CN103530899A - Geometric featuer-based point cloud simplification method - Google Patents

Abstract

The invention provides a geometric feature-based point cloud simplification method. The steps are as follows: by constructing the moving least square of the nearest neighbor point set of 3D (three-dimensional) sample points, the normal of the sample points is calculated, and moreover, by analyzing the neighbor point set according to covariances, the curvature of the sample points is estimated; by analyzing the normal voted tensor of the sample points, the feature edge intensity of the sample points is calculated, and accordingly, point cloud data are decomposed into a strange-edge part and a non-strong-edge part; by utilizing MeanShift clustering, surface area geometric feature similarity clustering is carried out on the non-strong-edge part; according to a curvature threshold and a search radius, the strange-edge part and each cluster are resampled, and thereby curvature-adaptive simplification is completed. According to the curvature threshold and the search radius, the method carries out curvature-adaptive simplification guaranteeing flat area-sampling density on point cloud data. Therefore, the method can be adopted to carry out high-quality simplification keeping feature boundaries and curved surface details on point cloud data.

Description

Point cloud simplification method based on geometric properties

Technical field

The present invention relates to computer graphics, computer vision and reverse-engineering field, particularly a kind of point cloud simplification method based on geometric properties.

Background technology

The fast development that technology is obtained in 3D scanning, makes 3D cloud data model become the voice data continue one dimension, the view data of two dimension and a kind of emerging Digital Media after video data.In the fields such as reverse-engineering, industrial products innovative design, digital entertainment, video display animation, physical simulation, historical relic's protection and reparation, cloud data model has a wide range of applications, and has produced more and more far-reaching influence.Because 3D scanning device precision greatly improves, when the cloud data that scanning is obtained has very high degree of precision, also contain a large amount of redundancies.The cloud data of redundancy should be simplified, to effectively carry out the follow-up works for the treatment of such as point set curved surface modeling, drafting and moulding.

The simplification of cloud data at present is mainly divided into based on two class methods grid and based on point, the operation that wherein triangle gridding has been saved in the simplification based on point, and simplification process is more simple, and time complexity is also lower.Alexa equals calendar year 2001 and has proposed first the cloud data short-cut method based on point, adopts the proper subclass that vertex deletion method is former point set by model simplification.Pauly etc. have proposed a kind of short-cut method of resampling based on Fourier theory, this method depends on the layout of cloud data piecemeal (dividing).Pauly is applied to several clustering methods relevant with grid on cloud data with Kobbelt, realizes its simplification; The cluster of Kalaiah based on sampled point hierarchical structure simplified cloud data; The importance based on sampled point such as Yu is carried out Local Clustering to cloud data and is carried out its simplification.These shortcut calculations based on point are not the similaritys according to cloud data surf zone geometric properties when cluster or division, but according to the spatial relationship of sampled point, have ignored the anisotropic inherent geometric properties of surf zone; So cluster must cause similar surf zone to be divided in different class bunch, thereby has affected simplification process and the point set error that makes to simplify strengthens.These algorithms, in the process of simplifying, are not distinguished the characteristic edge of sampled point, so can not guarantee that simplified model retains enough sampling densities in characteristic edge yet.

Summary of the invention

The present invention has overcome existing deficiency in above-mentioned prior art, and a kind of point cloud simplification method that can keep characteristic boundary and curved surface details high-quality to simplify to cloud data is provided.

Technical scheme of the present invention is achieved in that

A point cloud simplification method for geometric properties, comprises the steps: (1) structure sampled point p _ithe moving least squares surfaces of nearest-neighbor point set, thus computing method to; (2) covariance analysis neighborhood point set, estimating sampling point p _icurvature; (3) analytical sampling point p _inormal direction ballot tensor, calculated characteristics limit property, and to decompose accordingly cloud data be strong characteristic edge part and non-strong characteristic edge part; (4) utilize Mean Shift algorithm cluster, dividing non-strong characteristic edge is partly class bunch collection; (5) resample strong characteristic edge part and all kinds of bunches.

For realizing goal of the invention, in step (1), sampled point p _inormal direction be to calculate by constructing the moving least squares surfaces of its nearest-neighbor point set, specifically:

(a) utilize kD tree fast search sampled point p _ik nearest-neighbor N _k(p _i), according to the scale n of cloud data, get k ∈ [9,30];

Given point set P, its moving least squares surfaces (Moving least squares, MLS) is implicitly defined as the static state set of a projection operator ψ (p, x), and this projection operator is by r ∈ R ³project to MLS curved surface S={x ∈ R ³| on ψ (p, x)=x}.The calculating of its projection operator:

(b) by nonlinear optimization, the local reference planes of matching point set.Matching point set P, finds the local reference planes H={x ∈ R that makes formula (1) nonlinear energy function minimum ³| nx-D=0}:

$\arg \underset{n,q}{\min }\underset{p_i\∈P}{\mathrm{\Σ}}{(n\·p_i-n\·q)}^2\mathrm{\θ}\left(\right||p_i-q|\left|\right)$ Formula (1) wherein q is the projection of r on plane H; Kernel function is got θ (d)=exp (d ²/ h ²), (r is N to get h=r/3 _k(r) the encirclement radius of a ball) make the point in k-nearest-neighbor only have significant contribution to the least square optimization of formula (1);

(c), by nonlinear optimization, calculate the bivariate polynomial of matching point set.By the neighborhood point p to a r _ibe weighted least square fitting, find local bivariate polynomial to approach g:H → R ³.If q _ip _ito the rectangular projection on H, (x _i, y _i) be its two-dimensional coordinate in local coordinate system on H; f _i=n (p _i-q) be p _iheight on H, by minimizing following weighted error function:

$\arg \underset{g}{\min }\mathrm{\Σ}{(g(x_i,y_i)-f_i)}^2\mathrm{\θ}\left(\right||p_i-q|\left|\right)$ Formula (2)

Can obtain the coefficient of polynomial expression g (x, y).The projection of r is defined as ψ (r)=q+g (0,0) n.

(d) determine the normal direction that the normal direction of sampled point is local reference planes H, adopt minimum spanning tree Law of Communication to carry out overall unification processing to normal direction;

For realizing goal of the invention, the described point cloud simplification method based on geometric properties, in step (2),

Definition N _k(p _i) covariance matrix $C={\left[\begin{array}{c}{p}_{i_1}-\stackrel{\‾}{p}\\ \·\·\·\\ p_{i_k}-\stackrel{\‾}{p}\end{array}\right]}^T\·\left[\begin{array}{c}{p}_{i_1}-\stackrel{\‾}{p}\\ \·\·\·\\ p_{i_k}-\stackrel{\‾}{p}\end{array}\right],$ Wherein $\stackrel{\‾}{p}=\mathrm{\Σ}{p}_{i_k}/k$ For N _k(p _i) barycenter,

matrix C is symmetrical positive semi-definite, its 3 eigenvalue λ _i(i=0,1,2) negative real-valuedly (establishes 0≤λ for non- ₀≤ λ ₁≤ λ ₂), can determine sampled point p _icurvature be

For realizing goal of the invention, the described point cloud simplification method based on geometric properties, in step (3), according to sampled point p _icharacteristic edge, cloud data is decomposed into strong characteristic edge and non-strong characteristic edge two parts.Specifically: definition p _inormal direction ballot tensor be wherein N (i) is k nearest-neighbor point set N _k(p _i) in the indexed set of each point; u _ijwith || p _ij-p _i|| the weight coefficient of monotone decreasing, get u _ij=exp (|| p _ij-p _i||/σ _e), σ _e(r is n to=2r/3 _k(p _i) the encirclement radius of a ball); p _ijsampled point p _ik nearest-neighbor point set N _k(p _i) in a bit, p _ij-p _irepresent distance between the two; By conversion n _ijobtain n ' _ij=2 (n _ijw _ij) w _ij-n _ij, w wherein _ij=(p _i-p _ij) * n _ij* (p _i-p _ij) (|| w _ij||=1).This tensor T _ipositive semi-definite real symmetric matrix, by its eigenwert v ₁, v ₂, v ₃(v ₁>=v ₂>=v ₃>=0) and characteristic of correspondence vector e ₁, e ₂, e ₃, sampled point p _icharacteristic edge be defined as:

In formula<img TranNum="149" file="BSA0000096462750000042.GIF" he="80" img-content="drawing" img-format="GIF" inline="yes" orientation="portrait" wi="390"/>δ=0.3, α=0.2 and β=0.2.This formula is divided into four classes by sampled point: sharp-pointed edge point, angle point, millet cake and other point; If sample s on sharp edge or angle point<sub TranNum="150">i</sub>be 1, if sample s on face<sub TranNum="151">i</sub>be 0, otherwise other time 0<s<sub TranNum="152">i</sub><1; So s<sub TranNum="153">i</sub>the characteristic edge that has fully reflected sampled point px.

By the sampled point in cloud data, according to levying limit property ascending sort, getting a high-end 0.08n sampled point is that strong characteristic edge point puts strong characteristic edge part in cloud, and remainder is non-strong characteristic edge part.

For realizing goal of the invention, the described point cloud simplification method based on geometric properties, in step (4), utilizes Mean Shift technology, and non-strong characteristic edge is partly carried out to surf zone geometric properties similarity cluster, specifically:

Given d dimension theorem in Euclid space R ^din a point set S={x ₁, x ₂..., x _n, the multivariate core density Estimation function at some x place is:

$f\left(x\right)=\frac{1}{{\mathrm{nh}}_i^d}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}K\left(\frac{x-x_i}{h_i}\right)$ Formula (3)

Bandwidth h wherein _i>0 show to estimate the density at x point place in great x neighborhood; K (x) is DENSITY KERNEL function, and k (x) is profile function.Formula (3) is carried out to the gradient that differential obtains x place:

$M_G\left(x\right)=\frac{{\mathrm{\&Sigma;}}_{i=1}^n\frac{x_i}{h_i^{d+2}}g\left({\left|\right|\frac{x-x_i}{h_i}\left|\right|}^2\right)}{{\mathrm{\&Sigma;}}_{i=1}^n\frac{1}{h_i^{d+2}}g\left({\left|\right|\frac{x-x_i}{h_i}\left|\right|}^2\right)}-x$ Formula (4) wherein g (x)=-K ' is (x) gaussian kernel function.Formula (4) shows, if by x to bandwidth h _iin scope, move in the place of density maximum, along M _g(x) (being that MS is iterative vectorized) direction moves is the fastest; And

$y_k^{[j+1]}=\frac{{\mathrm{\&Sigma;}}_{i=1}^n\frac{x_i}{h_i^{d+2}}g\left({\left|\right|\frac{y_k^{\left[j\right]}-x_i}{h_i}\left|\right|}^2\right)}{{\mathrm{\&Sigma;}}_{i=1}^n\frac{1}{h_i^{d+2}}g\left({\left|\right|\frac{y_k^{\left[j\right]}-x_i}{h_i}\left|\right|}^2\right)}k\&Element;[1,n],j=\mathrm{0,1,2},...$ Formula (5)

Converge on nearest local mode point (being the local maximum point of density Estimation).Its process: Step1 arranges initial value for x _k, termination condition ε; Step2 is calculated by formula (5)

value; If Step3

set up and exit, otherwise

go to Step2.Thus, in the variable space of multidimensional, Mean Shift algorithm is defined in all first vegetarian refreshments (first vegetarian refreshments with local similarity) that specific characteristic is had to an identical local mode in same region (being class bunch).

The present invention, when cluster, not only considers sampled point p _ilocus (x _i, y _i, z _i), and consider p _inormal direction n _i=(n _ix, n _iy, n _iz) and curvature σ _i, p _ibe described to a vector in 7 dimensional feature space

non-strong characteristic edge is partly carried out to this cluster, make converge to nearest local mode point

all converging on

sampled point to gather be a class; So Mean Shift technology just non-strong characteristic edge in the feature space of appointment is partly divided into class bunch collection.Because cluster of the present invention is according to the propinquity of the locus of sampled point, normal direction and curvature, historical facts or anecdotes has showed surf zone geometric properties similarity cluster.

In iterative process, bandwidth h _ian important parameter, the present invention according to

k nearest-neighbor point get adaptively $h_i={\left|\right|{\stackrel{\&OverBar;}{p}}_i-{\stackrel{\&OverBar;}{p}}_{\mathrm{ik}}\left|\right|}_1.$

For realizing goal of the invention, the described point cloud simplification method based on geometric properties, in step (5), to in strong characteristic edge part and non-strong characteristic edge part all kinds of bunches divide respectively and simplify, the region that curvature is large retains more sampled point, and the little region of curvature retains less sampled point; And by the sampling density of the distance assurance flat site between sampled point.Specifically:

According to simplification rate d, to strong characteristic edge part P _hEwith all kinds of bunches of P of non-strong characteristic edge _cIin sampled point according to its proximity relations, divide respectively, make each divide in sampled point curvature and be not more than threshold value T.For the flatness of a cloud is consistent before and after simplifying, the mean curvature of some cloud after simplifying ${\stackrel{\&OverBar;}{\mathrm{\&sigma;}}}_m=\frac{1}{m}\underset{i=0}{\overset{m-1}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_k^i(m=d\&CenterDot;n)$ Should with simplify before ${\stackrel{\&OverBar;}{\mathrm{\&sigma;}}}_n=\frac{1}{n}\underset{i=0}{\overset{n-1}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_k^i$ Substantially be consistent, can obtain $T={\stackrel{\&OverBar;}{\mathrm{\&sigma;}}}_n/d;$ Thereby make the region that curvature is large keep more sampled point, the region that curvature is little retains less sampled point, realizes the adaptive simplification of curvature.

In order to keep certain sampled point at the little flat site of curvature, should control the sampling density in this region, the sampling density that the present invention realizes this region by the minimum distance between adjusting sampled point is controlled.Note initial point cloud p _nbetween middle closest approach, mean distance is

ultimate range is

(r _iminfor p _iand the distance between its closest approach), when dividing, the search radius that the present invention defines sampled point is

thereby guaranteed the sampling density of flat site.

Simplifying each divided block is barycenter separately, and barycenter point set is simplifies a some cloud.

Adopted the invention has the beneficial effects as follows of technique scheme:

The present invention utilizes and has reflected the normal direction ballot tensor analysis of sampled point characteristic edge and the Mean Shift clustering technique of surf zone geometric properties similarity, and cloud data is carried out to the simplification based on geometric properties; The present invention, according to curvature threshold and search radius, has guaranteed the curvature adaptive simplifying of flat site sampling density to cloud data.Therefore, adopt the present invention to keep the high-quality of characteristic boundary and curved surface details to simplify to cloud data.

Accompanying drawing explanation

Fig. 1 is the visual and strong characteristic edge point set figure of the some cloud Igea characteristic edge of case of the present invention, and wherein 1 (a) former cloud data (345680 sampled points), 1 (b) are that the point-rendering design sketch, 1 (c) of 1 (a) is that characteristic edge point-rendering design sketch, 1 (d) of 1 (a) is the point-rendering design sketch of the strong characteristic edge point set of 1 (a); Note: in 1 (a) presentation graphs 1, be labeled as the figure of (a), can analogize according to this, in 2 (a) presentation graphs 2, be labeled as the figure of (a)

The local mode point set that Fig. 2 restrains while being the Igea point cloud Mean Shift cluster of case of the present invention and the cluster result of distinct methods, wherein 2 (a) are local mode point sets of the present invention, 2 (b) are cluster results of the present invention, 2 (c) are hierarchical clustering method (Hierarchical Clustering, HCL) cluster result, 2 (d) are the cluster results of region growing clustering procedure (Region-Growing Clustering, RGC); Separately, in 2 (b), the figure on the right is the enlarged drawing of dotted portion in the figure of the left side, similarly, in 2 (c), 2 (d), is also like this;

Fig. 3 is case point cloud Igea simplification 90% of the present invention and point-rendering figure thereof, and 3 (a) are simplification effects of the present invention, and 3 (b) are the simplification effects of HCL, and 3 (c) are the simplification effects of RGC; Wherein, in the two row figure of Fig. 3, upper row simplifies some cloud, and lower row is the point-rendering figure of upper row's respective point cloud;

Fig. 4 be case point cloud Dragon of the present invention (437645 sampled points) simplify 92% and error visualization point draw design sketch, in two row figure, wherein upper row is that a simplification point cloud, lower row are the error visualization point drafting figure of upper row's respective point cloud, 4 (a) are the simplification effects of initial point cloud, 4 (b) are simplification effects of the present invention, 4 (c) are the simplification effects of HCL, and 4 (d) are the simplification effects of RGC;

Fig. 5 is that in case of the present invention, noise spot cloud Fandisk simplifies (366416 sampled points) 95% and point-rendering figure thereof, in two row figure, upper row simplifies some cloud, lower row is the point-rendering figure of upper row's respective point cloud, 5 (a) are the simplification effects of former noise spot cloud, 5 (b) are simplification effects of the present invention, and 5 (c) are the simplification effects of HCL, and 5 (d) are the simplification effects of RGC.

Embodiment

The specific embodiment of the present invention is as follows:

Embodiment: referring to Fig. 1～Fig. 5, a kind of point cloud simplification method based on geometric properties, described method comprises:

(1) structure sampled point p _ithe moving least squares surfaces of nearest-neighbor point set, thus computing method to.Specific as follows: the k nearest-neighbor point set N that (a) utilizes kD tree fast search sampled point _k(p _i); (b) by nonlinear optimization, matching N _k(p _i) local reference planes, find the formula (1) that makes

the local reference planes H={x ∈ R of nonlinear energy function minimum ³| nx-D=0}; (c) nonlinear optimization formula (2)

calculate matching N _k(p _i) bivariate polynomial g (x, y); (d) normal direction of determining local reference planes H is sampled point p _inormal direction n _i, adopt minimum spanning tree Law of Communication to carry out overall unification processing to normal direction.

(2) covariance analysis neighborhood point set, estimating sampling point p _icurvature.Specific as follows: definition N _k(p _i) covariance matrix $C={\left[\begin{array}{c}{p}_{i_1}-\stackrel{\&OverBar;}{p}\\ \&CenterDot;\&CenterDot;\&CenterDot;\\ p_{i_k}-\stackrel{\&OverBar;}{p}\end{array}\right]}^T\&CenterDot;\left[\begin{array}{c}{p}_{i_1}-\stackrel{\&OverBar;}{p}\\ \&CenterDot;\&CenterDot;\&CenterDot;\\ p_{i_k}-\stackrel{\&OverBar;}{p}\end{array}\right],$ Wherein $\stackrel{\&OverBar;}{p}={\mathrm{\&Sigma;p}}_{i_k}/k$ For N _k(p _i) barycenter,

matrix C is symmetrical positive semi-definite, its 3 eigenvalue λ _i(i=0,1,2) negative real-valuedly (establishes 0≤λ for non- ₀≤ λ ₁≤ λ ₂), determine sampled point p _icurvature be

(3) analytical sampling point p _inormal direction ballot tensor, calculate sampled point p _icharacteristic edge, and decomposition point cloud is strong characteristic edge and non-strong characteristic edge two parts.Specific as follows: definition sampled point p _inormal direction ballot tensor be

wherein N (i) is N _k(p _i) in the indexed set of each point; u _ijwith || p _ij-p _i|| the weight coefficient of monotone decreasing, get u _ij=exp (|| p _ij-p _i||/σ _e), σ _e(r is N to=2r/3 _k(p _i) the encirclement radius of a ball); By conversion n _ijobtain n ' _ij=2 (n _ijw _ij) w _ij-n _ij, w wherein _ij=(p _i-p _ij) * n _ij* (p _i-p _ij) (|| w _ij||=1).By the eigenwert v of this tensor ₁, v ₂, v ₃(v ₁>=v ₂>=v ₃>=0) and characteristic of correspondence vector e ₁, e ₂, e ₃, p _icharacteristic edge be defined as:

In formula δ=0.3, α=0.2 and β=0.2.By the sampled point in cloud data, according to levying limit property ascending sort, getting a high-end 0.08n sampled point is that strong characteristic edge point puts strong characteristic edge part in cloud, and remainder is non-strong characteristic edge part.

Fig. 1 is the visual and strong characteristic edge point set figure of the some cloud Igea characteristic edge of case of the present invention, wherein 1 (a) former cloud data (345680 sampled points), 1 (b) are that the point-rendering design sketch, 1 (c) of 1 (a) is that characteristic edge point-rendering design sketch (wherein pure blue identification characteristics limit property is minimum, and pure red identification characteristics limit property is maximum), 1 (d) of 1 (a) is the point-rendering design sketch of the strong characteristic edge point set of 1 (a).By legend, can be seen the s that the present invention calculates _ithe characteristic edge that has reflected fully some cloud.

(4) utilize Mean Shift cluster partly to carry out surf zone geometric properties similarity cluster to non-strong characteristic edge.Specific as follows: to describe the sampled point p in non-strong characteristic edge part _ifor ${\stackrel{\&OverBar;}{p}}_i=(x_i,y_i,z_i,n_{\mathrm{ix}},n_{\mathrm{iy}},n_{\mathrm{iz}},{\mathrm{\&sigma;}}_i);$ Step1 arranges initial value

for x _k, Step2 is by formula (5)

$y_k^{[j+1]}=\frac{{\mathrm{\&Sigma;}}_{i=1}^n\frac{x_i}{h_i^{d+2}}g\left({\left|\right|\frac{y_k^{\left[j\right]}-x_i}{h_i}\left|\right|}^2\right)}{{\mathrm{\&Sigma;}}_{i=1}^n\frac{1}{h_i^{d+2}}g\left({\left|\right|\frac{y_k^{\left[j\right]}-x_i}{h_i}\left|\right|}^2\right)}k\&Element;[1,n],j=\mathrm{0,1,2},...$

Calculate

value; If Step3

set up and exit, otherwise

go to Step2.Through this iteration, Mean Shift algorithm is defined in all first vegetarian refreshments (first vegetarian refreshments with local similarity) with identical local mode in same region (being class bunch), realizes surf zone geometric properties similarity cluster.

The local mode point set that Fig. 2 restrains while being the Igea point cloud Mean Shift cluster of case of the present invention and the cluster result of distinct methods, wherein 2 (a) are local mode point sets of the present invention, 2 (b) are cluster results of the present invention, 2 (c) are the cluster results of HCL, and 2 (d) are the cluster results of RGC.By legend, can be seen, the cluster of HCL and the cluster of RGC do not reflect the geometric properties similarity (be the sampled point of feature similarity be divided into be Bu Tong close in class bunch) of model; And cluster of the present invention has reflected the geometric properties similarity of surf zone fully.

(5) resample in strong characteristic edge part and non-strong characteristic edge part all kinds of bunches and be simplified cloud data.Specific as follows: according to simplification rate d, the sampled point in strong characteristic edge part and all kinds of bunches is divided according to its proximity relations respectively, make each divide in sampled point curvature be not more than threshold value

thereby make the region that curvature is large keep more sampled point, the region that curvature is little retains less sampled point, reach the adaptive simplification object of curvature.When dividing, the search radius that the present invention defines sampled point is simultaneously $R_q\&Element;[\frac{1}{d}\stackrel{\&OverBar;}{E},\frac{1}{d}(\stackrel{\&OverBar;}{E}+E_m)](\stackrel{\&OverBar;}{E}=\frac{1}{n}\underset{i=0}{\overset{n-1}{\mathrm{\&Sigma;}}}{r}_{i\min },E_m={\max }_{i=0}^{n-1}\left(r_{i\min }\right),$ R _iminfor p _iand the distance between its closest approach), reach the object of having controlled flat site sampling density.Simplifying each divided block is barycenter separately, and barycenter point set is simplifies a some cloud.

Fig. 3～Fig. 5 has shown simplification effect and the comparison thereof of the inventive method and HCL, RGC short-cut method, and curved surface quality and three aspects of noiseproof feature that the present invention keeps, simplifies some cloud from feature compare simplifying result.

1. feature keeps.Fig. 3～Fig. 5 has shown that the inventive method locates at the sending out of some cloud Igea, the corners of the mouth etc., the outstanding position such as the head of Dragon, ridge, foot and located to retain more sampled point at characteristic boundary of Fandisk etc., has kept characteristic boundary and curved surface details more fully compared with HCL and RGC algorithm.Reason is that the present invention is decomposed into strong characteristic edge and non-strong characteristic edge two parts by a cloud, and non-strong characteristic edge is partly carried out to surf zone geometric properties similarity cluster; So aspect characteristic boundary and the maintenance of curved surface details, the inventive method is better than the performance of HCL and RGC method.

2. simplify the curved surface quality of some cloud.The present invention adopts the error evaluation method based on MLS, assesses the curved surface quality of simplifying some cloud.Specifically:

Given two point set P and P ' represent respectively curved surface S and S ', and Q is that P carries out the point set that up-sampling obtains on S, for

its distance to curved surface S ' is d (q, S ')=min _{p ' ∈ s '}d (q, p '); Just can estimate thus maximum error Δ max (S, S ') and average error delta _avgthe metric of (S, S ')

${\mathrm{\&Delta;}}_{\max }(S,S^{\&prime;})\&ap;{\max }_{q\&Element;Q}d(q,S^{\&prime;}),{\mathrm{\&Delta;}}_{\mathrm{avg}}(S,S^{\&prime;})\&ap;\frac{1}{\left|Q\right|}\underset{q\&Element;Q}{\mathrm{\&Sigma;}}d(q,S^{\&prime;}).$

Obviously, MLS projection operator ψ can calculate the upper nearest some q ' of distance q of curved surface S ' effectively, makes

therefore there is q=q '+dn, put q and to the distance of curved surface S ' be

Utilize the method to carry out error evaluation to simplifying some cloud, table 1 has been listed the statistics of assessment errors, and shown error visualization point drafting design sketch at the 2nd row of Fig. 4 (b)～4 (d), and wherein pure blue sign error is minimum, and pure red sign error is maximum.As can be seen from Table 1, error of the present invention is lower than HCL and RGC algorithm, and Fig. 4 (b)～4 (d) the 2nd row has also showed this respect more intuitively.Reason is, the present invention has not only considered the characteristic edge of sampled point and the similarity of surf zone geometric properties, and has considered curvature threshold and sampling density, and when details is kept, flat site also can keep certain sampled point; So the curved surface quality after the present invention simplifies is better than HCL and RGC algorithm.

Table 1 assessment errors statistics

3. noiseproof feature.Fig. 5 is that in case of the present invention, noise spot cloud Fandisk simplifies (366416 sampled points) 95% and point-rendering figure thereof, and wherein upper row is that to simplify a some cloud, lower row be that the point-rendering figure, 5 (a) of upper row's respective point cloud is that former noise spot cloud, 5 (b) are that simplification effect of the present invention, 5 (c) are that the simplification effect, 5 (d) of HCL is the simplification effect of RGC.The figure illustrates, the noiseproof feature of the inventive method is better than HCL and RGC method.Main cause is that the Mean Shift technology itself that the inventive method adopts has noise removal function.

The simplification effect showing from Fig. 3～Fig. 5 and relatively can finding out, the inventive method can keep the high-quality of characteristic boundary and curved surface details to simplify to cloud data.

Claims (6)

1. the point cloud simplification method based on geometric properties, is characterized in that, described short-cut method comprises the steps: (1) structure sampled point p _ithe moving least squares surfaces of nearest-neighbor point set, thus computing method to; (2) covariance analysis neighborhood point set, estimating sampling point p _icurvature; (3) analytical sampling point p _inormal direction ballot tensor, calculated characteristics limit property, and to decompose accordingly cloud data be strong characteristic edge part and non-strong characteristic edge part; (4) utilize Mean Shift algorithm cluster, dividing non-strong characteristic edge is partly class bunch collection; (5) resample strong characteristic edge part and all kinds of bunches.

2. the point cloud simplification method based on geometric properties according to claim 1, is characterized in that: in step (1), and sampled point p _inormal direction be to calculate by constructing the moving least squares surfaces of its nearest-neighbor point set, specifically: (a) utilize kD tree fast search sampled point p _ik nearest-neighbor point set N _k(p _i), according to the scale n of cloud data, get k ∈ [9,30]; (b) by nonlinear optimization, matching k nearest-neighbor point set N _k(p _i) local reference planes; (c) by nonlinear optimization, calculate matching k nearest-neighbor point set N _k(p _i) bivariate polynomial; (d) determine sampled point p _ithe normal direction normal direction that is local reference planes, adopt minimum spanning tree Law of Communication to carry out overall unification processing to normal direction.

3. the point cloud simplification method based on geometric properties according to claim 1, is characterized in that: in step (2), define N _k(p _i) covariance matrix and analyze its 3 eigenvalue λ _i(i=0,1,2) negative real-valuedly (establishes 0≤λ for non- ₀≤ λ ₁≤ λ ₂), determine sampled point p _icurvature be

4. the point cloud simplification method based on geometric properties according to claim 1, is characterized in that: in step (3), specifically: definition sampled point p _inormal direction ballot tensor be

wherein N (i) is k nearest-neighbor point set N _k(p _i) in the indexed set of each point; u _ijwith || p _ij-p _i|| the weight coefficient of monotone decreasing, get u _ij=exp (|| p _ij-p _i||/σ _e), σ _e(r is N to=2r/3 _k(p _i) the encirclement radius of a ball); By conversion n _ijobtain n ' _ij=2 (n _ijw _ij) w _ij-n _ij, w wherein _ij=(p _i-p _ij) * n _ij* (p _i-p _ij) (|| w _ij||=1); This tensor T _ipositive semi-definite real symmetric matrix, by its eigenwert v ₁, v ₂, v ₃(v ₁>=v ₂>=v ₃>=0) and characteristic of correspondence vector e ₁, e ₂, e ₃, sampled point p _icharacteristic edge be defined as:

In formula δ=0.3, α=0.2 and β=0.2; By the sampled point in cloud data, according to levying limit property ascending sort, getting a high-end 0.08n sampled point is that strong characteristic edge point puts strong characteristic edge part in cloud, and remainder is non-strong characteristic edge part.

5. the point cloud simplification method based on geometric properties according to claim 1, it is characterized in that: in step (4), non-strong characteristic edge is partly carried out to surf zone geometric properties similarity cluster, specifically: non-strong characteristic edge is partly carried out to Mean Shift algorithm, make

converge to nearest local mode point

all converging on

sampled point to gather be a class; Thus, according to geometric properties similarity, Mean Shift algorithm is partly divided into class bunch collection by non-strong characteristic edge.

6. the point cloud simplification method based on geometric properties according to claim 1, it is characterized in that: in step (5), the strong characteristic edge of resampling part and all kinds of bunches are simplified cloud data, specifically: according to curvature threshold and search radius, the sampled point of all kinds of bunches of strong characteristic edge part and non-strong characteristic edge is divided according to its proximity relations respectively, simplifying each divided block is barycenter separately, and barycenter point set is simplifies a some cloud.

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