step 2 as the number D of representative point;

The representative point label of at every turn selecting joins in the same matrix, obtains final point set FD up to reaching desired value.

Further, in described step 2, at first calculating maximum coordinate figure in each dimension of a space, cloud place, constitute the external bounding box in space, then in bounding box between division of cells, represent for each minizone coding with Hash table, can index the minizone at its place, getting central point as this sampled point in the minizone more uniformly then to guarantee each point.

Technical conceive of the present invention is: affine clustering algorithm (AP clustering algorithm) is proved to be in a lot of fields and can effectively uses, as the facial image cluster, and the gene recognition of gene expression data, text character discriminator and optimum air lane are definite etc.Its main thought is that each data point is regarded as node in the network, then recurrence in pass-along message between node till good representative point is selected, rephrase the statement be exactly with all data points all as potential class representative point, can avoid being subject to the selection of initial representative point.AP constitutes similar matrix as input by the similarity of computational data point, and the similarity of some i and some k is labeled as S, and (i, k), similarity can reflect the close relationship of point-to-point transmission.Usually, the similarity value is chosen the negative value of distance between two points square usually.As

A(i，k)＝-(‖x _i-x _k‖ ²+‖y _i-y _k‖ ²+‖z _i-z _k‖ ²) (1)

Wherein, (xi, yi zi) are the D coordinates value of data point i.At the diagonal line S of similar matrix S (k, k), be called the deflection parameter p again, the deflection parameter is another input value of AP, can reflect that a k is selected as the probability of representative point, the p value is big more, the P value also can be regulated the number of finally selecting representative point when the selected probability as representative point of some k was also just got over Datong District, generally, increased the number that the p value can increase class, reduce the number that the p value then can reduce class, so the selection of p has vital role for the net result of AP clustering algorithm.

In AP clustering algorithm information exchanging process, there are two information to bring in constant renewal in, promptly represent matrix R and the suitable matrix A of selecting.In the process that the AP clustering algorithm is realized, the process brought in constant renewal in of the entrained information of these two matrixes just, the information in two matrixes has been represented different competition purposes.(i is to point to some k from an i k) to R, has represented the evidence of some k accumulation, and expression point k is fit to do the representative degree of an i representative point.(i is to point to some i from a k k) to A, has represented the evidence of some i accumulation, and representative point i selected element k is as the appropriate level of class representative point.R and A are upgrading and exchange message by known similarity between points, and after upgrading through some iteration, some points are chosen as representative point, and their applicability value can drop to below zero by some update rules.

AP clustering algorithm flow process

Input: similarity matrix S and deflection parameter P

Output: represent point set D

Step 1: initialization A (i, k)

Step 2: upgrade R

Step 3: upgrade A

Step 4: through after some iteration and information updating that ascertain the number, iteration stops obtaining final class center.

Send information synoptic diagram such as Fig. 1 and Fig. 2 between point.

For the arbitrfary point, calculate representative degree and grade of fit sum R+A.

R(i，k)+A(i，k)＝S(i，k)+A(i，k)-{A(i，j)+S(i，j)}.

The value of R+A has shown that point is as the validity of class representative point and can characterize a little selected probability.In the process of information iteration, all the similar matrix with input is relevant with suitable degree of choosing for representative degree, finally determines the class representative point therefrom.On the other hand, A (k, k) and R (k, growth k) and deflection parameter P be S (k, k) relevant.Simultaneously, in iterative process, shake, introduced a decay factor λ, add this parameter after, R, S, relationship change is as follows between three matrixes of A:

$R^{\left(t\right)}(i,k)=(1-\mathrm{\λ})*\{S(i,k)-\max \underset{j\≠k}{\{A(i,k)+S(i,j)\}}\}+\mathrm{\λ}*R^{(t-1)}(i,k)$

$A^{\left(t\right)}(i,k)=(1-\mathrm{\λ})*\{0,R(k,k)+\underset{j\∉\{i,k\}}{\mathrm{\Σ}}\max \{0,R(j,k)\left\}\right\}\}+\mathrm{\λ}*A^{(t-1)}(i,k)$

$A^{\left(t\right)}(k,k)=(1-\mathrm{\λ})*\left\{\underset{j\≠k}{\mathrm{\Σ}}\max \right\{0,R(j,k)\left\}\right\}+\mathrm{\λ}*A^{(t-1)}(k,k)$

In a cloud, disperse between points, do not comprise any topology information, at this time just need come topology information potential between the calculation level by the neighbor point of calculation level.Herein, thus by k the neighbor point that calculates each point draw this point around topological relation calculate the curvature information of this point.K arest neighbors sorting algorithm is one of simple machine learning algorithm, thinking is as follows: if the great majority in the sample of the k of sample in feature space (being the most contiguous in the feature space) the most similar belong to some classifications, then this sample also belongs to this classification.In the KNN algorithm, selected neighbours are the objects of correctly classifying.This method decides the classification for the treatment of under the branch sample only deciding in the class decision-making classification according to one or several the most contiguous samples.Though it is the KNN method also depends on limit theorem on principle, when the classification decision-making, only relevant with the adjacent sample of minute quantity.Since the KNN method mainly by around the sample of limited vicinity, rather than determine affiliated classification, so for the intersection of class field or the overlapping more branch sample set for the treatment of, the KNN method is more suitable than additive method by the method for differentiating class field.The KNN problem description is as follows: given data set D, find out k the nearest point of data point q.KNN (q)=| p _i-q|≤| p-q|, p _i∈ D}p _i(i=1 2...k) is the neighbor point of a q.Adopt the method search nearest neighbor point of grid dividing herein.At first each dimension of point data all is divided into n interval, is each regional code, seeks the point that drops in the adjacent domain by encoding.Algorithmic procedure is as follows:

Step 1: location sampling point q

Step 2: in same zone, seek neighbor point,,, then continue searching in the zone of the vicinity in this zone, till finding k closest approach if less than k point if k is arranged then stop to seek.

In the AP clustering algorithm was used, similar matrix S was the matrix of a n*n, and n is the number of data point, when n is bigger, stores this matrix and just need expend very big space.Therefore, this paper uses the AP clustering algorithm, again to improve its applicability after at first cloud data being carried out simple sampling processing.For uniform sampled point cloud, introduced a rule of dividing grid.The method of dividing grid with above k arest neighbors is similar, at first calculating maximum coordinate figure in each dimension of a space, cloud place, constitute the external bounding box in space, then in bounding box between division of cells, represent for each minizone coding with Hash table, to guarantee that each point can index the minizone at its place, getting central point as this sampled point in the minizone more uniformly then.

In order to keep the details of simplifying the back model, point cloud model need be that the higher curvature place keeps more point at the higher point of flexibility, and level and smooth place then can keep less relatively point.Be exactly to require the big point of curvature to have bigger probability to be chosen as representative point like this, and if smooth region has less probability selected, so just can guarantee the reservation of details as a result.The computing method of curvature have a lot, and for the discrete topology of a cloud, adopt utilizes neighbor point to come the curvature value of calculation level more.

Postulated point i has k neighbor point p _Ik(k=1,2...k), the coordinate mean value of this k+1 point is ap _i, the covariance matrix of some i is C.Relation between several amounts is expressed as follows:

ap _i＝(p _i1+p _i2+...p _ik)/(k+1)

$C={\left[\begin{array}{c}{p}_{i1}-{\mathrm{ap}}_i\\ p_{i2}-{\mathrm{ap}}_i\\ ..............\\ p_{\mathrm{ik}}-{\mathrm{ap}}_i\end{array}\right]}^T\left[\begin{array}{c}{p}_{i1}-{\mathrm{ap}}_i\\ p_{i2}-{\mathrm{ap}}_i\\ ..............\\ p_{\mathrm{ik}}-{\mathrm{ap}}_i\end{array}\right]$

C*V＝λ*V

C is the positive semidefinite matrix of a symmetry, and eigenwert is real-valued, and V is the proper vector of covariance matrix, λ ₁, λ ₂, λ ₃It is the eigenwert of the character pair vector of C.Suppose λ _iBe minimal eigenvalue, minimal eigenvalue can characterize the variation of an i, promptly can represent the curved transition value of an i with eigenwert.Cv _i=λ ₁/ (λ ₁+ λ ₂+ λ ₃) from then on formula as can be seen, the maximum curvature value

Cv _i=1/3, and when all points are on same plane cv _i=0.

Beneficial effect of the present invention mainly shows: simplify to calculate, reduce the memory size that takies, have good validity.

Description of drawings

Fig. 1 is the synoptic diagram that sends information between a kind of point.

Fig. 2 is the synoptic diagram that sends information between another kind of point.

Fig. 3 is under the simplification rate of rabbit model 84.4%, the result synoptic diagram of simplified process method of the present invention, K mean cluster method and method for resampling.

Fig. 4 is under the simplification rate of rabbit model 78.8%, the result synoptic diagram of simplified process method of the present invention, K mean cluster method and method for resampling.

Fig. 5 is under the simplification rate of imperial model 97.5%, the result synoptic diagram of simplified process method of the present invention, K mean cluster method and method for resampling.

Fig. 6 is under the simplification rate of imperial model 99.3%, the result synoptic diagram of simplified process method of the present invention, K mean cluster method and method for resampling.

Embodiment

Below in conjunction with accompanying drawing the present invention is further described.

With reference to Fig. 1～Fig. 6, a kind of point cloud simplifying treatment method based on method for resampling and affine clustering algorithm may further comprise the steps:

Step 1: set the threshold value of simplifying the impact point number;

Step 2: initial point cloud D uniform sampling is obtained its sub-point set SD, to each the point search k arest neighbors near point among the subclass SD, i.e. the k of data point q nearest point:

KNN (q)=| p _i-q|≤| p-q|, p _i∈ D}, p _i(i=1 2...k) is the neighbor point of a q;

Step 3: the k arest neighbors near point that utilizes step 2 to obtain calculates the curvature CV of each point among the SD, and the i that sets up an office has k neighbor point p _Ik(k=1,2...k), the coordinate mean value of k+1 point is ap _i, the covariance matrix of some i is C; Mutual relationship is expressed as follows:

ap _i＝(p _i1+p _i2+...p _ik)/(k+1)

$C={\left[\begin{array}{c}{p}_{i1}-{\mathrm{ap}}_i\\ p_{i2}-{\mathrm{ap}}_i\\ ..............\\ p_{\mathrm{ik}}-{\mathrm{ap}}_i\end{array}\right]}^T\left[\begin{array}{c}{p}_{i1}-{\mathrm{ap}}_i\\ p_{i2}-{\mathrm{ap}}_i\\ ..............\\ p_{\mathrm{ik}}-{\mathrm{ap}}_i\end{array}\right]$

C*V＝λ*V

Wherein, C is the positive semidefinite matrix of a symmetry, and eigenwert is real-valued, and V is the proper vector of covariance matrix, λ ₁, λ ₂, λ ₃It is the eigenwert of the character pair vector of C; Get λ _iBe minimal eigenvalue, represent the curved transition value of an i: cv with eigenwert _i=λ ₁/ (λ ₁+ λ ₂+ λ ₃);

Step 4: calculate similarity between points among the SD, obtain similarity matrix S, specifically have: the similarity of some i and some k be labeled as S (i, k), similarity can reflect the close relationship of point-to-point transmission, the similarity value is chosen the negative value of distance between two points square, as

S(i，k)＝-(‖x _i-x _k‖ ²+‖y _i-y _k‖ ²+‖z _i-z _k‖ ²) (1)

(x _i, y _i, z _i) be the D coordinates value of data point i;

Step 5: utilization AP clustering algorithm, S and CV are as the input of AP algorithm, and representative degree matrix between calculation level and suitable degree of choosing matrix specifically have:

For the arbitrfary point, calculate representative degree and grade of fit sum R+A:

R(i，k)+A(i，k)＝S(i，k)+A(i，k)-{A(i，j)+S(i，j)}.

The value representation point of R+A is as the validity of class representative point and can characterize a little selected probability;

A (k, k) and R (k, growth k) and deflection parameter P be S (k, k) relevant; Introduced a decay factor λ and carried out iteration, add this parameter after, R, S, relationship change is as follows between three matrixes of A:

$R^{\left(t\right)}(i,k)=(1-\mathrm{\λ})*\{S(i,k)-\max \underset{j\≠k}{\{A(i,k)+S(i,j)\}}\}+\mathrm{\λ}*R^{(t-1)}(i,k)$

$A^{\left(t\right)}(i,k)=(1-\mathrm{\λ})*\{0,R(k,k)+\underset{j\∉\{i,k\}}{\mathrm{\Σ}}\max \{0,R(j,k)\left\}\right\}\}+\mathrm{\λ}*A^{(t-1)}(i,k)$

$A^{\left(t\right)}(k,k)=(1-\mathrm{\λ})*\left\{\underset{j\≠k}{\mathrm{\Σ}}\max \right\{0,R(j,k)\left\}\right\}+\mathrm{\λ}*A^{(t-1)}(k,k)$

The result selects representative point according to iteration, and less than threshold value, promptly D=D-SD turns back to step 2 as the number D of representative point;

The representative point label of at every turn selecting joins in the same matrix, obtains final point set FD up to reaching desired value.

In described step 2, at first calculating maximum coordinate figure in each dimension of a space, cloud place, constitute the external bounding box in space, then in bounding box between division of cells, represent for each minizone coding with Hash table, to guarantee that each point can index the minizone at its place, getting central point as this sampled point in the minizone more uniformly then.

Present embodiment adopts short-cut method set forth above that experimental result is analyzed, and can prove its validity.The rabbit model of cloud data and imperial model derive from Stanford University Practice in Computer Graphics chamber.Hardware is PC, in save as 2GB, adopt matlab programming experiment.Mainly to method for resampling, the mixing AP method that k mean cluster method and this paper propose is carried out result's contrast.In Fig. 3～Fig. 6, (a) for the application proposes method, (b) be k mean cluster method, (c) be method for resampling.

Can observe imperial model and rabbit model detail from experimental result picture keeps this paper method better.Analyze from experimental result data, D is the initial point cloud, and FD is final back point cloud, the left point RD=D-FD of simplifying.Some pi among the FD seeks a closest approach pui in FD, pi is a summit in the triangular facet on the face after the simplification, the shared summit in normally several triangular facets.Calculation level pui is to several the bee-line di that with pi is the summit.All di can indicate the error of selecting behind the formation face of representing point set and initial point cloud with sum.Sum is more little, illustrates that face and the initial surface of simplifying result's formation are approaching more.

Analysis result such as table 1 and table 2. as can be seen from the table, the simplification resultant error minimum of this paper method,

Table 1

Table 2.

Claims (2)

1, a kind of point cloud simplifying treatment method based on method for resampling and affine clustering algorithm, it is characterized in that: described point cloud simplifying treatment method may further comprise the steps:

Step 1: set the threshold value of simplifying the impact point number;

Step 2: initial point cloud D uniform sampling is obtained its sub-point set SD, to each the point search k arest neighbors near point among the subclass SD, i.e. the k of data point q nearest point:

KNN (q)=| p _i-q |≤| p-q|, p _i∈ D}, p _i(i=1 2...k) is the neighbor point of a q;

Step 3: the k arest neighbors near point that utilizes step 2 to obtain calculates the curvature CV of each point among the SD, and the i that sets up an office has k neighbor point p _Ik(k=1,2...k), the coordinate mean value of k+1 point is ap _i, the covariance matrix of some i is C; Mutual relationship is expressed as follows:

ap _i＝(p _i1+p _i2+...p _ik)/(k+1)

$C={\left[\begin{array}{c}{p}_{i1}-{\mathrm{ap}}_i\\ p_{i2}-{\mathrm{ap}}_i\\ ..............\\ p_{\mathrm{ik}}-{\mathrm{ap}}_i\end{array}\right]}^T\left[\begin{array}{c}{p}_{i1}-{\mathrm{ap}}_i\\ p_{i2}-{\mathrm{ap}}_i\\ ..............\\ p_{\mathrm{ik}}-{\mathrm{ap}}_i\end{array}\right]$

C*＝λ*V

Wherein, C is the positive semidefinite matrix of a symmetry, and eigenwert is real-valued, and V is the proper vector of covariance matrix, λ ₁, λ ₂, λ ₃It is the eigenwert of the character pair vector of C; Get λ _iBe minimal eigenvalue, represent the curved transition value of an i: cv with eigenwert _i=λ ₁/ (λ ₁+ λ ₂+ λ ₃);

Step 4: calculate similarity between points among the SD, obtain similarity matrix S, specifically have: the similarity of some i and some k be labeled as S (i, k), similarity can reflect the close relationship of point-to-point transmission, the similarity value is chosen the negative value of distance between two points square, as

S(i，k)＝-(||x _i-x _k|| ²+||y _i-y _k|| ²+||z _i-z _k|| ²) (1)

(x _i, y _i, z _i) be the D coordinates value of data point i;

Step 5: utilization AP clustering algorithm, S and CV are as the input of AP algorithm, and representative degree matrix between calculation level and suitable degree of choosing matrix specifically have:

For the arbitrfary point, calculate representative degree and grade of fit sum R+A:

R(i，k)+A(i，k)＝S(i，k)+A(i，k)-{A(i，j)+S(i，j)}.

The value representation point of R+A is as the validity of class representative point and can characterize a little selected probability;

A (k, k) and R (k, growth k) and deflection parameter P be S (k, k) relevant; Introduced a decay factor λ and carried out iteration, add this parameter after, R, S, relationship change is as follows between three matrixes of A:

$R^{\left(t\right)}(i,k)=(1-\mathrm{\λ})*\{S(i,k)-\max \{A(i,j)+S(i,j)\left\}\right\}+\mathrm{\λ}*R^{(t-1)}(i,k)$

$A^{\left(t\right)}(i,k)=(1-\mathrm{\λ})*\{0,R(k,k)+\underset{j\∉\{i,k\}}{\overset{j\≠k}{\mathrm{\Σ}}}\max \{0,R(j,k)\left\}\right\}\}+\mathrm{\λ}*A^{(t-1)}(i,k)$

$A^{\left(t\right)}(k,k)=(1-\mathrm{\λ})*\left\{\underset{j\≠k}{\mathrm{\Σ}}\max \right\{0,R(j,k)\left\}\right\}+\mathrm{\λ}*A^{(t-1)}(k,k)$

The result selects representative point according to iteration, and less than threshold value, promptly D=D-SD turns back to step 2 as the number D of representative point;

The representative point label of at every turn selecting joins in the same matrix, obtains final point set FD up to reaching desired value.

2, the point cloud simplifying treatment method based on method for resampling and affine clustering algorithm as claimed in claim 1, it is characterized in that: in described step 2, at first calculating maximum coordinate figure in each dimension of a space, cloud place, constitute the external bounding box in space, then in bounding box between division of cells, represent for each minizone coding with Hash table, can index the minizone at its place, getting central point as this sampled point in the minizone more uniformly then to guarantee each point.

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