CN106780509A - Merge the building object point cloud layer time cluster segmentation method of multidimensional characteristic - Google Patents

Abstract

The invention discloses a kind of building object point cloud layer for merging multidimensional characteristic time cluster segmentation method, initial segmentation is carried out to mutual discontinuous cloud data in building cloud data first, then G K clustering algorithms are utilized, ground floor subdivision is carried out to it with reference to the spectral signature of cloud data, the normal direction measure feature and curvature feature for obtaining cloud data carry out second layer subdivision, are repeated twice segmentation and are required until meeting.Present invention building object point cloud layer time cluster segmentation method takes full advantage of the density information of Point Cloud Data from Three Dimension Laser Scanning, can be on the premise of no priori, multiple cloud data block apart from each other and than comparatively dense is carried out into initial segmentation, simultaneously, with reference to the spectral signature and geometric properties of cloud data, to being finely divided through the cloud data block after initial segmentation, until each cloud data block has single geometric properties, untill being modeled using simple Mathematical Modeling, the method can not only extract building cloud data from the environment of surrounding, and building object point cloud can be resolved into different planes, for the reconstruction of building is had laid a good foundation.

Description

Merge the building object point cloud layer time cluster segmentation method of multidimensional characteristic

Technical field

The present invention relates to a kind of cloud data partitioning algorithm, and in particular to one kind building object point cloud layer time cluster segmentation side Method.

Background technology

Technology is swept using three-dimensional laser and measurement is scanned to building, can obtain building and retouch cloud data, in order to Building body characteristicses, i.e. building or its composition structure, the shape at position, position, size, length are extracted based on cloud data The description of the key geometric sense such as degree, area, volume, it is necessary to carry out the weight of BUILDINGS MODELS to it using building three dimensional point cloud Build process.Whether correctly the correctness that model is set up directly influences the measurement of building body characteristicses, therefore reasonable utilization is swept It is extremely important that the cloud data retouched sets up building point cloud model.But building point cloud model is often special containing multiple surface geometries (such as plane, the face of cylinder, circular conical surface, sphere, free form surface) is levied, if directly carrying out model weight to it using cloud data Structure, then can cause the difficulty of mathematical notation and the fitting algorithm treatment of surface model to increase, or even cannot use suitable mathematical table The surface model of this complexity is described up to formula.In order to meet the requirement of Surface Reconstruction, it is necessary to be carried out to three dimensional point cloud Region segmentation, purpose seeks to the region with similar geometry characteristic in three dimensional point cloud to be split, combines, with after an action of the bowels Continuous three dimensional point cloud Surface Reconstruction.Therefore, for the architectural characteristic of building cloud data, research is adapted to building The method of cloud data segmentation is significant.

At present, cloud data partitioning algorithm mainly includes that the partitioning algorithm based on border, the segmentation based on region growing are calculated Method, cluster segmentation algorithm etc..But existing various partitioning algorithms, the generally a certain feature using cloud data or comprehensive utilization Multiple features of cloud data, it is intended to which cloud data is disposably separated, this comes for complicated building cloud data The situation for easily causing segmentation deficiency or over-segmentation is said, the correct segmentation of complex building cloud data is difficult to realize.

The content of the invention

Goal of the invention：The purpose of the present invention is to solve the shortcomings of the prior art, there is provided it is a kind of according to cloud data Spectral signature and geometric properties carry out the building object point cloud layer time cluster segmentation method of the fusion multidimensional characteristic of accurate segmentation.

Technical scheme：The invention provides a kind of building object point cloud layer for merging multidimensional characteristic time cluster segmentation method, bag Include following steps：

(1) cloud initial segmentation is put：Using DBSCAN (Density-Based Spatial Clustering of Applications with Noise) density partitioning algorithm enters to mutual discontinuous cloud data in building cloud data Row initial segmentation, the cloud data block being separated from each other；This be in order to apart from each other while again than the point cloud number of comparatively dense According to being clustered, the cloud data of initial segmentation has thus been obtained；

(2) spectral signature segmentation：By the continuous cloud data after initial segmentation, its spectral signature often shows difference Property, such as fabric structure is different with the color of the environment such as trees, meadow of surrounding, reflected intensity, the same beam of building masonry wall, post Color, the reflected intensity of son etc. be not also equal.Using G-K (Gustafson-Kessel) clustering algorithm, with reference to cloud data Spectral signature is further split to it, and building is finely divided between surrounding environment or building different structure, obtains To the cloud data based on the subdivision of spectral signature multilayer：

(3) geometric properties segmentation：Its normal direction measure feature and curvature feature are calculated according to cloud data, and using G-K clusters Algorithm, to splitting through spectral signature after cloud data carry out further geometric properties subdivision；

(4) data inspection：To carrying out geometry inspection by the cloud data after subdivision, the cloud data energy after segmentation is judged It is no to meet the requirement being modeled using simple Mathematical Modeling, if meet requiring, preserve the cloud data after segmentation；It is no Then, (2nd) and (3) step are repeated, continuation segmentation is carried out to cloud data.

Further, step (2) described spectral signature is extracted using scanner color characteristic and reflected intensity feature.

Further, the extraction of cloud data color characteristic is that the colorful CCD camera carried using scanner shoots tested The panorama photochrome of object, and the colouring information of testee is obtained, with reference to textures technology, by acquired testee Color, texture are added in surveyed cloud data, obtain the three-dimensional RGB information of measured object.

Further, the color space of the panorama photochrome for being obtained due to scanning is RGB, is to use for RGB color pattern Three kinds of primary colours of red, green, blue represent shades of colour, but RGB color can not be combined with color space perceptually well Get up, therefore need the conversion of RGB to HSV herein：

V=max

Wherein, (R, G, B) is respectively a red, green and blue coordinate for color, and their value is the real number between 0 to 1； Max is the maximum in R, G and B, and min is the minimum value in R, G and B value；(H, S, V) represents the tone of color, saturation respectively Degree, lightness.

In general, laser reflection energy is referred to as laser reflection intensity with the ratio of Laser emission energy.Work as laser When being transmitted into measured target surface with certain wavelength, can be because the degree of roughness on measured target surface be scattered, by a part Laser light scattering to other directions without being reflected back toward laser, while also can be because of the characteristic on measured target surface (physically or chemically Characteristic) absorb the factors such as laser energy and cause the laser energy being reflected back in laser to be less than the energy of Laser emission.Cause This, it is possible to use the equipment that scanner is carried obtains the data reflected intensity feature of point cloud.

Further, G-K clustering algorithms are comprised the following steps：

If being clustered cloud data collection is combined into X={ x₁,x₂,…,x_n, each of which data x_kThere is d feature to refer to Mark, thus its Characteristic index matrix is：

Data set X is divided into c classes (2≤c≤n), if c cluster centre vector is：

If μ_jk∈ [0,1] represents degree of membership of k-th data for jth class, and meetsThen Fuzzy partition matrix is：

G-K algorithms clustering criteria obtains minimum value to make following object function：

Wherein：m_jRepresent cluster centre, b>1 is Weighted Index, and the overlap between the more big each clusters of b is more；Similarity degree Flow function is

The distance of k-th data and the cluster centre of jth class is represented, it determines the shape of cluster；Wherein A_jIt is one Individual positive definite matrix, by the cluster covariance matrix F for approximately reflecting each cluster true form_jDetermine, work as A_jDuring for unit matrix, degree Flow function uses Euclidean distance；Wherein

ρ_jIt is a constant for each cluster, in the case where priori is lacked, takes ρ_j=1 causes each cluster Capacity it is roughly the same；

Object function J_f(U, M) is minimized can be expressed as about fasciculation problem：

Solved with lagrange Multiplier Methods：

And work asWhen, u_jk=1, u_lk=0 (l ≠ j)

Iterated to calculate more than, determine corresponding to cloud data cluster number and the cluster of each class cloud data in The heart.

Further, step (3) carries out the calculating of normal vector using the tangent plane of cloud data, first by partial points cloud number According to one tangent plane of fitting, arbitrfary point p_iNormal vector determined by the normal vector estimation of the plane：

Plane fitting：According to cloud data p_i(i=0,1 ..., n) in the quadratic sum for arriving the plan range a little most It is small, determine plane P (u_i,v_i)：

Wherein, n represents the number at cloud data midpoint；

The general type of the plane expression formula is:

Ax+by+cz+d=0

Least square plane fitting object function be：

Ax=0

Wherein：

Using Jacobi method calculating matrix A^TThe eigenvalue λ of A_iWith corresponding characteristic vector x_i(i=1 ..., 4), then definitely It is worth minimum eigenvalue λ_iCorresponding characteristic vector x_iIt is plane parameter a to be asked, the least square solution of b, c, d；

2. plane normal vector determines：According to the general expression of plane equation, plane normal vector is represented by To avoid the problem of plane parameter a, b, c, d dependent, unitization treatment is carried out to required plane normal vector, such as following formula institute Show：

The per unit system arrow of arbitrfary point in cloud data at local surface is：Realize cloud data The estimation of normal vector.

Further, in the curvature characteristic root strong point cloud of step (3) cloud data each point average curvature and Gaussian curvature meter Calculating needs to carry out quadric fitting to the vertex neighborhood, after determining the principal curvatures and its principal direction of curved surface S, it is possible to calculate The curvature characteristic of the data point；

A, Quadratic Surface Fitting：By cloud data p_i(i=1,2 ... k) carry out Quadratic Surface Fitting in local neighborhood, intend Close equation general type be：

S (u, v)=au²+buv+cv²+du+ev

The object function of fitting is：

In formula, u and v is Surface Parameters, and the least square solution of fitting surface can be obtained using singular value decomposition method；

B, Curvature Estimate：According to calculate quadratic surface S parametric equation, using the principal curvatures and principal direction of surface points as Point p_iPrincipal curvatures and principal direction, its parameter is calculated as follows：

S_u|_(0,0)=(1,0,2au+bv+d) |_(0,0)=(1,0, d) and S_uu|=(0,0,2a)

S_v|_(0,0)=(0,1, bu+2cv+e) |_(0,0)=(0,1, e) and S_vv|_(0,0)=(0,0,2c)

S_uv|_(0,0)=(0,0, b)

Wherein, S_uIt is curved surface S to the first derivative of parameter u, S_uuIt is second dervative；S_vFor curved surface S leads to the single order of parameter v Number, S_vvIt is second dervative；S_uvIt is curved surface S to parameter u, the second dervative of v；N is sweared for the per unit system of curved surface；

According to above parameter, can calculate：

E=S_u·S_u=1+d²And F=S_u·S_v=de

G=S_v·S_v=1+e²And

And

Wherein, E, F, G are the first fundamental quantity of curved surface, and L, M, N are the second fundamental quantity of curved surface；

Then the Gaussian curvature and average curvature values at P points are：

Minimum principal curvatures θ_minWith maximum principal curvatures θ_maxComputing formula is respectively：

Beneficial effect：Present invention building object point cloud layer time cluster segmentation method takes full advantage of 3 D laser scanning point cloud number According to density information, can be on the premise of no priori, by multiple cloud data blocks apart from each other and than comparatively dense Initial segmentation is carried out, meanwhile, with reference to the spectral signature and geometric properties of cloud data, to through the cloud data block after initial segmentation It is finely divided, until each cloud data block has single geometric properties, can be built using simple Mathematical Modeling Untill mould, the method can not only extract building cloud data from the environment of surrounding, and can be by building object point cloud point Solution, into different planes, is that the reconstruction of building is had laid a good foundation.

Brief description of the drawings

Fig. 1 is the original scan cloud data of building；

Fig. 2 is present invention building object point cloud layer time cluster segmentation flow chart；

Fig. 3 is the cloud data of initial segmentation；

Fig. 4 is segmented for the second layer of cloud data block；

Fig. 5 is segmented for the third layer of cloud data block；

Fig. 6 is split for the geometric properties of data block I；

Fig. 7 is split for the geometric properties of data set II-3- (4)；

Fig. 8 is split for the geometric properties of data set II-3- (3).

Specific embodiment

Technical solution of the present invention is described in detail below, but protection scope of the present invention is not limited to the implementation Example.

Embodiment：The present embodiment uses FARO companies of U.S. FOCUS^3DThree-dimensional laser scanner is to building and its surrounding ring Border is scanned measurement, and the cloud data of acquisition is as shown in Figure 1.First, by building original image understand the building and its Surrounding environment is divided into 1. top of building, 2. building masonry wall, 3. upstairs ground, 4. passageway barricade, 5. stair, 6. from top to bottom Seven parts constitute altogether for trees, 7. building outside ground etc., if to be modeled to building, by the same surrounding of building Environment separate, then building Each part is finely divided, can just access the cloud data of Direct Modeling.Cause This, is split using the building object point cloud layer time cluster segmentation method for merging multidimensional characteristic to the cloud data, including following Step, as shown in Figure 2：

1st, initial segmentation

Any one neighborhood of a point K is 20 for 1.97, in space to set the radius Eps in DBSCAN density partitioning algorithms, with The locus of cloud data is split as input object to original point cloud data, from as shown in Figure 3, the algorithm Will be apart from each other in original point cloud data while the cloud data such as roof, trees again than comparatively dense is separated, used Cloud data block I that green (top of building), red (building body and trees) and blueness (isolated trees) are represented respectively, II, III, due to that cannot be represented with color in figure, therefore are pointed out with arrow.

2nd, the segmentation based on spectral signature

By after initial segmentation, trees, the ground of the main part of building still with periphery etc. mixes, and builds The structure and its surrounding enviroment of thing are increasingly complex, therefore, segmentation can not use geometric properties.But between building and surrounding environment Have between spectral signature than larger difference.

(1) ground floor subdivision

Color characteristic (R, G, B) is assigned to cloud data first, and color mode is converted into by (R, G, B) (H, S, V), characteristic vector (X, Y, Z, H) is collectively constituted by H in locus feature (X, Y, Z) and color characteristic, using G-K cluster sides Method is further segmented to cloud data block II：

1. it is that 7, Weighted Index b is that 2, stopping criterion for iteration ε is 10 to set initialization clusters number c^-6, initial fuzzy division Matrix U is 210242 rows and 7 column matrix；

2. initial new cluster centre M is calculated₀It is the column matrix of 7 row 4：

3. initially fuzzy covariance matrix F and positive definite matrix A is calculated；

4. according to measuring similarity functionFuzzy partition matrix U is updated；

5. calculated through 202 loop iterations, condition ‖ U (I+1)-U (I) ‖ ＜ 1 × 10^-6Set up, calculate final cluster Center M is：

And each puts affiliated cluster number in obtaining cloud data.

As shown in figure 4, cluster identical each point in cloud data is classified as into a class, cloud data block II is divided into 7 parts, but only II-1 and II-2 are relatively complete, i.e., and outside ground and trees can intactly separate from data II；Its There is not enough and over-segmentation the situation of segmentation in remaining part point cloud data, will split incomplete cloud data and be classified as cloud data block II-3, in addition it is also necessary to further subdivision.

(2) second layer subdivision

The spectral signature of building main body point cloud II-3 is calculated also according to the above method, thus spectral signature and space are special Composition characteristic phasor (X, Y, Z, H) is levied, building main body point cloud II-3 is finely divided using G-K clustering algorithms.

As shown in figure 5, building main body has been divided into 6 parts：II-3- (1) is facade wall, II-3- (2) Upstairs ground, II-3- (3) is stair, and II-3- (4) is upstairs passageway wall, and II-3- (5) is building east side wall, II-3- (6) it is building west side wall.Wherein facade wall and upstairs ground has single geometric properties.

(3) segmented based on geometric properties point cloud

By after initial segmentation and spectral signature segmentation, cloud data block is for example：I (building roof), II-3- (3) (building Ladder), and II-3- (4) (passageway wall), still without single geometric properties.Accordingly, it would be desirable to enter to advance using geometric properties The subdivision of one step：

1. building roof

By after initial segmentation, the normal direction of building roof cloud data block I is calculated according to the method in claim Amount and curvatureBy the space characteristics and geometric properties composition characteristic phasor of cloud data block IWith reference to G-K clustering algorithms, are finely divided to cloud data block I.

As shown in fig. 6, building roof divide into four parts：I-1, I-2, I-3 and I-4, wherein, cloud data block I- 1st, I-2 and I-3 are the planes with single geometric properties, their normal vector be respectively (0.212, -0.313,0.926), (- 0.226,0.314,0.922) and (0.324,0.226,0.919).

2. passageway wall segmentation upstairs

By after second layer subdivision, calculating the normal vector and curvature in passageway barricade cloud data block II-3- (4) By the space characteristics and geometric properties composition characteristic phasor of cloud data block II-3- (4)With reference to G-K clusters Algorithm, is finely divided to cloud data block II-3- (4).

As shown in fig. 7, passageway wall II-3- (4) has been divided into three planes with single geometric properties：II-3- (4)-[1], II-3- (4)-[2] and II-3- (4)-[3].Their normal vector is respectively：(0.573, -0.819,0.018), (- 0.819, -0.573,0.025) and (- 0.572,0.819,0.040).

3. stair segmentation

By after second layer subdivision, calculating the normal vector and curvature of building stair cloud data block II-3- (3)By the space characteristics and geometric properties composition characteristic phasor of cloud data block II-3- (3)With reference to G-K clustering algorithms, are finely divided to cloud data block II-3- (3).

As shown in figure 8 above, stair are divided into four parts：II-3- (3)-[1] stair right side wall, II-3- (3)-[2] Stair left side wall, II-3- (3)-[3] stair perpendicular set, II-3- (3)-[4] stair horizontal plane set.Their method Vector be respectively (- 0.572,0.820, -0.003), (0.572, -0.821,0.002), (- 0.002, -0.002,1.000) and (0.820,0.572, -0.007).

Analyzed more than, the building object point cloud layer based on multidimensional characteristic proposed by the present invention time cluster segmentation method, Not only building can be extracted from complicated surrounding environment, detailed segmentation can also be carried out to building cloud data.Finally The building each several part cloud data with single geometric properties is obtained, is that the reconstruction and feature extraction of building lay good Basis.

Claims (7)

1. a kind of building object point cloud layer time cluster segmentation method for merging multidimensional characteristic, it is characterised in that：Comprise the following steps：

(1) cloud initial segmentation is put：Using DBSCAN density partitioning algorithm to mutual discrete point cloud in building cloud data Data carry out initial segmentation, the cloud data block being separated from each other；

(2) spectral signature segmentation：Using G-K clustering algorithms, it is further split with reference to the spectral signature of cloud data, Building is finely divided between surrounding environment or building different structure, the point cloud based on the subdivision of spectral signature multilayer is obtained Data：

(3) geometric properties segmentation：Its normal direction measure feature and curvature feature are calculated according to cloud data, and utilize G-K clustering algorithms, Cloud data after to splitting through spectral signature carries out further geometric properties subdivision；

(4) data inspection：To carrying out geometry inspection by the cloud data after subdivision, judge that can the cloud data after segmentation expire The requirement that foot is modeled using simple Mathematical Modeling, if meet requiring, preserves the cloud data after segmentation；Otherwise, weight Multiple (2nd) and (3) step, continuation segmentation is carried out to cloud data.

2. the building object point cloud layer time cluster segmentation method of fusion multidimensional characteristic according to claim 1, it is characterised in that： Color characteristic and reflected intensity feature that step (2) described spectral signature is extracted using scanner.

3. the building object point cloud layer time cluster segmentation method of fusion multidimensional characteristic according to claim 2, it is characterised in that： The extraction of cloud data color characteristic is the colored photograph of panorama that the colorful CCD camera carried using scanner shoots testee Piece, and the colouring information of testee is obtained, with reference to textures technology, the color of acquired testee, texture are added to In surveyed cloud data, the three-dimensional RGB information of measured object is obtained.

4. the building object point cloud layer time cluster segmentation method of fusion multidimensional characteristic according to claim 3, it is characterised in that： The color mode of the panorama photochrome that scanner is obtained is HSV patterns by RGB patten transformations：

$S=\left\{\begin{array}{cc}0,& ifmax=0\\ \frac{max-min}{max}=1-\frac{min}{max},& otherwise\end{array}\right.$

V=max

Wherein, (R, G, B) is respectively a red, green and blue coordinate for color, and their value is the real number between 0 to 1；max It is the maximum in R, G and B, min is the minimum value in R, G and B value；(H, S, V) represent respectively the tone of color, saturation degree, Lightness.

5. the building object point cloud layer time cluster segmentation method of fusion multidimensional characteristic according to claim 1, it is characterised in that： G-K clustering algorithms are comprised the following steps：

If being clustered cloud data collection is combined into X={ x₁,x₂,…,x_n, each of which data x_kThere is d characteristic index, thus Its Characteristic index matrix is：

Data set X is divided into c classes (2≤c≤n), if c cluster centre vector is：

If μ_jk∈ [0,1] represents degree of membership of k-th data for jth class, and meetsThen obscure Matrix dividing is：

G-K algorithms clustering criteria obtains minimum value to make following object function：

$J_f(U,M)=\underset{j=1}{\overset{c}{\Σ}}\underset{k=1}{\overset{n}{\Σ}}{\mathrm{\μ}}_{jk}^b\left|\right|x_k-m_j|{|}_A^2$

Wherein：m_jRepresent cluster centre, b>1 is Weighted Index, and the overlap between the more big each clusters of b is more；Measuring similarity function For

$D_{jk}^2=\left|\right|x_k-m_j|{|}_A^2={(x_k-m_j)}^T{A}_j(x_k-m_j)$

The distance of k-th data and the cluster centre of jth class is represented, it determines the shape of cluster；Wherein A_jFor one just Set matrix, by the cluster covariance matrix F for approximately reflecting each cluster true form_jDetermine, work as A_jDuring for unit matrix, letter is measured Number uses Euclidean distance；Wherein

$F_j=\frac{\underset{k=1}{\overset{n}{\Σ}}{\mathrm{\μ}}_{jk}^b(x_k-m_j){(x_k-m_j)}^T}{\underset{k=1}{\overset{n}{\Σ}}{\mathrm{\μ}}_{jk}^b}$

$A_j=\det {\left({\mathrm{\ρ}}_j{F}_j\right)}^{\frac{1}{n}}{F}_j^{-1},{\mathrm{\ρ}}_j>0$

ρ_jIt is a constant for each cluster, in the case where priori is lacked, takes ρ_j=1 appearance for causing each cluster Amount is roughly the same；

Object function J_f(U, M) is minimized can be expressed as about fasciculation problem：

$\min \underset{j=1}{\overset{c}{\Σ}}\underset{k=1}{\overset{n}{\Σ}}{u}_{jk}^b\left|\right|x_k-m_j|{|}^2$

$\begin{array}{cc}s.t.& \underset{j=1}{\overset{c}{\Σ}}{u}_{jk}=1,k=1,2,...,n\end{array}$

Solved with lagrange Multiplier Methods：

$u_{jk}=\frac{1}{\underset{l=1}{\overset{c}{\Σ}}{(D_{jk}/D_{lk})}^{2/(b-1)}}$

And work asWhen, u_jk=1, u_lk=0 (l ≠ j)

$m_j=\frac{\underset{k=1}{\overset{n}{\mathrm{\Σ}}}{u}_{jk}^b{x}_k}{\underset{k=1}{\overset{n}{\mathrm{\Σ}}}{u}_{jk}^b},j=1,2,\mathrm{...},c$

Iterated to calculate more than, determine the cluster centre of the cluster number and each class cloud data corresponding to cloud data.

6. the building object point cloud layer time cluster segmentation method of fusion multidimensional characteristic according to claim 1, it is characterised in that： Step (3) carries out the calculating of normal vector using the tangent plane of cloud data, is cut by local Points cloud Fitting one is micro- first Plane, arbitrfary point p_iNormal vector determined by the normal vector estimation of the plane：

1. plane fitting：According to making cloud data p_i(i=0,1 ..., n) in the quadratic sum for arriving the plan range a little most It is small, determine plane P (u_i,v_i)：

$\underset{i=0}{\overset{n}{\mathrm{\Σ}}}\left|\right|P\left(u_i,v_i\right)-p_i|{|}^2\→\min$

Wherein, n represents the number at cloud data midpoint；

The general type of the plane expression formula is:

Ax+by+cz+d=0

Least square plane fitting object function be：

Ax=0

Wherein：

$A=\left[\begin{array}{cccc}{x}_1& y_1& z_1& 1\\ x_2& y_2& z_2& 1\\ \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}\\ x_n& y_n& z_n& 1\end{array}\right],x={(a,b,c,d)}^T$

Using Jacobi method calculating matrix A^TThe eigenvalue λ of A_iWith corresponding characteristic vector x_i(i=1 ..., 4), then absolute value is most Small eigenvalue λ_iCorresponding characteristic vector x_iIt is plane parameter a to be asked, the least square solution of b, c, d；

2. plane normal vector determines：According to the general expression of plane equation, plane normal vector is represented byTo keep away Exempt from the problem of plane parameter a, b, c, d dependent, unitization treatment is carried out to required plane normal vector, be shown below：

$\left\{\begin{array}{c}{a}^{\′}=\frac{a}{\sqrt{a^2+b^2+c^2}}\\ b^{\′}=\frac{b}{\sqrt{a^2+b^2+c^2}}\\ c^{\′}=\frac{c}{\sqrt{a^2+b^2+c^2}}\\ d^{\′}=\frac{d}{\sqrt{a^2+b^2+c^2}}\end{array}\right.$

The per unit system arrow of arbitrfary point in cloud data at local surface is：Realize cloud data normal direction The estimation of amount.

7. the building object point cloud layer time cluster segmentation method of fusion multidimensional characteristic according to claim 1, it is characterised in that： The average curvature of each point and Gaussian curvature are calculated and needed to the vertex neighborhood in the curvature characteristic root strong point cloud of step (3) cloud data Quadric fitting is carried out, after determining the principal curvatures and its principal direction of curved surface S, it is possible to which the curvature for calculating the data point is special Property；

A, Quadratic Surface Fitting：By cloud data p_i(i=1,2 ... k) carry out Quadratic Surface Fitting, fitting side in local neighborhood The general type of journey is：

S (u, v)=au²+buv+cv²+du+ev

The object function of fitting is：

$min\underset{i=1}{\overset{k}{\mathrm{\Σ}}}{\[p_i-({\mathrm{au}}_i^2+{\mathrm{bu}}_i{v}_i+{\mathrm{cv}}_i^2+{\mathrm{du}}_i+{\mathrm{ev}}_i)\]}^2$

In formula, u and v is Surface Parameters, and the least square solution of fitting surface can be obtained using singular value decomposition method；

B, Curvature Estimate：According to the parametric equation of the quadratic surface S for calculating, using the principal curvatures and principal direction of surface points as point p_i Principal curvatures and principal direction, its parameter is calculated as follows：

S_u|_(0,0)=(1,0,2au+bv+d) |_(0,0)=(1,0, d) and S_uu|=(0,0,2a)

S_v|_(0,0)=(0,1, bu+2cv+e) |_(0,0)=(0,1, e) and S_vv|_(0,0)=(0,0,2c)

S_uv|_(0,0)=(0,0, b)

$n{|}_{(0,0)}=\frac{S_u\×S_v}{|S_u\×S_v|}{|}_{(0,0)}=(\frac{-d}{\sqrt{d^2+e^2+1}},\frac{-e}{\sqrt{d^2+e^2+1}},\frac{1}{\sqrt{d^2+e^2+1}})$

Wherein, S_uIt is curved surface S to the first derivative of parameter u, S_uuIt is second dervative；S_vIt is curved surface S to the first derivative of parameter v, S_vvIt is second dervative；S_uvIt is curved surface S to parameter u, the second dervative of v；N is sweared for the per unit system of curved surface；

According to above parameter, can calculate：

E=S_u·S_u=1+d²And F=S_u·S_v=de

G=S_v·S_v=1+e²And

And

Wherein, E, F, G are the first fundamental quantity of curved surface, and L, M, N are the second fundamental quantity of curved surface；

Then the Gaussian curvature and average curvature values at P points are：

$K=\frac{LN-M^2}{EG-F^2}$

$H=\frac{EN-2FM+GL}{2(EG-F^2)}$

Minimum principal curvatures θ_minWith maximum principal curvatures θ_maxComputing formula is respectively：

${\mathrm{\θ}}_{min}=H-\sqrt{H^2-K}$

${\mathrm{\θ}}_{max}=H+\sqrt{H^2-K}.$