CN106780524A - A kind of three-dimensional point cloud road boundary extraction method - Google Patents

Abstract

The present invention relates to points cloud processing field, a kind of three-dimensional point cloud road boundary extraction method is specifically disclosed, comprised the following steps：S1, the whole three dimensional point cloud collection P to obtaining, screening seed point carry out super voxel division；S2, use α shape algorithms to extract neighbouring non-coplanar super voxel between boundary point；S3, the Energy minimization that is cut based on figure is used to extract road boundary point；S4, based on Euclidean distance clustering algorithm remove outlier；S5, the road boundary point of extraction is fitted to smoothed curve.The method of the present invention can be run directly on extensive three-dimensional point cloud, can be used for different scenes, and calculating speed is fast, and algorithm robustness is good, can rapid extraction road boundary.

Description

A kind of three-dimensional point cloud road boundary extraction method

Technical field

The present invention relates to points cloud processing field, more particularly, to a kind of three-dimensional point cloud road boundary extraction method.

Background technology

, used as traffic infrastructure, its digitized management is with construction is for urban planning, traffic administration and leads for road The application such as boat has great importance.The high-new surveying and mapping technology that Vehicle-borne Laser Scanning technology quickly grows as one, compared to Traditional mapping means, with data acquisition speed it is fast, data precision is high, noncontact actively measurement, the advantage such as real-time, in car In normal traveling process can quick obtaining road and the detailed three-dimensional spatial information of both sides atural object, for the road of zonal distribution Acquisition of information has a clear superiority.

The method that tradition obtains road information mainly includes two modes of manual measurement and digital photogrammetry.Manual measurement Although being obtained in that the information such as accurate path coordinate, measuring speed is slower, and the road information update cycle is more long；Number Word is photogrammetric gradually to be developed and grows up with the extensive use of the new and high technology such as computer with the development of science and technology, but The reasons such as image resolution are constrained to, the link characteristic information and required precision of extraction still need and further carry in image It is high.Vehicle-borne Laser Scanning system is made up of global positioning system, inertial navigation system, laser scanner and CCD camera etc., turns into Obtain the new tool of three-dimensional space data.Time of measuring can be effectively saved using Vehicle-borne Laser Scanning technology, measurement is improved Efficiency, shortens the road information update cycle, it is to avoid operating personnel exposed danger is measured under traffic environment, is city space The exploration of resource provides strong technical guarantee with planning.

However, the usual environment in city is complicated, not only appurtenances complexity is various, and is mutually blocked between scanned target and make Into shortage of data, road boundary is automatically extracted and brings test.Additionally, complexity (the such as vehicle that different road environments cause Stop, vegetation surround, fence etc.) increase road boundary automatically extract difficulty.Therefore, from massive point cloud fast and automatically It is big that ground extracts road boundary difficulty, it is desirable to high, but the technology has important economy and application demand, is always both domestic and external grinding Study carefully focus.

At present, the research in terms of Vehicle-borne Laser Scanning data processing has focused largely on atural object point cloud classifications, building facade The aspect such as information extraction and modeling, the extraction of road affiliated facility, and the research to road boundary information extraction is relatively fewer, mainly Can be divided into work extract indirectly and directly extract two classes.

The method extracted indirectly is usually attribute (height, intensity and wavelength etc.) the generation depth map first by a cloud Picture, is then detected, is extracted road boundary using the method (cut, be fitted and filter) of image procossing.For carrying indirectly The method for taking, will put cloud and be converted into depth image, then extract road boundary, these method gesture using the method for image procossing Error must be produced in transfer process, it is difficult to obtain accurate road boundary result.

The method directly extracted is usually to detect, extract road roadside using roadway characteristic (such as plane, road serratd edge etc.) Boundary.Conventional method is to extract road surface with the method based on random sampling consistent (RANSAC), then with the calculation of linear fit Method obtains road boundary.Road serratd edge is detected with the method for gaussian filtering or the method for sliding window, road is derived from Border.For the method directly extracted, then the range of application to scene has larger limitation.Using consistent based on random sampling (RANSAC) method extracts road surface, can be had any problem in situation about being risen and fallen in face of road, and the road surface often extracted also can Lose some details.And the method for the method or sliding window using gaussian filtering often exists come the method for detecting road serratd edge Challenge is had during in face of the circular situation of irregular road boundary (such as wall, fence) or vegetation.

The content of the invention

It is an object of the invention to overcome above-mentioned the deficiencies in the prior art, the present invention to provide a kind of three-dimensional point cloud road boundary Extraction method, the method can be run directly on extensive three-dimensional point cloud, can be used for different scenes, and calculating speed is fast, Algorithm robustness is good, can rapid extraction road boundary.

Concrete technical scheme is as follows：

A kind of three-dimensional point cloud road boundary extraction method, comprises the following steps：

S1, the whole three dimensional point cloud collection P to obtaining, screening seed point carry out super voxel division；

S2, use α-shape algorithms to extract neighbouring non-coplanar super voxel between boundary point；

S3, the Energy minimization that is cut based on figure is used to extract road boundary point；

S4, based on Euclidean distance clustering algorithm remove outlier；

S5, the road boundary point of extraction is fitted to smoothed curve.

Preferably, step S1 is specific as follows to the partition process of super voxel:

S11, solution fit Plane T_p(p_i)：

For each input point p of whole three dimensional point cloud collection P_i, its section Tp (p_i) can be expressed as by its center Point o_iWith normal vector n_lTwo tuples of composition, i.e.,

Any point p to Tp (p in three dimensions_i) distance can be expressed as

Note p_iK nearest neighbor constitute collection be combined into Nb_k(p_i), can be obtained under least square meaning most by solving following formula Good fit Plane

Then the least square method for being weighted again using iteration is come the plane of Optimal Fitting

Solution cum rights least squares equation is the fit Plane Tp (p after being optimized_i)

To plane Tp (p_i) said process is repeated, until algorithmic statement.

S12, removal non-ground points：

Note finally constitutes section Tp (p_i) point set covariance matrix three characteristic values be λ₁,λ₂, and λ₃, and it is full Sufficient λ₁≥λ₂≥λ₃.Then point p_iSmoothness s (p_i) can be expressed as

Limited using following two and made a return journey except non-ground points：

A, removal apparently higher than road surface point (z_i≥5m)(z_iIt is point p_iHeight value)；

B, remove the point of its normal vector and Z axis angle more than 22.5 °.

S13, the super voxel f of calculating_i：

The later point set P of non-ground points will be removed_gSorted according to each smoothness put, the big point of smoothness is selected first As seed point.The mode for proceeding by region growth from seed point calculates super voxel.By super voxel f_iThe definition of formalization There is affiliated point set P for one_i, central point o_i, and normal vector n_lThe triple for being constitutedTo each seed Point seed_i, make its initial super voxel f_iInitial point set be { p_i, central point and normal vector are respectively Tp (p_i).o_iAnd Tp (p_i).n_l.Then, using the principle of breadth-first to f_iCarry out region growth.To each candidate point p_jIf meeting (1) p_jArrive p_iDistance be less than threshold value R_seed；(2) vector T p (p_j).n_lWith Tp (p_i).n_lAngle be less than 22.5 °；(3)p_jTo Tp (p_i) Distance is less than threshold value ∈；Then by p_jIt is added to f_iPoint concentrate.Work as f_iWhen cannot extend again, according to f_i.p_iUse least square method Fit Plane, and by f_i.n_lG is updated to the normal vector of fit Plane.It is equal using part K on the basis of these initial facets Value is clustered an assignment in super voxel, and ensures that the distance of the super voxel belonging to each point to its is less than to other super voxels Distance.Here distance function is defined as：

Wherein D_s,D_nAnd D_iIt is respectively Euclidean distance, normal vector distance and intensity distance.ω_s,ω_nAnd ω_iRespectively It is corresponding weights.

Preferably, step S2 extracts the specific of the boundary point between neighbouring non-coplanar super voxel using α-shape algorithms Step is：

By point cloud segmentation into after super voxel, for each super voxel, it is possible to use α-shape algorithms extract border Point, meanwhile, the boundary point between two super voxels coplanar with each other of removal, if the normal vector angle of that is, two super voxels is less than 22.5 °, then the boundary point between the two super voxels is deleted, boundary point P now_bIncluding road boundary point and non-rice habitats border Point.

Preferably, step S3 extracts road boundary point using the Energy minimization cut based on figure, specific as follows：

Vehicle driving trace line number evidence is provided by Vehicle-borne Laser Scanning system, the first of algorithm is cut using trajectory data as figure Beginning observation model.Energy theorem is defined as：

E (f)=E_data(f)+λ·E_smooth(f)

Here P_bIt refer to the set of the boundary point extracted in step 2.N is p_iThe point cardinality of affiliated super voxel.Δd_jIt is Give directions p_jTo straight line L_piDistance.Δd_iIt is to give directions p_iStraight line L is arrived a little in neighborhood_piAverage redundancy.σ₁Refer to a little Average redundancy.Straight line L_piIt is defined as passing point p_iAnd direction with apart from p_iThe direction of nearest trajectory.

(x_i,y_i,z_i),(x_j,y_j,z_j) it is respectively point p_iAnd p_jThree-dimensional coordinate,It is to give directions p_iAnd p_jIt is European away from From.HereWhat is represented is such as fruit dot p_iAnd p_jIf the label of distribution is consistent, cost is zero, instead Cost be

Here σ₂Refer to point set P_bSpatial resolution.The knot that algorithm tries to achieve above-mentioned energy theorem minimum value is cut using figure Fruit will boundary point be divided into two classes, a class is road boundary point, and another kind of is non-road boundary point.

The solution of the present invention compared with prior art, has the following advantages that：

(1) present invention can be run directly on extensive three-dimensional point cloud, for extraction and the positioning of road boundary provide one Cover fast and effeciently automation solutions.Need the artificial parameter for setting considerably less, reduce artificial Subjective Intervention.With it is existing Technology is compared, the minimum energy arithmetic that the present invention is split using super voxel and cut based on figure, in complicated urban environment situation Under still can effectively extract road boundary, calculated due to being used in combination onboard system trajectory data, overcome a little Cloud data are blocked, the shortcomings of Density Distribution is uneven so that result Stable Robust, all have universality to different scenes, it is easy to real Border uses.

(2) present invention has fully excavated the primary attribute (space length, geometric properties and strength information) of some clouds, by point Cloud carries out super voxel segmentation, while removing non-ground points, improves follow-up computational efficiency.Due to seed point being ranked up, The method of prioritizing selection, the result of super voxel segmentation is very good must to save boundary information, improve subsequent extracted road boundary The robustness of algorithm.

(3) present invention has carried out innovation optimization on model algorithm, and the Energy minimization cut based on figure is proposed first, The trajectory data provided using onboard system, figure are set up with reference to the internal characteristicses of road boundary and cut model, effectively and rapidly Extract road boundary.

Brief description of the drawings

The schematic flow sheet of Fig. 1 technical solution of the present invention；

Fig. 2 embodiment of the present invention original point cloud datas；

Design sketch after Fig. 3 treatment.

Specific embodiment

In order to make the purpose , technical scheme and advantage of the present invention be clearer, it is right below in conjunction with drawings and Examples The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and It is not used in the restriction present invention.

Embodiment

The specific embodiment party that road boundary extracting method is carried out based on Vehicle-borne Laser Scanning cloud data proposed by the present invention Case is following (total visible Fig. 1 of technical scheme flow)：

S1, the whole three dimensional point cloud collection P to obtaining, screening seed point carry out the super voxel division (original of the present embodiment Visible Fig. 2 of beginning cloud data)；

It refers to that to gather the consistent point of neighbouring property be a super point that super voxel is divided, and data processing is reduced with this Complexity；

S11, solution fit Plane T_p(p_i)：

For each input point p of whole three dimensional point cloud collection P_i, its section Tp (p_i) can be expressed as by its center Point o_iWith normal vector n_lTwo tuples of composition, i.e.,

Any point p to Tp (p in three dimensions_i) distance can be expressed as

Note p_iK nearest neighbor constitute collection be combined into Nb_k(p_i), can be obtained under least square meaning most by solving following formula Good fit Plane

Then the least square method for being weighted again using iteration is come the plane of Optimal Fitting

Solution cum rights least squares equation is the fit Plane Tp (p after being optimized_i)

To plane Tp (p_i) said process is repeated, until algorithmic statement.

S12, removal non-ground points：

Note finally constitutes section Tp (p_i) point set covariance matrix three characteristic values be λ₁,λ₂, and λ₃, and it is full Sufficient λ₁≥λ₂≥λ₃.Then point p_iSmoothness s (p_i) can be expressed as

Limited using following two and made a return journey except non-ground points：

A, removal apparently higher than road surface point (z_i≥5m)(z_iIt is point p_iHeight value)；

B, remove the point of its normal vector and Z axis angle more than 22.5 °.

S13, the super voxel f of calculating_i：

Thus, the later point set P of non-ground points will be removed_gSorted according to each smoothness put, smoothness is selected first Big point is used as seed point.The mode for proceeding by region growth from seed point calculates super voxel.By super voxel f_iFormalization Definition have affiliated point set P for one_i, central point o_i, and normal vector n_lThe triple for being constitutedTo every Individual seed point seed_i, make its initial super voxel f_iInitial point set be { p_i, central point and normal vector are respectively Tp (p_i).o_i With Tp (p_i).n_l.Then, using the principle of breadth-first to f_iCarry out region growth.To each candidate point p_jIf met (1) p_jTo p_iDistance be less than threshold value R_seed；(2) vector T p (p_j).n_lWith Tp (p_i).n_lAngle be less than 22.5 °；(3)p_jTo Tp (p_i) distance be less than threshold value ∈；Then by p_jIt is added to f_iPoint concentrate.Work as f_iWhen cannot extend again, according to f_i.p_iUse minimum Square law fit Plane, and by f_i.n_lG is updated to the normal vector of fit Plane.Office is used on the basis of these initial facets , by an assignment in super voxel, and it is super to other to ensure that each point is less than to the distance of the super voxel belonging to it for portion's K mean cluster The distance of voxel.Here distance function is defined as：

Wherein D_s,D_nAnd D_iIt is respectively Euclidean distance, normal vector distance and intensity distance.ω_s,ω_nAnd ω_iRespectively It is corresponding weights.

S2, use α-shape algorithms to extract neighbouring non-coplanar super voxel between boundary point；

By point cloud segmentation into after super voxel, for each super voxel, it is possible to use α-shape algorithms extract border Point.Meanwhile, the boundary point between two super voxels coplanar with each other of removal, if the normal vector angle of that is, two super voxels is less than 22.5 °, then delete the boundary point between the two super voxels.Boundary point P now_bIncluding road boundary point and non-rice habitats border Point.

α-shape algorithms can be regarded as the extension of closure Convex Hull, and it can be calculated more by adjusting alpha parameter Fine closure specifically removes set one so as to substantially describe plane or the spatially profile of a group point with the circle of certain radii fixus To a pair of point, all just fall when a pair points on circle and also in circle not comprising any other when, the two points are exactly The boundary point of shape.All of boundary point is found out by such method, Alpha shape have just been depicted.

S3, the Energy minimization that is cut based on figure is used to extract road boundary point；

Next road boundary point is extracted using the Energy minimization cut based on figure.Vehicle-borne Laser Scanning system is carried For vehicle driving trace line number evidence, it was observed that trajectory data keep basically identical with measurement road locality.Thus by rail Trace data cuts the initial observation model of algorithm as figure.Energy theorem is defined as：

E (f)=E_data(f)+λ·E_smooth(f)

Here P_bIt refer to the set of the boundary point extracted in step 2.N is p_iThe point cardinality of affiliated super voxel.Δd_jIt is Give directions p_jTo straight lineDistance.Δd_iIt is to give directions p_iStraight line is arrived a little in neighborhoodAverage redundancy.σ₁Refer to a little Average redundancy.Straight lineIt is defined as passing point p_iAnd direction with apart from p_iThe direction of nearest trajectory.

(x_i,y_i,z_i),(x_j,y_j,z_j) it is respectively point p_iAnd p_jThree-dimensional coordinate,It is to give directions p_iAnd p_jIt is European away from From.HereWhat is represented is such as fruit dot p_iAnd p_jIf the label of distribution is consistent, cost is zero, instead Cost be

Here σ₂Refer to point set P_bSpatial resolution.The knot that algorithm tries to achieve above-mentioned energy theorem minimum value is cut using figure Fruit will boundary point be divided into two classes, a class is road boundary point, and another kind of is non-road boundary point.

S4, based on Euclidean distance clustering algorithm remove outlier；

The road boundary point of above-mentioned acquisition is clustered using Euclidean distance clustering algorithm, and is deleted points very little Classification, that is, after clustering, if the number of point that classification is included deletes this classification less than 5.

S5, the road boundary point of extraction is fitted to smoothed curve.

Remaining class is fitted to smooth curve respectively, road boundary has thus just been obtained.Used here as cubic spline Interpolation (Cubic Spline Interpolation) carrys out fitting a straight line.

Wherein, Fig. 3 is the design sketch after treatment, represents the road for extracting.

The above, the only present invention preferably specific embodiment, but protection scope of the present invention is not limited thereto, Any one skilled in the art the invention discloses technical scope in, the change or replacement that can be readily occurred in, Should all be included within the scope of the present invention.Therefore, protection scope of the present invention should be with scope of the claims It is defined.

Claims (7)

1. a kind of three-dimensional point cloud road boundary extraction method, it is characterised in that：Comprise the following steps：

S1, the whole three dimensional point cloud collection P to obtaining, screening seed point carry out super voxel division；

S2, use α-shape algorithms to extract neighbouring non-coplanar super voxel between boundary point；

S3, the Energy minimization that is cut based on figure is used to extract road boundary point；

S4, based on Euclidean distance clustering algorithm remove outlier；

S5, the road boundary point of extraction is fitted to smoothed curve.

2. a kind of three-dimensional point cloud road boundary extraction method according to claim 1, it is characterised in that：Step S1 pairs The partition process of super voxel comprises the following steps:

S11, solution fit Plane T_p(p_i)；

S12, removal non-ground points；

S13, the super voxel f of calculating_i。

3. a kind of three-dimensional point cloud road boundary extraction method according to claim 1, it is characterised in that：Step S2 makes Concretely comprising the following steps for the boundary point between neighbouring non-coplanar super voxel is extracted with α-shape algorithms：

By point cloud segmentation into after super voxel, for each super voxel, it is possible to use α-shape algorithms extract boundary point, together When, the boundary point between two super voxels coplanar with each other of removal, if the normal vector angle of that is, two super voxels is less than 22.5 °, then the boundary point between the two super voxels is deleted, boundary point P now_bIncluding road boundary point and non-rice habitats border Point.

4. a kind of three-dimensional point cloud road boundary extraction method according to claim 2, it is characterised in that：

S11, solution fit Plane T_p(p_i) comprise the following steps that：

For each input point p of whole three dimensional point cloud collection P_i, its section Tp (p_i) can be expressed as by its central point o_i With normal vector n_lTwo tuples of composition, i.e.,：

$Tp\left(x_i\right)=(o_i,\widehat{n_i})$

Any point p to Tp (p in three dimensions_i) distance can be expressed as：

$dist(p,Tp(x_i\left)\right)=|(p-o_i)\·\widehat{n_i}|$

Note p_iK nearest neighbor constitute collection be combined into Nb_k(p_i), by solving the optimal plan that following formula can obtain under least square meaning Close plane：

$\underset{Tp\left(x_i\right)}{\mathrm{argmin}}\underset{p\∈{\mathrm{Nb}}_K\left(p_i\right)}{\Σ}dist{(p,Tp(x_i\left)\right)}^2$

Then the least square method for being weighted again using iteration is come the plane of Optimal Fitting：

$w\left(p\right)=\left\{\begin{array}{cc}{(1-{\left(\frac{dist(p,T_p(p_i\left)\right)}{\&Element;}\right)}^2)}^2,& dist(p,T_p(p_i\left)\right)<\&Element;\\ 0,& dist(p,T_p(p_i\left)\right)\&GreaterEqual;\&Element;\end{array}\right.$

Solution cum rights least squares equation is the fit Plane Tp (p after being optimized_i)

$\underset{Tp\left(x_i\right)}{\arg \min }\underset{p\&Element;{\mathrm{Nb}}_K\left(x_i\right)}{\&Sigma;}w\left(p\right)*dist{(p,T_P(p_i\left)\right)}^2.$

To plane Tp (p_i) said process is repeated, until algorithmic statement.

5. a kind of three-dimensional point cloud road boundary extraction method according to claim 2, it is characterised in that：

S12, removal non-ground points are comprised the following steps that：

Note finally constitutes section Tp (p_i) point set covariance matrix three characteristic values be λ₁,λ₂, and λ₃, and meet λ₁≥ λ₂≥λ₃, then point p_iSmoothness s (p_i) can be expressed as：

$s\left(x_i\right)=\frac{{\mathrm{\&lambda;}}_2}{{\mathrm{\&lambda;}}_3}$

Limited using following two and made a return journey except non-ground points：

A, removal apparently higher than road surface point (z_i≥5m)(z_iIt is point p_iHeight value)；

B, remove the point of its normal vector and Z axis angle more than 22.5 °.

6. a kind of three-dimensional point cloud road boundary extraction method according to claim 2, it is characterised in that：

S13, the super voxel f of calculating_iComprise the following steps that：

The later point set P of non-ground points will be removed_gSorted according to each smoothness put, the big point conduct of smoothness is selected first Seed point, the mode for proceeding by region growth from seed point calculates super voxel；By super voxel f_iThe definition of formalization is one It is individual to have affiliated point set P_i, central point o_i, and normal vector n_lThe triple for being constitutedTo each seed point seed_i, make its initial super voxel f_iInitial point set be { p_i, central point and normal vector are respectively Tp (p_i).o_iWith Tp (p_i) .n_l；Then, using the principle of breadth-first to f_iRegion growth is carried out, to each candidate point p_jIf meeting (1) p_jTo p_i's Distance is less than threshold value R_seed；(2) vector T p (p_j).n_lWith Tp (p_i).n_lAngle be less than 22.5 °；(3)p_jTo Tp (p_i) distance Less than threshold value ∈；Then by p_jIt is added to f_iPoint concentrate, work as f_iWhen cannot extend again, according to f_i.p_iUse least square fitting Plane, and by f_i.n_lG is updated to the normal vector of fit Plane；It is poly- using part K averages on the basis of these initial facets Class by an assignment in super voxel, and ensure each point to the super voxel belonging to it distance less than to other super voxels away from From distance function here is defined as：

$D(p,f)=\sqrt{{\mathrm{\&omega;}}_s*D_s^2+{\mathrm{\&omega;}}_n*D_n^2+{\mathrm{\&omega;}}_i*D_i^2}$

Wherein D_s,D_nAnd D_iIt is respectively Euclidean distance, normal vector distance and intensity distance, ω_s,ω_nAnd ω_iIt is respectively this The corresponding weights of three distance values.

7. according to claim 1 based on the urban road tree features catalogue acquisition algorithm for moving laser scanning system, It is characterized in that：Step S3 extracts road boundary point using the Energy minimization cut based on figure, specific as follows：

The vehicle driving trace line number evidence that Vehicle-borne Laser Scanning system is provided, as initial observation model, algorithm is cut using figure Boundary point is divided into two categories below { " road boundary point ", " non-rice habitats boundary point " }, i.e., the target that figure cuts algorithm is to try to achieve one Classification function f gives each point distribution one label f_p∈ L (L is category set { " road boundary point ", " non-rice habitats boundary point " }), So that the Least-cost paid, that is, cause that energy theorem is minimized,

Here energy theorem is defined as：

E (f)=E_data(f)+λ·E_smooth(f)

Here E_dataF the data item in (), i.e. energy theorem, refers to the error that classification results compare with initial observation model, be To the cost of each point distribution label, E in assorting process_smoothF the smooth item in (), i.e. energy theorem, refers to classification function The degree of f Non-smooth surfaces, each puts the inconsistent cost of classification results and neighbor point between in specifically referring to assorting process, and λ is light Sliding item E_smoothF the weight of (), is empirically set to 32 here, wherein,

$E_{data}\left(f\right)={\mathrm{\&Sigma;}}_{p_i\&Element;P_b}d\left(f_{p_i}\right)$

${\mathrm{\&Delta;d}}_i=\frac{1}{n}\underset{p_j}{\&Sigma;}{\mathrm{\&Delta;d}}_j$

Here P_bIt refer to the set of the boundary point extracted in step 2.N is p_iThe point cardinality of affiliated super voxel, Δ d_jIt is to give directions p_jTo straight lineDistance, Δ d_iIt is to give directions p_iStraight line is arrived a little in neighborhoodAverage redundancy.σ₁Refer to a little flat Equal redundancy, straight lineIt is defined as passing point p_iAnd direction with apart from p_iThe direction of nearest trajectory,

$E_{smooth}\left(f\right)=\underset{\{p_i,p_j\}\&Element;P_b}{\&Sigma;}B\{p_i,p_j\}\&CenterDot;\mathrm{\&delta;}(f_{p_i},f_{p_j})$

$\mathrm{\&delta;}(\&CenterDot;)=\left\{\begin{array}{cc}1& if{f}_{p_i}\&NotEqual;f_{p_j}\\ 0& otherwise.\end{array}\right.$

$B_{\left\{p_i,p_j\right\}}=e^{-\frac{D_{p_i,p_j}}{{\mathrm{\&sigma;}}_2}}$

$D_{p_i,p_j}=\sqrt{{(x_i-x_j)}^2+{(y_i-y_j)}^2+{(z_i-z_j)}^2}$

(x_i,y_i,z_i),(x_j,y_j,z_j) it is respectively point p_iAnd p_jThree-dimensional coordinate,It is to give directions p_iAnd p_jEuclidean distance, this InWhat is represented is such as fruit dot p_iAnd p_jIf the label of distribution is consistent, cost is zero, on the contrary cost For

Here σ₂Refer to point set P_bSpatial resolution, cut result that algorithm tries to achieve above-mentioned energy theorem minimum value i.e. using figure Boundary point is divided into two classes, a class is road boundary point, another kind of is non-road boundary point.